diff --git a/.github/workflows/pr.yml b/.github/workflows/pr.yml index b0cfa1c3d6..6068d6e3e1 100644 --- a/.github/workflows/pr.yml +++ b/.github/workflows/pr.yml @@ -1,5 +1,5 @@ on: pull_request -env: +env: GOPROXY: "https://proxy.golang.org" name: pull_request @@ -10,7 +10,7 @@ jobs: - name: install Go uses: actions/setup-go@v2 with: - go-version: 1.19.x + go-version: 1.20.x - name: checkout code uses: actions/checkout@v2 with: @@ -39,11 +39,11 @@ jobs: git update-index --assume-unchanged go.mod git update-index --assume-unchanged go.sum if [[ -n $(git status --porcelain) ]]; then echo "git repo is dirty after runing go generate -- please don't modify generated files"; echo $(git diff);echo $(git status --porcelain); exit 1; fi - + test: strategy: matrix: - go-version: [1.18.x, 1.19.x] + go-version: [1.19.x, 1.20.x] os: [ubuntu-latest] runs-on: ${{ matrix.os }} needs: @@ -72,12 +72,12 @@ jobs: go test -p=1 -v -timeout=30m ./... go test -p=1 -tags=purego -v -timeout=30m ./... - name: Test (32 bits & race) - if: (matrix.os == 'ubuntu-latest') && (matrix.go-version == '1.18.x') + if: (matrix.os == 'ubuntu-latest') && (matrix.go-version == '1.19.x') run: | go test -p=1 -v -timeout=30m -short -race ./ecc/bn254/... go test -p=1 -v -timeout=30m -short -tags=noadx ./ecc/bn254/... GOARCH=386 go test -p=1 -timeout=30m -short -v ./ecc/bn254/... - + slack-workflow-status-failed: if: failure() name: post workflow status to slack diff --git a/README.md b/README.md index 37d81d3a29..1310829b97 100644 --- a/README.md +++ b/README.md @@ -38,7 +38,7 @@ ### Go version -`gnark-crypto` is tested with the last 2 major releases of Go (1.17 and 1.18). +`gnark-crypto` is tested with the last 2 major releases of Go (currently 1.19 and 1.20). ### Install `gnark-crypto` diff --git a/ecc/bls12-377/bls12-377.go b/ecc/bls12-377/bls12-377.go index 8abee780dc..43fbe1f6c7 100644 --- a/ecc/bls12-377/bls12-377.go +++ b/ecc/bls12-377/bls12-377.go @@ -40,7 +40,8 @@ import ( // ID bls377 ID const ID = ecc.BLS12_377 -// bCurveCoeff b coeff of the curve Y²=X³+b +// aCurveCoeff is the a coefficients of the curve Y²=X³+ax+b +var aCurveCoeff fp.Element var bCurveCoeff fp.Element // twist @@ -97,7 +98,7 @@ type E6 = fptower.E6 type E12 = fptower.E12 func init() { - + aCurveCoeff.SetUint64(0) bCurveCoeff.SetUint64(1) // D-twist twist.A1.SetUint64(1) @@ -148,3 +149,8 @@ func Generators() (g1Jac G1Jac, g2Jac G2Jac, g1Aff G1Affine, g2Aff G2Affine) { g2Jac = g2Gen return } + +// CurveCoefficients returns the a, b coefficients of the curve equation. +func CurveCoefficients() (a, b fp.Element) { + return aCurveCoeff, bCurveCoeff +} diff --git a/ecc/bls12-377/ecdsa/ecdsa.go b/ecc/bls12-377/ecdsa/ecdsa.go index cc13e8ac60..89445e2117 100644 --- a/ecc/bls12-377/ecdsa/ecdsa.go +++ b/ecc/bls12-377/ecdsa/ecdsa.go @@ -22,7 +22,6 @@ import ( "crypto/rand" "crypto/sha512" "crypto/subtle" - "errors" "hash" "io" "math/big" @@ -33,8 +32,6 @@ import ( "github.com/consensys/gnark-crypto/signature" ) -var errInvalidSig = errors.New("invalid signature") - const ( sizeFr = fr.Bytes sizeFp = fp.Bytes @@ -213,6 +210,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) kInv.ModInverse(k, order) P.X.BigInt(r) + r.Mod(r, order) if r.Sign() != 0 { break diff --git a/ecc/bls12-377/fp/element.go b/ecc/bls12-377/fp/element.go index 3a3ccdd3f4..1080d80b33 100644 --- a/ecc/bls12-377/fp/element.go +++ b/ecc/bls12-377/fp/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -844,12 +845,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -859,7 +860,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bls12-377/fr/element.go b/ecc/bls12-377/fr/element.go index b95577df37..457dc215c6 100644 --- a/ecc/bls12-377/fr/element.go +++ b/ecc/bls12-377/fr/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -692,12 +693,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -707,7 +708,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bls12-377/fr/fft/domain.go b/ecc/bls12-377/fr/fft/domain.go index 579aee8e43..7f32c42b65 100644 --- a/ecc/bls12-377/fr/fft/domain.go +++ b/ecc/bls12-377/fr/fft/domain.go @@ -63,30 +63,27 @@ type Domain struct { // NewDomain returns a subgroup with a power of 2 cardinality // cardinality >= m -func NewDomain(m uint64) *Domain { +// shift: when specified, it's the element by which the set of root of unity is shifted. +func NewDomain(m uint64, shift ...fr.Element) *Domain { domain := &Domain{} x := ecc.NextPowerOfTwo(m) domain.Cardinality = uint64(x) // generator of the largest 2-adic subgroup - var rootOfUnity fr.Element - rootOfUnity.SetString("8065159656716812877374967518403273466521432693661810619979959746626482506078") - const maxOrderRoot uint64 = 47 domain.FrMultiplicativeGen.SetUint64(22) + if len(shift) != 0 { + domain.FrMultiplicativeGen.Set(&shift[0]) + } domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen) - // find generator for Z/2^(log(m))Z - logx := uint64(bits.TrailingZeros64(x)) - if logx > maxOrderRoot { - panic(fmt.Sprintf("m (%d) is too big: the required root of unity does not exist", m)) + var err error + domain.Generator, err = Generator(m) + if err != nil { + panic(err) } - - // Generator = FinerGenerator^2 has order x - expo := uint64(1 << (maxOrderRoot - logx)) - domain.Generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x domain.GeneratorInv.Inverse(&domain.Generator) domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv) @@ -99,6 +96,28 @@ func NewDomain(m uint64) *Domain { return domain } +// Generator returns a generator for Z/2^(log(m))Z +// or an error if m is too big (required root of unity doesn't exist) +func Generator(m uint64) (fr.Element, error) { + x := ecc.NextPowerOfTwo(m) + + var rootOfUnity fr.Element + + rootOfUnity.SetString("8065159656716812877374967518403273466521432693661810619979959746626482506078") + const maxOrderRoot uint64 = 47 + + // find generator for Z/2^(log(m))Z + logx := uint64(bits.TrailingZeros64(x)) + if logx > maxOrderRoot { + return fr.Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m) + } + + expo := uint64(1 << (maxOrderRoot - logx)) + var generator fr.Element + generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x + return generator, nil +} + func (d *Domain) reverseCosetTables() { d.CosetTableReversed = make([]fr.Element, d.Cardinality) d.CosetTableInvReversed = make([]fr.Element, d.Cardinality) diff --git a/ecc/bls12-377/fr/fft/fft.go b/ecc/bls12-377/fr/fft/fft.go index ea9db946a5..7927925999 100644 --- a/ecc/bls12-377/fr/fft/fft.go +++ b/ecc/bls12-377/fr/fft/fft.go @@ -18,7 +18,6 @@ package fft import ( "math/bits" - "runtime" "github.com/consensys/gnark-crypto/ecc" "github.com/consensys/gnark-crypto/internal/parallel" @@ -40,24 +39,18 @@ const butterflyThreshold = 16 // FFT computes (recursively) the discrete Fourier transform of a and stores the result in a // if decimation == DIT (decimation in time), the input must be in bit-reversed order // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order -// if coset if set, the FFT(a) returns the evaluation of a on a coset. -func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) { +func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option) { - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } + opt := options(opts...) // if coset != 0, scale by coset table - if _coset { + if opt.coset { scale := func(cosetTable []fr.Element) { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &cosetTable[i]) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableReversed) @@ -69,16 +62,16 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.Twiddles, 0, maxSplits, nil) + difFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.Twiddles, 0, maxSplits, nil) + ditFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } @@ -89,37 +82,31 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order // coset sets the shift of the fft (0 = no shift, standard fft) // len(a) must be a power of 2, and w must be a len(a)th root of unity in field F. -func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset ...bool) { - - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } +func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...Option) { + opt := options(opts...) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } // scale by CardinalityInv - if !_coset { + if !opt.coset { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) return } @@ -129,7 +116,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. a[i].Mul(&a[i], &cosetTable[i]). Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableInv) @@ -141,7 +128,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. } -func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -159,7 +146,7 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for i := start; i < end; i++ { fr.Butterfly(&a[i], &a[i+m]) @@ -182,17 +169,17 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon nextStage := stage + 1 if stage < maxSplits { chDone := make(chan struct{}, 1) - go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone) - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone, nbTasks) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - difFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + difFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } } -func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -210,12 +197,12 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon if stage < maxSplits { // that's the only time we fire go routines chDone := make(chan struct{}, 1) - go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone) - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone, nbTasks) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } @@ -223,7 +210,7 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for k := start; k < end; k++ { a[k+m].Mul(&a[k+m], &twiddles[stage][k]) diff --git a/ecc/bls12-377/fr/fft/fft_test.go b/ecc/bls12-377/fr/fft/fft_test.go index 4758928f44..0a1c17d985 100644 --- a/ecc/bls12-377/fr/fft/fft_test.go +++ b/ecc/bls12-377/fr/fft/fft_test.go @@ -52,7 +52,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIF) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -79,7 +79,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIF, OnCoset()) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -108,7 +108,7 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFT(pol, DIT) sample := domainWithPrecompute.Generator sample.Exp(sample, big.NewInt(int64(ithpower))) @@ -134,8 +134,8 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) - domainWithPrecompute.FFTInverse(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIT) + domainWithPrecompute.FFTInverse(pol, DIF) BitReverse(pol) check := true @@ -163,8 +163,8 @@ func TestFFT(t *testing.T) { for i := 1; i <= nbCosets; i++ { BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, true) - domainWithPrecompute.FFTInverse(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) BitReverse(pol) for i := 0; i < len(pol); i++ { @@ -188,8 +188,8 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, false) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFTInverse(pol, DIF) + domainWithPrecompute.FFT(pol, DIT) check := true for i := 0; i < len(pol); i++ { @@ -211,14 +211,26 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, true) - domainWithPrecompute.FFT(pol, DIT, true) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) - check := true for i := 0; i < len(pol); i++ { - check = check && (pol[i] == backupPol[i]) + if !(pol[i].Equal(&backupPol[i])) { + return false + } } - return check + + // compute with nbTasks == 1 + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset(), WithNbTasks(1)) + domainWithPrecompute.FFT(pol, DIT, OnCoset(), WithNbTasks(1)) + + for i := 0; i < len(pol); i++ { + if !(pol[i].Equal(&backupPol[i])) { + return false + } + } + + return true }, )) @@ -265,14 +277,14 @@ func BenchmarkFFT(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, false) + domain.FFT(pol[:sizeDomain], DIT) } }) b.Run("fft 2**"+strconv.Itoa(i)+"bits (coset)", func(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, true) + domain.FFT(pol[:sizeDomain], DIT, OnCoset()) } }) } @@ -292,7 +304,7 @@ func BenchmarkFFTDITCosetReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIT, true) + domain.FFT(pol, DIT, OnCoset()) } } @@ -309,7 +321,7 @@ func BenchmarkFFTDIFReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIF, false) + domain.FFT(pol, DIF) } } diff --git a/ecc/bls12-377/fr/fft/options.go b/ecc/bls12-377/fr/fft/options.go new file mode 100644 index 0000000000..603b76f299 --- /dev/null +++ b/ecc/bls12-377/fr/fft/options.go @@ -0,0 +1,61 @@ +// Copyright 2020 ConsenSys Software Inc. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +// Code generated by consensys/gnark-crypto DO NOT EDIT + +package fft + +import "runtime" + +// Option defines option for altering the behavior of FFT methods. +// See the descriptions of functions returning instances of this type for +// particular options. +type Option func(*fftConfig) + +type fftConfig struct { + coset bool + nbTasks int +} + +// OnCoset if provided, FFT(a) returns the evaluation of a on a coset. +func OnCoset() Option { + return func(opt *fftConfig) { + opt.coset = true + } +} + +// WithNbTasks sets the max number of task (go routine) to spawn. Must be between 1 and 512. +func WithNbTasks(nbTasks int) Option { + if nbTasks < 1 { + nbTasks = 1 + } else if nbTasks > 512 { + nbTasks = 512 + } + return func(opt *fftConfig) { + opt.nbTasks = nbTasks + } +} + +// default options +func options(opts ...Option) fftConfig { + // apply options + opt := fftConfig{ + coset: false, + nbTasks: runtime.NumCPU(), + } + for _, option := range opts { + option(&opt) + } + return opt +} diff --git a/ecc/bls12-377/fr/iop/polynomial.go b/ecc/bls12-377/fr/iop/polynomial.go index b1dc46beaa..48115aba9c 100644 --- a/ecc/bls12-377/fr/iop/polynomial.go +++ b/ecc/bls12-377/fr/iop/polynomial.go @@ -146,11 +146,13 @@ func (p *Polynomial) Evaluate(x fr.Element) fr.Element { return p.polynomial.evaluate(x) } - // TODO find a way to retrieve the root properly instead of re generating the fft domain - d := fft.NewDomain(uint64(p.size)) var g fr.Element if p.shift <= 5 { - g = smallExp(d.Generator, p.shift) + gen, err := fft.Generator(uint64(p.size)) + if err != nil { + panic(err) + } + g = smallExp(gen, p.shift) x.Mul(&x, &g) return p.polynomial.evaluate(x) } @@ -288,11 +290,11 @@ func (p *Polynomial) ToLagrange(d *fft.Domain) *Polynomial { return p case lagrangeCosetRegular: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIT) case lagrangeCosetBitReverse: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIF) default: panic("unknown ID") @@ -317,10 +319,10 @@ func (p *Polynomial) ToCanonical(d *fft.Domain) *Polynomial { d.FFTInverse((*p.coefficients), fft.DIT) case lagrangeCosetRegular: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetBitReverse: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) default: panic("unknown ID") } @@ -342,18 +344,18 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial { switch id { case canonicalRegular: p.Layout = BitReverse - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case canonicalBitReverse: p.Layout = Regular - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeRegular: p.Layout = Regular d.FFTInverse((*p.coefficients), fft.DIF) - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeBitReverse: p.Layout = BitReverse d.FFTInverse((*p.coefficients), fft.DIT) - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetRegular, lagrangeCosetBitReverse: return p default: diff --git a/ecc/bls12-377/fr/iop/polynomial_test.go b/ecc/bls12-377/fr/iop/polynomial_test.go index 1233ddb6c2..32e439748a 100644 --- a/ecc/bls12-377/fr/iop/polynomial_test.go +++ b/ecc/bls12-377/fr/iop/polynomial_test.go @@ -240,7 +240,7 @@ func fromLagrange4(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = Regular d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) return r } @@ -250,7 +250,7 @@ func fromLagrange5(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = BitReverse d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) fft.BitReverse(r.Coefficients()) return r } @@ -438,7 +438,7 @@ func fromCanonical4(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = Regular - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -448,7 +448,7 @@ func fromCanonical5(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = BitReverse - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -566,7 +566,7 @@ func fromLagrangeCoset0(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -576,7 +576,7 @@ func fromLagrangeCoset1(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -585,7 +585,7 @@ func fromLagrangeCoset2(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) return _p } @@ -595,7 +595,7 @@ func fromLagrangeCoset3(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) fft.BitReverse(_p.Coefficients()) return _p diff --git a/ecc/bls12-377/fr/iop/ratios.go b/ecc/bls12-377/fr/iop/ratios.go index 3f5633712d..77ceb0e573 100644 --- a/ecc/bls12-377/fr/iop/ratios.go +++ b/ecc/bls12-377/fr/iop/ratios.go @@ -18,7 +18,10 @@ package iop import ( "errors" + "math/big" "math/bits" + "runtime" + "sync" "github.com/consensys/gnark-crypto/internal/parallel" @@ -213,16 +216,38 @@ func BuildRatioCopyConstraint( } }) - for i := 0; i < n-1; i++ { - coeffs[i+1].Mul(&coeffs[i+1], &coeffs[i]) - t[i+1].Mul(&t[i+1], &t[i]) + chCoeffs := make(chan struct{}, 1) + go func() { + for i := 2; i < n; i++ { + // ignoring coeffs[0] + coeffs[i].Mul(&coeffs[i], &coeffs[i-1]) + } + close(chCoeffs) + }() + + for i := 2; i < n; i++ { + // ignoring t[0] + t[i].Mul(&t[i], &t[i-1]) } + <-chCoeffs - t = fr.BatchInvert(t) - for i := 1; i < n; i++ { - coeffs[i].Mul(&coeffs[i], &t[i]) + // rough ratio inverse to mul; see if it makes sense to parallelize the batch inverse. + const ratioInvMul = 1000 / 17 + nbTasks := runtime.NumCPU() + if ratio := n / ratioInvMul; ratio < nbTasks { + nbTasks = ratio } + parallel.Execute(n-1, func(start, end int) { + // ignoring t[0] and coeff[0] + start++ + end++ + tInv := fr.BatchInvert(t[start:end]) + for i := start; i < end; i++ { + coeffs[i].Mul(&coeffs[i], &tInv[i-start]) + } + }, nbTasks) + res := NewPolynomial(&coeffs, expectedForm) // at this stage the result is in Lagrange form, Regular layout putInExpectedFormFromLagrangeRegular(res, domain, expectedForm) @@ -245,7 +270,7 @@ func putInExpectedFormFromLagrangeRegular(p *Polynomial, domain *fft.Domain, exp if expectedForm.Basis == LagrangeCoset { domain.FFTInverse(p.Coefficients(), fft.DIF) - domain.FFT(p.Coefficients(), fft.DIT, true) + domain.FFT(p.Coefficients(), fft.DIT, fft.OnCoset()) if expectedForm.Layout == BitReverse { fft.BitReverse(p.Coefficients()) } @@ -308,16 +333,42 @@ func getSupportIdentityPermutation(nbCopies int, domain *fft.Domain) []fr.Elemen res := make([]fr.Element, uint64(nbCopies)*domain.Cardinality) sizePoly := int(domain.Cardinality) - res[0].SetOne() - for i := 0; i < sizePoly-1; i++ { + // len(domain.Twiddle) == sizePoly / 2 + copy(res, domain.Twiddles[0]) + // remaining ones. + for i := (sizePoly / 2) - 1; i < sizePoly-1; i++ { res[i+1].Mul(&res[i], &domain.Generator) } + if nbCopies <= 1 { + return res + } + var wg sync.WaitGroup + wg.Add(nbCopies - 1) for i := 1; i < nbCopies; i++ { - copy(res[i*sizePoly:], res[(i-1)*sizePoly:i*int(domain.Cardinality)]) - for j := 0; j < sizePoly; j++ { - res[i*sizePoly+j].Mul(&res[i*sizePoly+j], &domain.FrMultiplicativeGen) + i := i + + var coset fr.Element + if i == 1 { + coset = domain.FrMultiplicativeGen + } else { + if len(domain.CosetTable) > i { + coset = domain.CosetTable[i] + } else { + coset.Exp(domain.FrMultiplicativeGen, big.NewInt(int64(i))) + } } + + go func() { + parallel.Execute(sizePoly, func(start, end int) { + for j := start; j < end; j++ { + res[i*sizePoly+j].Mul(&res[j], &coset) + } + }, (runtime.NumCPU()/(nbCopies-1))+1) + wg.Done() + }() } + wg.Wait() + return res } diff --git a/ecc/bls12-377/fr/kzg/kzg.go b/ecc/bls12-377/fr/kzg/kzg.go index c7d579af3f..a1b3a7690a 100644 --- a/ecc/bls12-377/fr/kzg/kzg.go +++ b/ecc/bls12-377/fr/kzg/kzg.go @@ -26,6 +26,8 @@ import ( "github.com/consensys/gnark-crypto/ecc/bls12-377" "github.com/consensys/gnark-crypto/ecc/bls12-377/fr" "github.com/consensys/gnark-crypto/fiat-shamir" + + "github.com/consensys/gnark-crypto/internal/parallel" ) var ( @@ -275,14 +277,21 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr // gamma n in parallel, before reducing into foldedPolynomials foldedPolynomials := make([]fr.Element, largestPoly) copy(foldedPolynomials, polynomials[0]) - acc := gamma - var pj fr.Element + gammas := make([]fr.Element, len(polynomials)) + gammas[0] = gamma for i := 1; i < len(polynomials); i++ { - for j := 0; j < len(polynomials[i]); j++ { - pj.Mul(&polynomials[i][j], &acc) - foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) - } - acc.Mul(&acc, &gamma) + gammas[i].Mul(&gammas[i-1], &gamma) + } + + for i := 1; i < len(polynomials); i++ { + i := i + parallel.Execute(len(polynomials[i]), func(start, end int) { + var pj fr.Element + for j := start; j < end; j++ { + pj.Mul(&polynomials[i][j], &gammas[i-1]) + foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) + } + }) } // compute H diff --git a/ecc/bls12-377/fr/permutation/permutation.go b/ecc/bls12-377/fr/permutation/permutation.go index 36f1c1a61a..7031fd3b50 100644 --- a/ecc/bls12-377/fr/permutation/permutation.go +++ b/ecc/bls12-377/fr/permutation/permutation.go @@ -191,15 +191,15 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } lz := make([]fr.Element, s) copy(lz, cz) - d.FFT(lz, fft.DIF, true) + d.FFT(lz, fft.DIF, fft.OnCoset()) // compute the first part of the numerator lt1 := make([]fr.Element, s) lt2 := make([]fr.Element, s) copy(lt1, ct1) copy(lt2, ct2) - d.FFT(lt1, fft.DIF, true) - d.FFT(lt2, fft.DIF, true) + d.FFT(lt1, fft.DIF, fft.OnCoset()) + d.FFT(lt2, fft.DIF, fft.OnCoset()) lsNumFirstPart := evaluateFirstPartNumReverse(lt1, lt2, lz, epsilon) // compute second part of the numerator @@ -222,7 +222,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } // get the quotient and commit it - d.FFTInverse(lsNum, fft.DIT, true) + d.FFTInverse(lsNum, fft.DIT, fft.OnCoset()) proof.q, err = kzg.Commit(lsNum, srs) if err != nil { return proof, err diff --git a/ecc/bls12-377/fr/plookup/vector.go b/ecc/bls12-377/fr/plookup/vector.go index e8a5c216c8..36c4ad7767 100644 --- a/ecc/bls12-377/fr/plookup/vector.go +++ b/ecc/bls12-377/fr/plookup/vector.go @@ -340,7 +340,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element Mul(&res[_i], &numLn[i%2]) } - domainBig.FFTInverse(res, fft.DIT, true) + domainBig.FFTInverse(res, fft.DIT, fft.OnCoset()) return res } @@ -476,11 +476,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) copy(_lh2, ch2) copy(_lt, ct) copy(_lf, cf) - domainBig.FFT(_lz, fft.DIF, true) - domainBig.FFT(_lh1, fft.DIF, true) - domainBig.FFT(_lh2, fft.DIF, true) - domainBig.FFT(_lt, fft.DIF, true) - domainBig.FFT(_lf, fft.DIF, true) + domainBig.FFT(_lz, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh1, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh2, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lt, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lf, fft.DIF, fft.OnCoset()) // compute h lh := evaluateNumBitReversed(_lz, _lh1, _lh2, _lt, _lf, beta, gamma, domainBig) diff --git a/ecc/bls12-377/internal/fptower/e12_pairing.go b/ecc/bls12-377/internal/fptower/e12_pairing.go index 86a918d846..6888dfc4fc 100644 --- a/ecc/bls12-377/internal/fptower/e12_pairing.go +++ b/ecc/bls12-377/internal/fptower/e12_pairing.go @@ -61,3 +61,53 @@ func (z *E12) MulBy034(c0, c3, c4 *E2) *E12 { return z } + +// Mul034By034 multiplication of sparse element (c0,0,0,c3,c4,0) by sparse element (d0,0,0,d3,d4,0) +func Mul034By034(d0, d3, d4, c0, c3, c4 *E2) [5]E2 { + var z00, tmp, x0, x3, x4, x04, x03, x34 E2 + x0.Mul(c0, d0) + x3.Mul(c3, d3) + x4.Mul(c4, d4) + tmp.Add(c0, c4) + x04.Add(d0, d4). + Mul(&x04, &tmp). + Sub(&x04, &x0). + Sub(&x04, &x4) + tmp.Add(c0, c3) + x03.Add(d0, d3). + Mul(&x03, &tmp). + Sub(&x03, &x0). + Sub(&x03, &x3) + tmp.Add(c3, c4) + x34.Add(d3, d4). + Mul(&x34, &tmp). + Sub(&x34, &x3). + Sub(&x34, &x4) + + z00.MulByNonResidue(&x4). + Add(&z00, &x0) + + return [5]E2{z00, x3, x34, x03, x04} +} + +// MulBy01234 multiplies z by an E12 sparse element of the form (x0, x1, x2, x3, x4, 0) +func (z *E12) MulBy01234(x *[5]E2) *E12 { + var c1, a, b, c, z0, z1 E6 + c0 := &E6{B0: x[0], B1: x[1], B2: x[2]} + c1.B0 = x[3] + c1.B1 = x[4] + a.Add(&z.C0, &z.C1) + b.Add(c0, &c1) + a.Mul(&a, &b) + b.Mul(&z.C0, c0) + c.Set(&z.C1).MulBy01(&x[3], &x[4]) + z1.Sub(&a, &b) + z1.Sub(&z1, &c) + z0.MulByNonResidue(&c) + z0.Add(&z0, &b) + + z.C0 = z0 + z.C1 = z1 + + return z +} diff --git a/ecc/bls12-377/internal/fptower/e6.go b/ecc/bls12-377/internal/fptower/e6.go index 8ae7216ec5..d4f80de958 100644 --- a/ecc/bls12-377/internal/fptower/e6.go +++ b/ecc/bls12-377/internal/fptower/e6.go @@ -126,6 +126,34 @@ func (z *E6) MulByE2(x *E6, y *E2) *E6 { return z } +// MulBy12 multiplication by sparse element (0,b1,b2) +func (x *E6) MulBy12(b1, b2 *E2) *E6 { + var t1, t2, c0, tmp, c1, c2 E2 + t1.Mul(&x.B1, b1) + t2.Mul(&x.B2, b2) + c0.Add(&x.B1, &x.B2) + tmp.Add(b1, b2) + c0.Mul(&c0, &tmp) + c0.Sub(&c0, &t1) + c0.Sub(&c0, &t2) + c0.MulByNonResidue(&c0) + c1.Add(&x.B0, &x.B1) + c1.Mul(&c1, b1) + c1.Sub(&c1, &t1) + tmp.MulByNonResidue(&t2) + c1.Add(&c1, &tmp) + tmp.Add(&x.B0, &x.B2) + c2.Mul(b2, &tmp) + c2.Sub(&c2, &t2) + c2.Add(&c2, &t1) + + x.B0 = c0 + x.B1 = c1 + x.B2 = c2 + + return x +} + // MulBy01 multiplication by sparse element (c0,c1,0) func (z *E6) MulBy01(c0, c1 *E2) *E6 { diff --git a/ecc/bls12-377/marshal.go b/ecc/bls12-377/marshal.go index b71e1c2dc4..6140b863d8 100644 --- a/ecc/bls12-377/marshal.go +++ b/ecc/bls12-377/marshal.go @@ -50,6 +50,8 @@ const ( // SizeOfGT represents the size in bytes that a GT element need in binary form const SizeOfGT = fptower.SizeOfGT +var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding") + // Encoder writes bls12-377 object values to an output stream type Encoder struct { w io.Writer @@ -365,6 +367,19 @@ func NoSubgroupChecks() func(*Decoder) { } } +// isZeroed checks that the provided bytes are at 0 +func isZeroed(firstByte byte, buf []byte) bool { + if firstByte != 0 { + return false + } + for _, b := range buf { + if b != 0 { + return false + } + } + return true +} + func (enc *Encoder) encode(v interface{}) (err error) { rv := reflect.ValueOf(v) if v == nil || (rv.Kind() == reflect.Ptr && rv.IsNil()) { @@ -674,13 +689,19 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineUncompressed, nil @@ -796,9 +817,12 @@ func (p *G1Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } @@ -861,7 +885,7 @@ func (p *G2Affine) Bytes() (res [SizeOfG2AffineCompressed]byte) { } // we store X and mask the most significant word with our metadata mask - // p.X.A1 | p.X.A0 + // p.X.A1 | p.X.A0 fp.BigEndian.PutElement((*[fp.Bytes]byte)(res[48:48+fp.Bytes]), p.X.A0) fp.BigEndian.PutElement((*[fp.Bytes]byte)(res[0:0+fp.Bytes]), p.X.A1) @@ -927,13 +951,19 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineUncompressed, nil @@ -1063,9 +1093,12 @@ func (p *G2Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } diff --git a/ecc/bls12-377/pairing.go b/ecc/bls12-377/pairing.go index b1ed68e1a1..ede3a03803 100644 --- a/ecc/bls12-377/pairing.go +++ b/ecc/bls12-377/pairing.go @@ -104,7 +104,7 @@ func FinalExponentiation(z *GT, _z ...*GT) GT { } // MillerLoop computes the multi-Miller loop -// ∏ᵢ MillerLoop(Pᵢ, Qᵢ) +// ∏ᵢ MillerLoop(Pᵢ, Qᵢ) = ∏ᵢ { fᵢ_{x,Qᵢ}(Pᵢ) } func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { // check input size match n := len(P) @@ -134,49 +134,113 @@ func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { var result GT result.SetOne() + var l1, l2 lineEvaluation + var prodLines [5]E2 + + // Compute ∏ᵢ { fᵢ_{x₀,Q}(P) } + if n >= 1 { + // i = 62, separately to avoid an E12 Square + // (Square(res) = 1² = 1) + // loopCounter[62] = 0 + // k = 0, separately to avoid MulBy034 (res × ℓ) + // (assign line to res) + + // qProj[0] ← 2qProj[0] and l1 the tangent ℓ passing 2qProj[0] + qProj[0].doubleStep(&l1) + // line evaluation at P[0] (assign) + result.C0.B0.MulByElement(&l1.r0, &p[0].Y) + result.C1.B0.MulByElement(&l1.r1, &p[0].X) + result.C1.B1.Set(&l1.r2) + } - var l lineEvaluation + if n >= 2 { + // k = 1, separately to avoid MulBy034 (res × ℓ) + // (res is also a line at this point, so we use Mul034By034 ℓ × ℓ) + + // qProj[1] ← 2qProj[1] and l1 the tangent ℓ passing 2qProj[1] + qProj[1].doubleStep(&l1) + // line evaluation at P[1] + l1.r0.MulByElement(&l1.r0, &p[1].Y) + l1.r1.MulByElement(&l1.r1, &p[1].X) + // ℓ × res + prodLines = fptower.Mul034By034(&l1.r0, &l1.r1, &l1.r2, &result.C0.B0, &result.C1.B0, &result.C1.B1) + result.C0.B0 = prodLines[0] + result.C0.B1 = prodLines[1] + result.C0.B2 = prodLines[2] + result.C1.B0 = prodLines[3] + result.C1.B1 = prodLines[4] + } - // i == len(loopCounter) - 2 - for k := 0; k < n; k++ { - qProj[k].DoubleStep(&l) - // line eval - l.r0.MulByElement(&l.r0, &p[k].Y) - l.r1.MulByElement(&l.r1, &p[k].X) - result.MulBy034(&l.r0, &l.r1, &l.r2) + // k >= 2 + for k := 2; k < n; k++ { + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] + l1.r0.MulByElement(&l1.r0, &p[k].Y) + l1.r1.MulByElement(&l1.r1, &p[k].X) + // ℓ × res + result.MulBy034(&l1.r0, &l1.r1, &l1.r2) } - for i := len(loopCounter) - 3; i >= 0; i-- { + // i <= 61 + for i := len(loopCounter) - 3; i >= 1; i-- { + // mutualize the square among n Miller loops // (∏ᵢfᵢ)² result.Square(&result) for k := 0; k < n; k++ { - qProj[k].DoubleStep(&l) - // line eval - l.r0.MulByElement(&l.r0, &p[k].Y) - l.r1.MulByElement(&l.r1, &p[k].X) - result.MulBy034(&l.r0, &l.r1, &l.r2) + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] + l1.r0.MulByElement(&l1.r0, &p[k].Y) + l1.r1.MulByElement(&l1.r1, &p[k].X) + + if loopCounter[i] == 0 { + // ℓ × res + result.MulBy034(&l1.r0, &l1.r1, &l1.r2) + } else { + // qProj[k] ← qProj[k]+Q[k] and + // l2 the line ℓ passing qProj[k] and Q[k] + qProj[k].addMixedStep(&l2, &q[k]) + // line evaluation at P[k] + l2.r0.MulByElement(&l2.r0, &p[k].Y) + l2.r1.MulByElement(&l2.r1, &p[k].X) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) + } } - if loopCounter[i] == 0 { - continue - } + } - for k := 0; k < n; k++ { - qProj[k].AddMixedStep(&l, &q[k]) - // line eval - l.r0.MulByElement(&l.r0, &p[k].Y) - l.r1.MulByElement(&l.r1, &p[k].X) - result.MulBy034(&l.r0, &l.r1, &l.r2) - } + // i = 0, separately to avoid a point addition + // loopCounter[0] = 1 + result.Square(&result) + for k := 0; k < n; k++ { + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] + l1.r0.MulByElement(&l1.r0, &p[k].Y) + l1.r1.MulByElement(&l1.r1, &p[k].X) + + // l2 the line passing qProj[k] and Q + qProj[k].lineCompute(&l2, &q[k]) + // line evaluation at P[k] + l2.r0.MulByElement(&l2.r0, &p[k].Y) + l2.r1.MulByElement(&l2.r1, &p[k].X) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) } return result, nil } -// DoubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop +// doubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g2Proj) DoubleStep(evaluations *lineEvaluation) { +func (p *g2Proj) doubleStep(evaluations *lineEvaluation) { // get some Element from our pool var t1, A, B, C, D, E, EE, F, G, H, I, J, K fptower.E2 @@ -215,9 +279,9 @@ func (p *g2Proj) DoubleStep(evaluations *lineEvaluation) { evaluations.r2.Set(&I) } -// AddMixedStep point addition in Mixed Homogenous projective and Affine coordinates +// addMixedStep point addition in Mixed Homogenous projective and Affine coordinates // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g2Proj) AddMixedStep(evaluations *lineEvaluation, a *G2Affine) { +func (p *g2Proj) addMixedStep(evaluations *lineEvaluation, a *G2Affine) { // get some Element from our pool var Y2Z1, X2Z1, O, L, C, D, E, F, G, H, t0, t1, t2, J fptower.E2 @@ -251,3 +315,23 @@ func (p *g2Proj) AddMixedStep(evaluations *lineEvaluation, a *G2Affine) { evaluations.r1.Neg(&O) evaluations.r2.Set(&J) } + +// lineCompute computes the line through p in Homogenous projective coordinates +// and a in affine coordinates. It does not compute the resulting point p+a. +func (p *g2Proj) lineCompute(evaluations *lineEvaluation, a *G2Affine) { + + // get some Element from our pool + var Y2Z1, X2Z1, O, L, t2, J fptower.E2 + Y2Z1.Mul(&a.Y, &p.z) + O.Sub(&p.y, &Y2Z1) + X2Z1.Mul(&a.X, &p.z) + L.Sub(&p.x, &X2Z1) + t2.Mul(&L, &a.Y) + J.Mul(&a.X, &O). + Sub(&J, &t2) + + // Line evaluation + evaluations.r0.Set(&L) + evaluations.r1.Neg(&O) + evaluations.r2.Set(&J) +} diff --git a/ecc/bls12-378/bls12-378.go b/ecc/bls12-378/bls12-378.go index e1f438b29c..d80db02fdc 100644 --- a/ecc/bls12-378/bls12-378.go +++ b/ecc/bls12-378/bls12-378.go @@ -40,7 +40,8 @@ import ( // ID bls378 ID const ID = ecc.BLS12_378 -// bCurveCoeff b coeff of the curve Y²=X³+b +// aCurveCoeff is the a coefficients of the curve Y²=X³+ax+b +var aCurveCoeff fp.Element var bCurveCoeff fp.Element // bTwistCurveCoeff b coeff of the twist (defined over 𝔽p²) curve @@ -94,7 +95,7 @@ type E6 = fptower.E6 type E12 = fptower.E12 func init() { - + aCurveCoeff.SetUint64(0) bCurveCoeff.SetUint64(1) bTwistCurveCoeff.A1.SetUint64(1) // M-twist @@ -145,3 +146,8 @@ func Generators() (g1Jac G1Jac, g2Jac G2Jac, g1Aff G1Affine, g2Aff G2Affine) { g2Jac = g2Gen return } + +// CurveCoefficients returns the a, b coefficients of the curve equation. +func CurveCoefficients() (a, b fp.Element) { + return aCurveCoeff, bCurveCoeff +} diff --git a/ecc/bls12-378/ecdsa/ecdsa.go b/ecc/bls12-378/ecdsa/ecdsa.go index 44c297cc82..f1766e1599 100644 --- a/ecc/bls12-378/ecdsa/ecdsa.go +++ b/ecc/bls12-378/ecdsa/ecdsa.go @@ -22,7 +22,6 @@ import ( "crypto/rand" "crypto/sha512" "crypto/subtle" - "errors" "hash" "io" "math/big" @@ -33,8 +32,6 @@ import ( "github.com/consensys/gnark-crypto/signature" ) -var errInvalidSig = errors.New("invalid signature") - const ( sizeFr = fr.Bytes sizeFp = fp.Bytes @@ -213,6 +210,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) kInv.ModInverse(k, order) P.X.BigInt(r) + r.Mod(r, order) if r.Sign() != 0 { break diff --git a/ecc/bls12-378/fp/element.go b/ecc/bls12-378/fp/element.go index 1b9164a8d7..51105fe164 100644 --- a/ecc/bls12-378/fp/element.go +++ b/ecc/bls12-378/fp/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -844,12 +845,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -859,7 +860,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bls12-378/fr/element.go b/ecc/bls12-378/fr/element.go index 0b6a914804..d35ec5336d 100644 --- a/ecc/bls12-378/fr/element.go +++ b/ecc/bls12-378/fr/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -692,12 +693,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -707,7 +708,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bls12-378/fr/fft/domain.go b/ecc/bls12-378/fr/fft/domain.go index 522dd3ca52..3a55852f7d 100644 --- a/ecc/bls12-378/fr/fft/domain.go +++ b/ecc/bls12-378/fr/fft/domain.go @@ -63,30 +63,27 @@ type Domain struct { // NewDomain returns a subgroup with a power of 2 cardinality // cardinality >= m -func NewDomain(m uint64) *Domain { +// shift: when specified, it's the element by which the set of root of unity is shifted. +func NewDomain(m uint64, shift ...fr.Element) *Domain { domain := &Domain{} x := ecc.NextPowerOfTwo(m) domain.Cardinality = uint64(x) // generator of the largest 2-adic subgroup - var rootOfUnity fr.Element - rootOfUnity.SetString("4045585818372166415418670827807793147093034396422209590578257013290761627990") - const maxOrderRoot uint64 = 42 domain.FrMultiplicativeGen.SetUint64(22) + if len(shift) != 0 { + domain.FrMultiplicativeGen.Set(&shift[0]) + } domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen) - // find generator for Z/2^(log(m))Z - logx := uint64(bits.TrailingZeros64(x)) - if logx > maxOrderRoot { - panic(fmt.Sprintf("m (%d) is too big: the required root of unity does not exist", m)) + var err error + domain.Generator, err = Generator(m) + if err != nil { + panic(err) } - - // Generator = FinerGenerator^2 has order x - expo := uint64(1 << (maxOrderRoot - logx)) - domain.Generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x domain.GeneratorInv.Inverse(&domain.Generator) domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv) @@ -99,6 +96,28 @@ func NewDomain(m uint64) *Domain { return domain } +// Generator returns a generator for Z/2^(log(m))Z +// or an error if m is too big (required root of unity doesn't exist) +func Generator(m uint64) (fr.Element, error) { + x := ecc.NextPowerOfTwo(m) + + var rootOfUnity fr.Element + + rootOfUnity.SetString("4045585818372166415418670827807793147093034396422209590578257013290761627990") + const maxOrderRoot uint64 = 42 + + // find generator for Z/2^(log(m))Z + logx := uint64(bits.TrailingZeros64(x)) + if logx > maxOrderRoot { + return fr.Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m) + } + + expo := uint64(1 << (maxOrderRoot - logx)) + var generator fr.Element + generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x + return generator, nil +} + func (d *Domain) reverseCosetTables() { d.CosetTableReversed = make([]fr.Element, d.Cardinality) d.CosetTableInvReversed = make([]fr.Element, d.Cardinality) diff --git a/ecc/bls12-378/fr/fft/fft.go b/ecc/bls12-378/fr/fft/fft.go index 2e9b257700..88e88503f7 100644 --- a/ecc/bls12-378/fr/fft/fft.go +++ b/ecc/bls12-378/fr/fft/fft.go @@ -18,7 +18,6 @@ package fft import ( "math/bits" - "runtime" "github.com/consensys/gnark-crypto/ecc" "github.com/consensys/gnark-crypto/internal/parallel" @@ -40,24 +39,18 @@ const butterflyThreshold = 16 // FFT computes (recursively) the discrete Fourier transform of a and stores the result in a // if decimation == DIT (decimation in time), the input must be in bit-reversed order // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order -// if coset if set, the FFT(a) returns the evaluation of a on a coset. -func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) { +func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option) { - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } + opt := options(opts...) // if coset != 0, scale by coset table - if _coset { + if opt.coset { scale := func(cosetTable []fr.Element) { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &cosetTable[i]) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableReversed) @@ -69,16 +62,16 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.Twiddles, 0, maxSplits, nil) + difFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.Twiddles, 0, maxSplits, nil) + ditFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } @@ -89,37 +82,31 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order // coset sets the shift of the fft (0 = no shift, standard fft) // len(a) must be a power of 2, and w must be a len(a)th root of unity in field F. -func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset ...bool) { - - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } +func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...Option) { + opt := options(opts...) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } // scale by CardinalityInv - if !_coset { + if !opt.coset { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) return } @@ -129,7 +116,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. a[i].Mul(&a[i], &cosetTable[i]). Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableInv) @@ -141,7 +128,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. } -func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -159,7 +146,7 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for i := start; i < end; i++ { fr.Butterfly(&a[i], &a[i+m]) @@ -182,17 +169,17 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon nextStage := stage + 1 if stage < maxSplits { chDone := make(chan struct{}, 1) - go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone) - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone, nbTasks) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - difFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + difFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } } -func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -210,12 +197,12 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon if stage < maxSplits { // that's the only time we fire go routines chDone := make(chan struct{}, 1) - go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone) - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone, nbTasks) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } @@ -223,7 +210,7 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for k := start; k < end; k++ { a[k+m].Mul(&a[k+m], &twiddles[stage][k]) diff --git a/ecc/bls12-378/fr/fft/fft_test.go b/ecc/bls12-378/fr/fft/fft_test.go index c2305807af..1c0f64ac07 100644 --- a/ecc/bls12-378/fr/fft/fft_test.go +++ b/ecc/bls12-378/fr/fft/fft_test.go @@ -52,7 +52,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIF) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -79,7 +79,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIF, OnCoset()) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -108,7 +108,7 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFT(pol, DIT) sample := domainWithPrecompute.Generator sample.Exp(sample, big.NewInt(int64(ithpower))) @@ -134,8 +134,8 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) - domainWithPrecompute.FFTInverse(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIT) + domainWithPrecompute.FFTInverse(pol, DIF) BitReverse(pol) check := true @@ -163,8 +163,8 @@ func TestFFT(t *testing.T) { for i := 1; i <= nbCosets; i++ { BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, true) - domainWithPrecompute.FFTInverse(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) BitReverse(pol) for i := 0; i < len(pol); i++ { @@ -188,8 +188,8 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, false) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFTInverse(pol, DIF) + domainWithPrecompute.FFT(pol, DIT) check := true for i := 0; i < len(pol); i++ { @@ -211,14 +211,26 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, true) - domainWithPrecompute.FFT(pol, DIT, true) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) - check := true for i := 0; i < len(pol); i++ { - check = check && (pol[i] == backupPol[i]) + if !(pol[i].Equal(&backupPol[i])) { + return false + } } - return check + + // compute with nbTasks == 1 + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset(), WithNbTasks(1)) + domainWithPrecompute.FFT(pol, DIT, OnCoset(), WithNbTasks(1)) + + for i := 0; i < len(pol); i++ { + if !(pol[i].Equal(&backupPol[i])) { + return false + } + } + + return true }, )) @@ -265,14 +277,14 @@ func BenchmarkFFT(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, false) + domain.FFT(pol[:sizeDomain], DIT) } }) b.Run("fft 2**"+strconv.Itoa(i)+"bits (coset)", func(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, true) + domain.FFT(pol[:sizeDomain], DIT, OnCoset()) } }) } @@ -292,7 +304,7 @@ func BenchmarkFFTDITCosetReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIT, true) + domain.FFT(pol, DIT, OnCoset()) } } @@ -309,7 +321,7 @@ func BenchmarkFFTDIFReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIF, false) + domain.FFT(pol, DIF) } } diff --git a/ecc/bls12-378/fr/fft/options.go b/ecc/bls12-378/fr/fft/options.go new file mode 100644 index 0000000000..603b76f299 --- /dev/null +++ b/ecc/bls12-378/fr/fft/options.go @@ -0,0 +1,61 @@ +// Copyright 2020 ConsenSys Software Inc. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +// Code generated by consensys/gnark-crypto DO NOT EDIT + +package fft + +import "runtime" + +// Option defines option for altering the behavior of FFT methods. +// See the descriptions of functions returning instances of this type for +// particular options. +type Option func(*fftConfig) + +type fftConfig struct { + coset bool + nbTasks int +} + +// OnCoset if provided, FFT(a) returns the evaluation of a on a coset. +func OnCoset() Option { + return func(opt *fftConfig) { + opt.coset = true + } +} + +// WithNbTasks sets the max number of task (go routine) to spawn. Must be between 1 and 512. +func WithNbTasks(nbTasks int) Option { + if nbTasks < 1 { + nbTasks = 1 + } else if nbTasks > 512 { + nbTasks = 512 + } + return func(opt *fftConfig) { + opt.nbTasks = nbTasks + } +} + +// default options +func options(opts ...Option) fftConfig { + // apply options + opt := fftConfig{ + coset: false, + nbTasks: runtime.NumCPU(), + } + for _, option := range opts { + option(&opt) + } + return opt +} diff --git a/ecc/bls12-378/fr/iop/polynomial.go b/ecc/bls12-378/fr/iop/polynomial.go index 7985351685..d6fb4729c3 100644 --- a/ecc/bls12-378/fr/iop/polynomial.go +++ b/ecc/bls12-378/fr/iop/polynomial.go @@ -146,11 +146,13 @@ func (p *Polynomial) Evaluate(x fr.Element) fr.Element { return p.polynomial.evaluate(x) } - // TODO find a way to retrieve the root properly instead of re generating the fft domain - d := fft.NewDomain(uint64(p.size)) var g fr.Element if p.shift <= 5 { - g = smallExp(d.Generator, p.shift) + gen, err := fft.Generator(uint64(p.size)) + if err != nil { + panic(err) + } + g = smallExp(gen, p.shift) x.Mul(&x, &g) return p.polynomial.evaluate(x) } @@ -288,11 +290,11 @@ func (p *Polynomial) ToLagrange(d *fft.Domain) *Polynomial { return p case lagrangeCosetRegular: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIT) case lagrangeCosetBitReverse: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIF) default: panic("unknown ID") @@ -317,10 +319,10 @@ func (p *Polynomial) ToCanonical(d *fft.Domain) *Polynomial { d.FFTInverse((*p.coefficients), fft.DIT) case lagrangeCosetRegular: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetBitReverse: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) default: panic("unknown ID") } @@ -342,18 +344,18 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial { switch id { case canonicalRegular: p.Layout = BitReverse - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case canonicalBitReverse: p.Layout = Regular - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeRegular: p.Layout = Regular d.FFTInverse((*p.coefficients), fft.DIF) - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeBitReverse: p.Layout = BitReverse d.FFTInverse((*p.coefficients), fft.DIT) - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetRegular, lagrangeCosetBitReverse: return p default: diff --git a/ecc/bls12-378/fr/iop/polynomial_test.go b/ecc/bls12-378/fr/iop/polynomial_test.go index 81fe25e178..301af41bf9 100644 --- a/ecc/bls12-378/fr/iop/polynomial_test.go +++ b/ecc/bls12-378/fr/iop/polynomial_test.go @@ -240,7 +240,7 @@ func fromLagrange4(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = Regular d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) return r } @@ -250,7 +250,7 @@ func fromLagrange5(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = BitReverse d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) fft.BitReverse(r.Coefficients()) return r } @@ -438,7 +438,7 @@ func fromCanonical4(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = Regular - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -448,7 +448,7 @@ func fromCanonical5(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = BitReverse - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -566,7 +566,7 @@ func fromLagrangeCoset0(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -576,7 +576,7 @@ func fromLagrangeCoset1(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -585,7 +585,7 @@ func fromLagrangeCoset2(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) return _p } @@ -595,7 +595,7 @@ func fromLagrangeCoset3(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) fft.BitReverse(_p.Coefficients()) return _p diff --git a/ecc/bls12-378/fr/iop/ratios.go b/ecc/bls12-378/fr/iop/ratios.go index c695a975dc..81ff7af5eb 100644 --- a/ecc/bls12-378/fr/iop/ratios.go +++ b/ecc/bls12-378/fr/iop/ratios.go @@ -18,7 +18,10 @@ package iop import ( "errors" + "math/big" "math/bits" + "runtime" + "sync" "github.com/consensys/gnark-crypto/internal/parallel" @@ -213,16 +216,38 @@ func BuildRatioCopyConstraint( } }) - for i := 0; i < n-1; i++ { - coeffs[i+1].Mul(&coeffs[i+1], &coeffs[i]) - t[i+1].Mul(&t[i+1], &t[i]) + chCoeffs := make(chan struct{}, 1) + go func() { + for i := 2; i < n; i++ { + // ignoring coeffs[0] + coeffs[i].Mul(&coeffs[i], &coeffs[i-1]) + } + close(chCoeffs) + }() + + for i := 2; i < n; i++ { + // ignoring t[0] + t[i].Mul(&t[i], &t[i-1]) } + <-chCoeffs - t = fr.BatchInvert(t) - for i := 1; i < n; i++ { - coeffs[i].Mul(&coeffs[i], &t[i]) + // rough ratio inverse to mul; see if it makes sense to parallelize the batch inverse. + const ratioInvMul = 1000 / 17 + nbTasks := runtime.NumCPU() + if ratio := n / ratioInvMul; ratio < nbTasks { + nbTasks = ratio } + parallel.Execute(n-1, func(start, end int) { + // ignoring t[0] and coeff[0] + start++ + end++ + tInv := fr.BatchInvert(t[start:end]) + for i := start; i < end; i++ { + coeffs[i].Mul(&coeffs[i], &tInv[i-start]) + } + }, nbTasks) + res := NewPolynomial(&coeffs, expectedForm) // at this stage the result is in Lagrange form, Regular layout putInExpectedFormFromLagrangeRegular(res, domain, expectedForm) @@ -245,7 +270,7 @@ func putInExpectedFormFromLagrangeRegular(p *Polynomial, domain *fft.Domain, exp if expectedForm.Basis == LagrangeCoset { domain.FFTInverse(p.Coefficients(), fft.DIF) - domain.FFT(p.Coefficients(), fft.DIT, true) + domain.FFT(p.Coefficients(), fft.DIT, fft.OnCoset()) if expectedForm.Layout == BitReverse { fft.BitReverse(p.Coefficients()) } @@ -308,16 +333,42 @@ func getSupportIdentityPermutation(nbCopies int, domain *fft.Domain) []fr.Elemen res := make([]fr.Element, uint64(nbCopies)*domain.Cardinality) sizePoly := int(domain.Cardinality) - res[0].SetOne() - for i := 0; i < sizePoly-1; i++ { + // len(domain.Twiddle) == sizePoly / 2 + copy(res, domain.Twiddles[0]) + // remaining ones. + for i := (sizePoly / 2) - 1; i < sizePoly-1; i++ { res[i+1].Mul(&res[i], &domain.Generator) } + if nbCopies <= 1 { + return res + } + var wg sync.WaitGroup + wg.Add(nbCopies - 1) for i := 1; i < nbCopies; i++ { - copy(res[i*sizePoly:], res[(i-1)*sizePoly:i*int(domain.Cardinality)]) - for j := 0; j < sizePoly; j++ { - res[i*sizePoly+j].Mul(&res[i*sizePoly+j], &domain.FrMultiplicativeGen) + i := i + + var coset fr.Element + if i == 1 { + coset = domain.FrMultiplicativeGen + } else { + if len(domain.CosetTable) > i { + coset = domain.CosetTable[i] + } else { + coset.Exp(domain.FrMultiplicativeGen, big.NewInt(int64(i))) + } } + + go func() { + parallel.Execute(sizePoly, func(start, end int) { + for j := start; j < end; j++ { + res[i*sizePoly+j].Mul(&res[j], &coset) + } + }, (runtime.NumCPU()/(nbCopies-1))+1) + wg.Done() + }() } + wg.Wait() + return res } diff --git a/ecc/bls12-378/fr/kzg/kzg.go b/ecc/bls12-378/fr/kzg/kzg.go index 984ece8f19..d0cde383bb 100644 --- a/ecc/bls12-378/fr/kzg/kzg.go +++ b/ecc/bls12-378/fr/kzg/kzg.go @@ -26,6 +26,8 @@ import ( "github.com/consensys/gnark-crypto/ecc/bls12-378" "github.com/consensys/gnark-crypto/ecc/bls12-378/fr" "github.com/consensys/gnark-crypto/fiat-shamir" + + "github.com/consensys/gnark-crypto/internal/parallel" ) var ( @@ -275,14 +277,21 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr // gamma n in parallel, before reducing into foldedPolynomials foldedPolynomials := make([]fr.Element, largestPoly) copy(foldedPolynomials, polynomials[0]) - acc := gamma - var pj fr.Element + gammas := make([]fr.Element, len(polynomials)) + gammas[0] = gamma for i := 1; i < len(polynomials); i++ { - for j := 0; j < len(polynomials[i]); j++ { - pj.Mul(&polynomials[i][j], &acc) - foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) - } - acc.Mul(&acc, &gamma) + gammas[i].Mul(&gammas[i-1], &gamma) + } + + for i := 1; i < len(polynomials); i++ { + i := i + parallel.Execute(len(polynomials[i]), func(start, end int) { + var pj fr.Element + for j := start; j < end; j++ { + pj.Mul(&polynomials[i][j], &gammas[i-1]) + foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) + } + }) } // compute H diff --git a/ecc/bls12-378/fr/permutation/permutation.go b/ecc/bls12-378/fr/permutation/permutation.go index 5bc4ea4924..59eab17b37 100644 --- a/ecc/bls12-378/fr/permutation/permutation.go +++ b/ecc/bls12-378/fr/permutation/permutation.go @@ -191,15 +191,15 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } lz := make([]fr.Element, s) copy(lz, cz) - d.FFT(lz, fft.DIF, true) + d.FFT(lz, fft.DIF, fft.OnCoset()) // compute the first part of the numerator lt1 := make([]fr.Element, s) lt2 := make([]fr.Element, s) copy(lt1, ct1) copy(lt2, ct2) - d.FFT(lt1, fft.DIF, true) - d.FFT(lt2, fft.DIF, true) + d.FFT(lt1, fft.DIF, fft.OnCoset()) + d.FFT(lt2, fft.DIF, fft.OnCoset()) lsNumFirstPart := evaluateFirstPartNumReverse(lt1, lt2, lz, epsilon) // compute second part of the numerator @@ -222,7 +222,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } // get the quotient and commit it - d.FFTInverse(lsNum, fft.DIT, true) + d.FFTInverse(lsNum, fft.DIT, fft.OnCoset()) proof.q, err = kzg.Commit(lsNum, srs) if err != nil { return proof, err diff --git a/ecc/bls12-378/fr/plookup/vector.go b/ecc/bls12-378/fr/plookup/vector.go index 6a0981bd32..c8759cba47 100644 --- a/ecc/bls12-378/fr/plookup/vector.go +++ b/ecc/bls12-378/fr/plookup/vector.go @@ -340,7 +340,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element Mul(&res[_i], &numLn[i%2]) } - domainBig.FFTInverse(res, fft.DIT, true) + domainBig.FFTInverse(res, fft.DIT, fft.OnCoset()) return res } @@ -476,11 +476,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) copy(_lh2, ch2) copy(_lt, ct) copy(_lf, cf) - domainBig.FFT(_lz, fft.DIF, true) - domainBig.FFT(_lh1, fft.DIF, true) - domainBig.FFT(_lh2, fft.DIF, true) - domainBig.FFT(_lt, fft.DIF, true) - domainBig.FFT(_lf, fft.DIF, true) + domainBig.FFT(_lz, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh1, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh2, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lt, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lf, fft.DIF, fft.OnCoset()) // compute h lh := evaluateNumBitReversed(_lz, _lh1, _lh2, _lt, _lf, beta, gamma, domainBig) diff --git a/ecc/bls12-378/internal/fptower/e12_pairing.go b/ecc/bls12-378/internal/fptower/e12_pairing.go index 49d9119ad7..64cde6c4f7 100644 --- a/ecc/bls12-378/internal/fptower/e12_pairing.go +++ b/ecc/bls12-378/internal/fptower/e12_pairing.go @@ -95,8 +95,8 @@ func (z *E12) MulBy014(c0, c1, c4 *E2) *E12 { } // Mul014By014 multiplication of sparse element (c0,c1,0,0,c4,0) by sparse element (d0,d1,0,0,d4,0) -func (z *E12) Mul014By014(d0, d1, d4, c0, c1, c4 *E2) *E12 { - var tmp, x0, x1, x4, x04, x01, x14 E2 +func Mul014By014(d0, d1, d4, c0, c1, c4 *E2) [5]E2 { + var z00, tmp, x0, x1, x4, x04, x01, x14 E2 x0.Mul(c0, d0) x1.Mul(c1, d1) x4.Mul(c4, d4) @@ -116,13 +116,30 @@ func (z *E12) Mul014By014(d0, d1, d4, c0, c1, c4 *E2) *E12 { Sub(&x14, &x1). Sub(&x14, &x4) - z.C0.B0.MulByNonResidue(&x4). - Add(&z.C0.B0, &x0) - z.C0.B1.Set(&x01) - z.C0.B2.Set(&x1) - z.C1.B0.SetZero() - z.C1.B1.Set(&x04) - z.C1.B2.Set(&x14) + z00.MulByNonResidue(&x4). + Add(&z00, &x0) + + return [5]E2{z00, x01, x1, x04, x14} +} + +// MulBy01245 multiplies z by an E12 sparse element of the form (x0, x1, x2, 0, x4, x5) +func (z *E12) MulBy01245(x *[5]E2) *E12 { + var c1, a, b, c, z0, z1 E6 + c0 := &E6{B0: x[0], B1: x[1], B2: x[2]} + c1.B1 = x[3] + c1.B2 = x[4] + a.Add(&z.C0, &z.C1) + b.Add(c0, &c1) + a.Mul(&a, &b) + b.Mul(&z.C0, c0) + c.Set(&z.C1).MulBy12(&x[3], &x[4]) + z1.Sub(&a, &b) + z1.Sub(&z1, &c) + z0.MulByNonResidue(&c) + z0.Add(&z0, &b) + + z.C0 = z0 + z.C1 = z1 return z } diff --git a/ecc/bls12-378/internal/fptower/e6.go b/ecc/bls12-378/internal/fptower/e6.go index 8ae7216ec5..d4f80de958 100644 --- a/ecc/bls12-378/internal/fptower/e6.go +++ b/ecc/bls12-378/internal/fptower/e6.go @@ -126,6 +126,34 @@ func (z *E6) MulByE2(x *E6, y *E2) *E6 { return z } +// MulBy12 multiplication by sparse element (0,b1,b2) +func (x *E6) MulBy12(b1, b2 *E2) *E6 { + var t1, t2, c0, tmp, c1, c2 E2 + t1.Mul(&x.B1, b1) + t2.Mul(&x.B2, b2) + c0.Add(&x.B1, &x.B2) + tmp.Add(b1, b2) + c0.Mul(&c0, &tmp) + c0.Sub(&c0, &t1) + c0.Sub(&c0, &t2) + c0.MulByNonResidue(&c0) + c1.Add(&x.B0, &x.B1) + c1.Mul(&c1, b1) + c1.Sub(&c1, &t1) + tmp.MulByNonResidue(&t2) + c1.Add(&c1, &tmp) + tmp.Add(&x.B0, &x.B2) + c2.Mul(b2, &tmp) + c2.Sub(&c2, &t2) + c2.Add(&c2, &t1) + + x.B0 = c0 + x.B1 = c1 + x.B2 = c2 + + return x +} + // MulBy01 multiplication by sparse element (c0,c1,0) func (z *E6) MulBy01(c0, c1 *E2) *E6 { diff --git a/ecc/bls12-378/marshal.go b/ecc/bls12-378/marshal.go index 2b12b7bbb8..33bd800ddd 100644 --- a/ecc/bls12-378/marshal.go +++ b/ecc/bls12-378/marshal.go @@ -50,6 +50,8 @@ const ( // SizeOfGT represents the size in bytes that a GT element need in binary form const SizeOfGT = fptower.SizeOfGT +var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding") + // Encoder writes bls12-378 object values to an output stream type Encoder struct { w io.Writer @@ -365,6 +367,19 @@ func NoSubgroupChecks() func(*Decoder) { } } +// isZeroed checks that the provided bytes are at 0 +func isZeroed(firstByte byte, buf []byte) bool { + if firstByte != 0 { + return false + } + for _, b := range buf { + if b != 0 { + return false + } + } + return true +} + func (enc *Encoder) encode(v interface{}) (err error) { rv := reflect.ValueOf(v) if v == nil || (rv.Kind() == reflect.Ptr && rv.IsNil()) { @@ -674,13 +689,19 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineUncompressed, nil @@ -796,9 +817,12 @@ func (p *G1Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } @@ -861,7 +885,7 @@ func (p *G2Affine) Bytes() (res [SizeOfG2AffineCompressed]byte) { } // we store X and mask the most significant word with our metadata mask - // p.X.A1 | p.X.A0 + // p.X.A1 | p.X.A0 fp.BigEndian.PutElement((*[fp.Bytes]byte)(res[48:48+fp.Bytes]), p.X.A0) fp.BigEndian.PutElement((*[fp.Bytes]byte)(res[0:0+fp.Bytes]), p.X.A1) @@ -927,13 +951,19 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineUncompressed, nil @@ -1063,9 +1093,12 @@ func (p *G2Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } diff --git a/ecc/bls12-378/pairing.go b/ecc/bls12-378/pairing.go index c88db75481..1796944080 100644 --- a/ecc/bls12-378/pairing.go +++ b/ecc/bls12-378/pairing.go @@ -103,7 +103,7 @@ func FinalExponentiation(z *GT, _z ...*GT) GT { } // MillerLoop computes the multi-Miller loop -// ∏ᵢ MillerLoop(Pᵢ, Qᵢ) +// ∏ᵢ MillerLoop(Pᵢ, Qᵢ) = ∏ᵢ { fᵢ_{x,Qᵢ}(Pᵢ) } func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { // check input size match n := len(P) @@ -131,51 +131,114 @@ func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { qProj[k].FromAffine(&q[k]) } - var result, lines GT + var result GT result.SetOne() - var l1, l2 lineEvaluation + var prodLines [5]E2 + + // Compute ∏ᵢ { fᵢ_{x₀,Q}(P) } + if n >= 1 { + // i = 62, separately to avoid an E12 Square + // (Square(res) = 1² = 1) + // loopCounter[62] = 0 + // k = 0, separately to avoid MulBy014 (res × ℓ) + // (assign line to res) + + // qProj[0] ← 2qProj[0] and l1 the tangent ℓ passing 2qProj[0] + qProj[0].doubleStep(&l1) + // line evaluation at P[0] (assign) + result.C0.B0.Set(&l1.r0) + result.C0.B1.MulByElement(&l1.r1, &p[0].X) + result.C1.B1.MulByElement(&l1.r2, &p[0].Y) + } - // i == len(loopCounter) - 2 - for k := 0; k < n; k++ { - qProj[k].DoubleStep(&l1) - // line eval + if n >= 2 { + // k = 1, separately to avoid MulBy014 (res × ℓ) + // (res is also a line at this point, so we use Mul014By014 ℓ × ℓ) + + // qProj[1] ← 2qProj[1] and l1 the tangent ℓ passing 2qProj[1] + qProj[1].doubleStep(&l1) + // line evaluation at P[1] + l1.r1.MulByElement(&l1.r1, &p[1].X) + l1.r2.MulByElement(&l1.r2, &p[1].Y) + // ℓ × res + prodLines = fptower.Mul014By014(&l1.r0, &l1.r1, &l1.r2, &result.C0.B0, &result.C0.B1, &result.C1.B1) + result.C0.B0 = prodLines[0] + result.C0.B1 = prodLines[1] + result.C0.B2 = prodLines[2] + result.C1.B1 = prodLines[3] + result.C1.B2 = prodLines[4] + } + + // k >= 2 + for k := 2; k < n; k++ { + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] l1.r1.MulByElement(&l1.r1, &p[k].X) l1.r2.MulByElement(&l1.r2, &p[k].Y) + // ℓ × res result.MulBy014(&l1.r0, &l1.r1, &l1.r2) } - for i := len(loopCounter) - 3; i >= 0; i-- { + // i <= 61 + for i := len(loopCounter) - 3; i >= 1; i-- { + // mutualize the square among n Miller loops // (∏ᵢfᵢ)² result.Square(&result) for k := 0; k < n; k++ { - qProj[k].DoubleStep(&l1) - // line eval + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] l1.r1.MulByElement(&l1.r1, &p[k].X) l1.r2.MulByElement(&l1.r2, &p[k].Y) if loopCounter[i] == 0 { + // ℓ × res result.MulBy014(&l1.r0, &l1.r1, &l1.r2) } else { - qProj[k].AddMixedStep(&l2, &q[k]) - // line eval + // qProj[k] ← qProj[k]+Q[k] and + // l2 the line ℓ passing qProj[k] and Q[k] + qProj[k].addMixedStep(&l2, &q[k]) + // line evaluation at P[k] l2.r1.MulByElement(&l2.r1, &p[k].X) l2.r2.MulByElement(&l2.r2, &p[k].Y) // ℓ × ℓ - lines.Mul014By014(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) + prodLines = fptower.Mul014By014(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) // (ℓ × ℓ) × result - result.Mul(&result, &lines) + result.MulBy01245(&prodLines) } } } + // i = 0, separately to avoid a point addition + // loopCounter[0] = 1 + result.Square(&result) + for k := 0; k < n; k++ { + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] + l1.r1.MulByElement(&l1.r1, &p[k].X) + l1.r2.MulByElement(&l1.r2, &p[k].Y) + + // l2 the line passing qProj[k] and Q + qProj[k].lineCompute(&l2, &q[k]) + // line evaluation at P[k] + l2.r1.MulByElement(&l2.r1, &p[k].X) + l2.r2.MulByElement(&l2.r2, &p[k].Y) + // ℓ × ℓ + prodLines = fptower.Mul014By014(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) + // (ℓ × ℓ) × result + result.MulBy01245(&prodLines) + } + return result, nil } -// DoubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop +// doubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g2Proj) DoubleStep(l *lineEvaluation) { +func (p *g2Proj) doubleStep(l *lineEvaluation) { // get some Element from our pool var t1, A, B, C, D, E, EE, F, G, H, I, J, K fptower.E2 @@ -215,9 +278,9 @@ func (p *g2Proj) DoubleStep(l *lineEvaluation) { } -// AddMixedStep point addition in Mixed Homogenous projective and Affine coordinates +// addMixedStep point addition in Mixed Homogenous projective and Affine coordinates // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g2Proj) AddMixedStep(l *lineEvaluation, a *G2Affine) { +func (p *g2Proj) addMixedStep(l *lineEvaluation, a *G2Affine) { // get some Element from our pool var Y2Z1, X2Z1, O, L, C, D, E, F, G, H, t0, t1, t2, J fptower.E2 @@ -251,3 +314,23 @@ func (p *g2Proj) AddMixedStep(l *lineEvaluation, a *G2Affine) { l.r1.Neg(&O) l.r2.Set(&L) } + +// lineCompute computes the line through p in Homogenous projective coordinates +// and a in affine coordinates. It does not compute the resulting point p+a. +func (p *g2Proj) lineCompute(evaluations *lineEvaluation, a *G2Affine) { + + // get some Element from our pool + var Y2Z1, X2Z1, O, L, t2, J fptower.E2 + Y2Z1.Mul(&a.Y, &p.z) + O.Sub(&p.y, &Y2Z1) + X2Z1.Mul(&a.X, &p.z) + L.Sub(&p.x, &X2Z1) + t2.Mul(&L, &a.Y) + J.Mul(&a.X, &O). + Sub(&J, &t2) + + // Line evaluation + evaluations.r0.Set(&J) + evaluations.r1.Neg(&O) + evaluations.r2.Set(&L) +} diff --git a/ecc/bls12-381/bls12-381.go b/ecc/bls12-381/bls12-381.go index 796369ed68..86ab933a19 100644 --- a/ecc/bls12-381/bls12-381.go +++ b/ecc/bls12-381/bls12-381.go @@ -40,7 +40,8 @@ import ( // ID bls381 ID const ID = ecc.BLS12_381 -// bCurveCoeff b coeff of the curve Y²=X³+b +// aCurveCoeff is the a coefficients of the curve Y²=X³+ax+b +var aCurveCoeff fp.Element var bCurveCoeff fp.Element // twist @@ -85,8 +86,17 @@ var endo struct { // seed x₀ of the curve var xGen big.Int -func init() { +// 𝔽p² +type E2 = fptower.E2 + +// 𝔽p⁶ +type E6 = fptower.E6 + +// 𝔽p¹² +type E12 = fptower.E12 +func init() { + aCurveCoeff.SetUint64(0) bCurveCoeff.SetUint64(4) // M-twist twist.A0.SetUint64(1) @@ -140,3 +150,8 @@ func Generators() (g1Jac G1Jac, g2Jac G2Jac, g1Aff G1Affine, g2Aff G2Affine) { g2Jac = g2Gen return } + +// CurveCoefficients returns the a, b coefficients of the curve equation. +func CurveCoefficients() (a, b fp.Element) { + return aCurveCoeff, bCurveCoeff +} diff --git a/ecc/bls12-381/ecdsa/ecdsa.go b/ecc/bls12-381/ecdsa/ecdsa.go index 9039ee3885..db56267894 100644 --- a/ecc/bls12-381/ecdsa/ecdsa.go +++ b/ecc/bls12-381/ecdsa/ecdsa.go @@ -22,7 +22,6 @@ import ( "crypto/rand" "crypto/sha512" "crypto/subtle" - "errors" "hash" "io" "math/big" @@ -33,8 +32,6 @@ import ( "github.com/consensys/gnark-crypto/signature" ) -var errInvalidSig = errors.New("invalid signature") - const ( sizeFr = fr.Bytes sizeFp = fp.Bytes @@ -213,6 +210,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) kInv.ModInverse(k, order) P.X.BigInt(r) + r.Mod(r, order) if r.Sign() != 0 { break diff --git a/ecc/bls12-381/fp/element.go b/ecc/bls12-381/fp/element.go index 198dc73c0e..0cc4fe61f7 100644 --- a/ecc/bls12-381/fp/element.go +++ b/ecc/bls12-381/fp/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -844,12 +845,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -859,7 +860,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bls12-381/fr/element.go b/ecc/bls12-381/fr/element.go index 4a88420901..a956f7bd9d 100644 --- a/ecc/bls12-381/fr/element.go +++ b/ecc/bls12-381/fr/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -692,12 +693,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -707,7 +708,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bls12-381/fr/fft/domain.go b/ecc/bls12-381/fr/fft/domain.go index a338e27397..7c5d6bd11f 100644 --- a/ecc/bls12-381/fr/fft/domain.go +++ b/ecc/bls12-381/fr/fft/domain.go @@ -63,30 +63,27 @@ type Domain struct { // NewDomain returns a subgroup with a power of 2 cardinality // cardinality >= m -func NewDomain(m uint64) *Domain { +// shift: when specified, it's the element by which the set of root of unity is shifted. +func NewDomain(m uint64, shift ...fr.Element) *Domain { domain := &Domain{} x := ecc.NextPowerOfTwo(m) domain.Cardinality = uint64(x) // generator of the largest 2-adic subgroup - var rootOfUnity fr.Element - rootOfUnity.SetString("10238227357739495823651030575849232062558860180284477541189508159991286009131") - const maxOrderRoot uint64 = 32 domain.FrMultiplicativeGen.SetUint64(7) + if len(shift) != 0 { + domain.FrMultiplicativeGen.Set(&shift[0]) + } domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen) - // find generator for Z/2^(log(m))Z - logx := uint64(bits.TrailingZeros64(x)) - if logx > maxOrderRoot { - panic(fmt.Sprintf("m (%d) is too big: the required root of unity does not exist", m)) + var err error + domain.Generator, err = Generator(m) + if err != nil { + panic(err) } - - // Generator = FinerGenerator^2 has order x - expo := uint64(1 << (maxOrderRoot - logx)) - domain.Generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x domain.GeneratorInv.Inverse(&domain.Generator) domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv) @@ -99,6 +96,28 @@ func NewDomain(m uint64) *Domain { return domain } +// Generator returns a generator for Z/2^(log(m))Z +// or an error if m is too big (required root of unity doesn't exist) +func Generator(m uint64) (fr.Element, error) { + x := ecc.NextPowerOfTwo(m) + + var rootOfUnity fr.Element + + rootOfUnity.SetString("10238227357739495823651030575849232062558860180284477541189508159991286009131") + const maxOrderRoot uint64 = 32 + + // find generator for Z/2^(log(m))Z + logx := uint64(bits.TrailingZeros64(x)) + if logx > maxOrderRoot { + return fr.Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m) + } + + expo := uint64(1 << (maxOrderRoot - logx)) + var generator fr.Element + generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x + return generator, nil +} + func (d *Domain) reverseCosetTables() { d.CosetTableReversed = make([]fr.Element, d.Cardinality) d.CosetTableInvReversed = make([]fr.Element, d.Cardinality) diff --git a/ecc/bls12-381/fr/fft/fft.go b/ecc/bls12-381/fr/fft/fft.go index 476b85a337..cd0c2d274e 100644 --- a/ecc/bls12-381/fr/fft/fft.go +++ b/ecc/bls12-381/fr/fft/fft.go @@ -18,7 +18,6 @@ package fft import ( "math/bits" - "runtime" "github.com/consensys/gnark-crypto/ecc" "github.com/consensys/gnark-crypto/internal/parallel" @@ -40,24 +39,18 @@ const butterflyThreshold = 16 // FFT computes (recursively) the discrete Fourier transform of a and stores the result in a // if decimation == DIT (decimation in time), the input must be in bit-reversed order // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order -// if coset if set, the FFT(a) returns the evaluation of a on a coset. -func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) { +func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option) { - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } + opt := options(opts...) // if coset != 0, scale by coset table - if _coset { + if opt.coset { scale := func(cosetTable []fr.Element) { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &cosetTable[i]) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableReversed) @@ -69,16 +62,16 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.Twiddles, 0, maxSplits, nil) + difFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.Twiddles, 0, maxSplits, nil) + ditFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } @@ -89,37 +82,31 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order // coset sets the shift of the fft (0 = no shift, standard fft) // len(a) must be a power of 2, and w must be a len(a)th root of unity in field F. -func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset ...bool) { - - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } +func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...Option) { + opt := options(opts...) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } // scale by CardinalityInv - if !_coset { + if !opt.coset { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) return } @@ -129,7 +116,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. a[i].Mul(&a[i], &cosetTable[i]). Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableInv) @@ -141,7 +128,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. } -func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -159,7 +146,7 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for i := start; i < end; i++ { fr.Butterfly(&a[i], &a[i+m]) @@ -182,17 +169,17 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon nextStage := stage + 1 if stage < maxSplits { chDone := make(chan struct{}, 1) - go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone) - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone, nbTasks) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - difFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + difFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } } -func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -210,12 +197,12 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon if stage < maxSplits { // that's the only time we fire go routines chDone := make(chan struct{}, 1) - go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone) - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone, nbTasks) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } @@ -223,7 +210,7 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for k := start; k < end; k++ { a[k+m].Mul(&a[k+m], &twiddles[stage][k]) diff --git a/ecc/bls12-381/fr/fft/fft_test.go b/ecc/bls12-381/fr/fft/fft_test.go index 0b0053f43c..ad7139e6ea 100644 --- a/ecc/bls12-381/fr/fft/fft_test.go +++ b/ecc/bls12-381/fr/fft/fft_test.go @@ -52,7 +52,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIF) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -79,7 +79,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIF, OnCoset()) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -108,7 +108,7 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFT(pol, DIT) sample := domainWithPrecompute.Generator sample.Exp(sample, big.NewInt(int64(ithpower))) @@ -134,8 +134,8 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) - domainWithPrecompute.FFTInverse(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIT) + domainWithPrecompute.FFTInverse(pol, DIF) BitReverse(pol) check := true @@ -163,8 +163,8 @@ func TestFFT(t *testing.T) { for i := 1; i <= nbCosets; i++ { BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, true) - domainWithPrecompute.FFTInverse(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) BitReverse(pol) for i := 0; i < len(pol); i++ { @@ -188,8 +188,8 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, false) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFTInverse(pol, DIF) + domainWithPrecompute.FFT(pol, DIT) check := true for i := 0; i < len(pol); i++ { @@ -211,14 +211,26 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, true) - domainWithPrecompute.FFT(pol, DIT, true) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) - check := true for i := 0; i < len(pol); i++ { - check = check && (pol[i] == backupPol[i]) + if !(pol[i].Equal(&backupPol[i])) { + return false + } } - return check + + // compute with nbTasks == 1 + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset(), WithNbTasks(1)) + domainWithPrecompute.FFT(pol, DIT, OnCoset(), WithNbTasks(1)) + + for i := 0; i < len(pol); i++ { + if !(pol[i].Equal(&backupPol[i])) { + return false + } + } + + return true }, )) @@ -265,14 +277,14 @@ func BenchmarkFFT(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, false) + domain.FFT(pol[:sizeDomain], DIT) } }) b.Run("fft 2**"+strconv.Itoa(i)+"bits (coset)", func(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, true) + domain.FFT(pol[:sizeDomain], DIT, OnCoset()) } }) } @@ -292,7 +304,7 @@ func BenchmarkFFTDITCosetReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIT, true) + domain.FFT(pol, DIT, OnCoset()) } } @@ -309,7 +321,7 @@ func BenchmarkFFTDIFReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIF, false) + domain.FFT(pol, DIF) } } diff --git a/ecc/bls12-381/fr/fft/options.go b/ecc/bls12-381/fr/fft/options.go new file mode 100644 index 0000000000..603b76f299 --- /dev/null +++ b/ecc/bls12-381/fr/fft/options.go @@ -0,0 +1,61 @@ +// Copyright 2020 ConsenSys Software Inc. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +// Code generated by consensys/gnark-crypto DO NOT EDIT + +package fft + +import "runtime" + +// Option defines option for altering the behavior of FFT methods. +// See the descriptions of functions returning instances of this type for +// particular options. +type Option func(*fftConfig) + +type fftConfig struct { + coset bool + nbTasks int +} + +// OnCoset if provided, FFT(a) returns the evaluation of a on a coset. +func OnCoset() Option { + return func(opt *fftConfig) { + opt.coset = true + } +} + +// WithNbTasks sets the max number of task (go routine) to spawn. Must be between 1 and 512. +func WithNbTasks(nbTasks int) Option { + if nbTasks < 1 { + nbTasks = 1 + } else if nbTasks > 512 { + nbTasks = 512 + } + return func(opt *fftConfig) { + opt.nbTasks = nbTasks + } +} + +// default options +func options(opts ...Option) fftConfig { + // apply options + opt := fftConfig{ + coset: false, + nbTasks: runtime.NumCPU(), + } + for _, option := range opts { + option(&opt) + } + return opt +} diff --git a/ecc/bls12-381/fr/iop/polynomial.go b/ecc/bls12-381/fr/iop/polynomial.go index fdea3cb1aa..3d8daacdf4 100644 --- a/ecc/bls12-381/fr/iop/polynomial.go +++ b/ecc/bls12-381/fr/iop/polynomial.go @@ -146,11 +146,13 @@ func (p *Polynomial) Evaluate(x fr.Element) fr.Element { return p.polynomial.evaluate(x) } - // TODO find a way to retrieve the root properly instead of re generating the fft domain - d := fft.NewDomain(uint64(p.size)) var g fr.Element if p.shift <= 5 { - g = smallExp(d.Generator, p.shift) + gen, err := fft.Generator(uint64(p.size)) + if err != nil { + panic(err) + } + g = smallExp(gen, p.shift) x.Mul(&x, &g) return p.polynomial.evaluate(x) } @@ -288,11 +290,11 @@ func (p *Polynomial) ToLagrange(d *fft.Domain) *Polynomial { return p case lagrangeCosetRegular: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIT) case lagrangeCosetBitReverse: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIF) default: panic("unknown ID") @@ -317,10 +319,10 @@ func (p *Polynomial) ToCanonical(d *fft.Domain) *Polynomial { d.FFTInverse((*p.coefficients), fft.DIT) case lagrangeCosetRegular: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetBitReverse: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) default: panic("unknown ID") } @@ -342,18 +344,18 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial { switch id { case canonicalRegular: p.Layout = BitReverse - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case canonicalBitReverse: p.Layout = Regular - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeRegular: p.Layout = Regular d.FFTInverse((*p.coefficients), fft.DIF) - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeBitReverse: p.Layout = BitReverse d.FFTInverse((*p.coefficients), fft.DIT) - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetRegular, lagrangeCosetBitReverse: return p default: diff --git a/ecc/bls12-381/fr/iop/polynomial_test.go b/ecc/bls12-381/fr/iop/polynomial_test.go index b3dc44c0e4..de1d26b743 100644 --- a/ecc/bls12-381/fr/iop/polynomial_test.go +++ b/ecc/bls12-381/fr/iop/polynomial_test.go @@ -240,7 +240,7 @@ func fromLagrange4(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = Regular d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) return r } @@ -250,7 +250,7 @@ func fromLagrange5(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = BitReverse d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) fft.BitReverse(r.Coefficients()) return r } @@ -438,7 +438,7 @@ func fromCanonical4(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = Regular - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -448,7 +448,7 @@ func fromCanonical5(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = BitReverse - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -566,7 +566,7 @@ func fromLagrangeCoset0(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -576,7 +576,7 @@ func fromLagrangeCoset1(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -585,7 +585,7 @@ func fromLagrangeCoset2(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) return _p } @@ -595,7 +595,7 @@ func fromLagrangeCoset3(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) fft.BitReverse(_p.Coefficients()) return _p diff --git a/ecc/bls12-381/fr/iop/ratios.go b/ecc/bls12-381/fr/iop/ratios.go index 6a0c6eb94e..273096b132 100644 --- a/ecc/bls12-381/fr/iop/ratios.go +++ b/ecc/bls12-381/fr/iop/ratios.go @@ -18,7 +18,10 @@ package iop import ( "errors" + "math/big" "math/bits" + "runtime" + "sync" "github.com/consensys/gnark-crypto/internal/parallel" @@ -213,16 +216,38 @@ func BuildRatioCopyConstraint( } }) - for i := 0; i < n-1; i++ { - coeffs[i+1].Mul(&coeffs[i+1], &coeffs[i]) - t[i+1].Mul(&t[i+1], &t[i]) + chCoeffs := make(chan struct{}, 1) + go func() { + for i := 2; i < n; i++ { + // ignoring coeffs[0] + coeffs[i].Mul(&coeffs[i], &coeffs[i-1]) + } + close(chCoeffs) + }() + + for i := 2; i < n; i++ { + // ignoring t[0] + t[i].Mul(&t[i], &t[i-1]) } + <-chCoeffs - t = fr.BatchInvert(t) - for i := 1; i < n; i++ { - coeffs[i].Mul(&coeffs[i], &t[i]) + // rough ratio inverse to mul; see if it makes sense to parallelize the batch inverse. + const ratioInvMul = 1000 / 17 + nbTasks := runtime.NumCPU() + if ratio := n / ratioInvMul; ratio < nbTasks { + nbTasks = ratio } + parallel.Execute(n-1, func(start, end int) { + // ignoring t[0] and coeff[0] + start++ + end++ + tInv := fr.BatchInvert(t[start:end]) + for i := start; i < end; i++ { + coeffs[i].Mul(&coeffs[i], &tInv[i-start]) + } + }, nbTasks) + res := NewPolynomial(&coeffs, expectedForm) // at this stage the result is in Lagrange form, Regular layout putInExpectedFormFromLagrangeRegular(res, domain, expectedForm) @@ -245,7 +270,7 @@ func putInExpectedFormFromLagrangeRegular(p *Polynomial, domain *fft.Domain, exp if expectedForm.Basis == LagrangeCoset { domain.FFTInverse(p.Coefficients(), fft.DIF) - domain.FFT(p.Coefficients(), fft.DIT, true) + domain.FFT(p.Coefficients(), fft.DIT, fft.OnCoset()) if expectedForm.Layout == BitReverse { fft.BitReverse(p.Coefficients()) } @@ -308,16 +333,42 @@ func getSupportIdentityPermutation(nbCopies int, domain *fft.Domain) []fr.Elemen res := make([]fr.Element, uint64(nbCopies)*domain.Cardinality) sizePoly := int(domain.Cardinality) - res[0].SetOne() - for i := 0; i < sizePoly-1; i++ { + // len(domain.Twiddle) == sizePoly / 2 + copy(res, domain.Twiddles[0]) + // remaining ones. + for i := (sizePoly / 2) - 1; i < sizePoly-1; i++ { res[i+1].Mul(&res[i], &domain.Generator) } + if nbCopies <= 1 { + return res + } + var wg sync.WaitGroup + wg.Add(nbCopies - 1) for i := 1; i < nbCopies; i++ { - copy(res[i*sizePoly:], res[(i-1)*sizePoly:i*int(domain.Cardinality)]) - for j := 0; j < sizePoly; j++ { - res[i*sizePoly+j].Mul(&res[i*sizePoly+j], &domain.FrMultiplicativeGen) + i := i + + var coset fr.Element + if i == 1 { + coset = domain.FrMultiplicativeGen + } else { + if len(domain.CosetTable) > i { + coset = domain.CosetTable[i] + } else { + coset.Exp(domain.FrMultiplicativeGen, big.NewInt(int64(i))) + } } + + go func() { + parallel.Execute(sizePoly, func(start, end int) { + for j := start; j < end; j++ { + res[i*sizePoly+j].Mul(&res[j], &coset) + } + }, (runtime.NumCPU()/(nbCopies-1))+1) + wg.Done() + }() } + wg.Wait() + return res } diff --git a/ecc/bls12-381/fr/kzg/kzg.go b/ecc/bls12-381/fr/kzg/kzg.go index 6a8036740f..3f5c98b034 100644 --- a/ecc/bls12-381/fr/kzg/kzg.go +++ b/ecc/bls12-381/fr/kzg/kzg.go @@ -26,6 +26,8 @@ import ( "github.com/consensys/gnark-crypto/ecc/bls12-381" "github.com/consensys/gnark-crypto/ecc/bls12-381/fr" "github.com/consensys/gnark-crypto/fiat-shamir" + + "github.com/consensys/gnark-crypto/internal/parallel" ) var ( @@ -275,14 +277,21 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr // gamma n in parallel, before reducing into foldedPolynomials foldedPolynomials := make([]fr.Element, largestPoly) copy(foldedPolynomials, polynomials[0]) - acc := gamma - var pj fr.Element + gammas := make([]fr.Element, len(polynomials)) + gammas[0] = gamma for i := 1; i < len(polynomials); i++ { - for j := 0; j < len(polynomials[i]); j++ { - pj.Mul(&polynomials[i][j], &acc) - foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) - } - acc.Mul(&acc, &gamma) + gammas[i].Mul(&gammas[i-1], &gamma) + } + + for i := 1; i < len(polynomials); i++ { + i := i + parallel.Execute(len(polynomials[i]), func(start, end int) { + var pj fr.Element + for j := start; j < end; j++ { + pj.Mul(&polynomials[i][j], &gammas[i-1]) + foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) + } + }) } // compute H diff --git a/ecc/bls12-381/fr/permutation/permutation.go b/ecc/bls12-381/fr/permutation/permutation.go index e2dab3991b..996b48d040 100644 --- a/ecc/bls12-381/fr/permutation/permutation.go +++ b/ecc/bls12-381/fr/permutation/permutation.go @@ -191,15 +191,15 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } lz := make([]fr.Element, s) copy(lz, cz) - d.FFT(lz, fft.DIF, true) + d.FFT(lz, fft.DIF, fft.OnCoset()) // compute the first part of the numerator lt1 := make([]fr.Element, s) lt2 := make([]fr.Element, s) copy(lt1, ct1) copy(lt2, ct2) - d.FFT(lt1, fft.DIF, true) - d.FFT(lt2, fft.DIF, true) + d.FFT(lt1, fft.DIF, fft.OnCoset()) + d.FFT(lt2, fft.DIF, fft.OnCoset()) lsNumFirstPart := evaluateFirstPartNumReverse(lt1, lt2, lz, epsilon) // compute second part of the numerator @@ -222,7 +222,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } // get the quotient and commit it - d.FFTInverse(lsNum, fft.DIT, true) + d.FFTInverse(lsNum, fft.DIT, fft.OnCoset()) proof.q, err = kzg.Commit(lsNum, srs) if err != nil { return proof, err diff --git a/ecc/bls12-381/fr/plookup/vector.go b/ecc/bls12-381/fr/plookup/vector.go index a4c5fe21e0..9f23921aee 100644 --- a/ecc/bls12-381/fr/plookup/vector.go +++ b/ecc/bls12-381/fr/plookup/vector.go @@ -340,7 +340,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element Mul(&res[_i], &numLn[i%2]) } - domainBig.FFTInverse(res, fft.DIT, true) + domainBig.FFTInverse(res, fft.DIT, fft.OnCoset()) return res } @@ -476,11 +476,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) copy(_lh2, ch2) copy(_lt, ct) copy(_lf, cf) - domainBig.FFT(_lz, fft.DIF, true) - domainBig.FFT(_lh1, fft.DIF, true) - domainBig.FFT(_lh2, fft.DIF, true) - domainBig.FFT(_lt, fft.DIF, true) - domainBig.FFT(_lf, fft.DIF, true) + domainBig.FFT(_lz, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh1, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh2, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lt, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lf, fft.DIF, fft.OnCoset()) // compute h lh := evaluateNumBitReversed(_lz, _lh1, _lh2, _lt, _lf, beta, gamma, domainBig) diff --git a/ecc/bls12-381/internal/fptower/e12_pairing.go b/ecc/bls12-381/internal/fptower/e12_pairing.go index 4aaf830747..880520f815 100644 --- a/ecc/bls12-381/internal/fptower/e12_pairing.go +++ b/ecc/bls12-381/internal/fptower/e12_pairing.go @@ -67,8 +67,8 @@ func (z *E12) MulBy014(c0, c1, c4 *E2) *E12 { } // Mul014By014 multiplication of sparse element (c0,c1,0,0,c4,0) by sparse element (d0,d1,0,0,d4,0) -func (z *E12) Mul014By014(d0, d1, d4, c0, c1, c4 *E2) *E12 { - var tmp, x0, x1, x4, x04, x01, x14 E2 +func Mul014By014(d0, d1, d4, c0, c1, c4 *E2) [5]E2 { + var z00, tmp, x0, x1, x4, x04, x01, x14 E2 x0.Mul(c0, d0) x1.Mul(c1, d1) x4.Mul(c4, d4) @@ -88,13 +88,30 @@ func (z *E12) Mul014By014(d0, d1, d4, c0, c1, c4 *E2) *E12 { Sub(&x14, &x1). Sub(&x14, &x4) - z.C0.B0.MulByNonResidue(&x4). - Add(&z.C0.B0, &x0) - z.C0.B1.Set(&x01) - z.C0.B2.Set(&x1) - z.C1.B0.SetZero() - z.C1.B1.Set(&x04) - z.C1.B2.Set(&x14) + z00.MulByNonResidue(&x4). + Add(&z00, &x0) + + return [5]E2{z00, x01, x1, x04, x14} +} + +// MulBy01245 multiplies z by an E12 sparse element of the form (x0, x1, x2, 0, x4, x5) +func (z *E12) MulBy01245(x *[5]E2) *E12 { + var c1, a, b, c, z0, z1 E6 + c0 := &E6{B0: x[0], B1: x[1], B2: x[2]} + c1.B1 = x[3] + c1.B2 = x[4] + a.Add(&z.C0, &z.C1) + b.Add(c0, &c1) + a.Mul(&a, &b) + b.Mul(&z.C0, c0) + c.Set(&z.C1).MulBy12(&x[3], &x[4]) + z1.Sub(&a, &b) + z1.Sub(&z1, &c) + z0.MulByNonResidue(&c) + z0.Add(&z0, &b) + + z.C0 = z0 + z.C1 = z1 return z } diff --git a/ecc/bls12-381/internal/fptower/e6.go b/ecc/bls12-381/internal/fptower/e6.go index 8ae7216ec5..d4f80de958 100644 --- a/ecc/bls12-381/internal/fptower/e6.go +++ b/ecc/bls12-381/internal/fptower/e6.go @@ -126,6 +126,34 @@ func (z *E6) MulByE2(x *E6, y *E2) *E6 { return z } +// MulBy12 multiplication by sparse element (0,b1,b2) +func (x *E6) MulBy12(b1, b2 *E2) *E6 { + var t1, t2, c0, tmp, c1, c2 E2 + t1.Mul(&x.B1, b1) + t2.Mul(&x.B2, b2) + c0.Add(&x.B1, &x.B2) + tmp.Add(b1, b2) + c0.Mul(&c0, &tmp) + c0.Sub(&c0, &t1) + c0.Sub(&c0, &t2) + c0.MulByNonResidue(&c0) + c1.Add(&x.B0, &x.B1) + c1.Mul(&c1, b1) + c1.Sub(&c1, &t1) + tmp.MulByNonResidue(&t2) + c1.Add(&c1, &tmp) + tmp.Add(&x.B0, &x.B2) + c2.Mul(b2, &tmp) + c2.Sub(&c2, &t2) + c2.Add(&c2, &t1) + + x.B0 = c0 + x.B1 = c1 + x.B2 = c2 + + return x +} + // MulBy01 multiplication by sparse element (c0,c1,0) func (z *E6) MulBy01(c0, c1 *E2) *E6 { diff --git a/ecc/bls12-381/marshal.go b/ecc/bls12-381/marshal.go index fad5940db2..f1efa51ff2 100644 --- a/ecc/bls12-381/marshal.go +++ b/ecc/bls12-381/marshal.go @@ -50,6 +50,8 @@ const ( // SizeOfGT represents the size in bytes that a GT element need in binary form const SizeOfGT = fptower.SizeOfGT +var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding") + // Encoder writes bls12-381 object values to an output stream type Encoder struct { w io.Writer @@ -365,6 +367,19 @@ func NoSubgroupChecks() func(*Decoder) { } } +// isZeroed checks that the provided bytes are at 0 +func isZeroed(firstByte byte, buf []byte) bool { + if firstByte != 0 { + return false + } + for _, b := range buf { + if b != 0 { + return false + } + } + return true +} + func (enc *Encoder) encode(v interface{}) (err error) { rv := reflect.ValueOf(v) if v == nil || (rv.Kind() == reflect.Ptr && rv.IsNil()) { @@ -674,13 +689,19 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineUncompressed, nil @@ -796,9 +817,12 @@ func (p *G1Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } @@ -861,7 +885,7 @@ func (p *G2Affine) Bytes() (res [SizeOfG2AffineCompressed]byte) { } // we store X and mask the most significant word with our metadata mask - // p.X.A1 | p.X.A0 + // p.X.A1 | p.X.A0 fp.BigEndian.PutElement((*[fp.Bytes]byte)(res[48:48+fp.Bytes]), p.X.A0) fp.BigEndian.PutElement((*[fp.Bytes]byte)(res[0:0+fp.Bytes]), p.X.A1) @@ -927,13 +951,19 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineUncompressed, nil @@ -1063,9 +1093,12 @@ func (p *G2Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } diff --git a/ecc/bls12-381/pairing.go b/ecc/bls12-381/pairing.go index 9a78d328dc..4c2c867f86 100644 --- a/ecc/bls12-381/pairing.go +++ b/ecc/bls12-381/pairing.go @@ -103,7 +103,7 @@ func FinalExponentiation(z *GT, _z ...*GT) GT { } // MillerLoop computes the multi-Miller loop -// ∏ᵢ MillerLoop(Pᵢ, Qᵢ) +// ∏ᵢ MillerLoop(Pᵢ, Qᵢ) = ∏ᵢ { fᵢ_{x,Qᵢ}(Pᵢ) } func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { // check input size match n := len(P) @@ -131,62 +131,114 @@ func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { qProj[k].FromAffine(&q[k]) } - var result, lines GT + var result GT result.SetOne() - var l1, l2 lineEvaluation + var prodLines [5]E2 + + // Compute ∏ᵢ { fᵢ_{x₀,Q}(P) } + if n >= 1 { + // i = 62, separately to avoid an E12 Square + // (Square(res) = 1² = 1) + // loopCounter[62] = 1 + // k = 0, separately to avoid MulBy014 (res × ℓ) + // (assign line to res) + + // qProj[0] ← 2qProj[0] and l1 the tangent ℓ passing 2qProj[0] + qProj[0].doubleStep(&l1) + // line evaluation at P[0] (assign) + result.C0.B0.Set(&l1.r0) + result.C0.B1.MulByElement(&l1.r1, &p[0].X) + result.C1.B1.MulByElement(&l1.r2, &p[0].Y) + + // qProj[0] ← qProj[0]+Q[0] and + // l2 the line ℓ passing qProj[0] and Q[0] + qProj[0].addMixedStep(&l2, &q[0]) + // line evaluation at P[0] (assign) + l2.r1.MulByElement(&l2.r1, &p[0].X) + l2.r2.MulByElement(&l2.r2, &p[0].Y) + // ℓ × res + prodLines = fptower.Mul014By014(&l2.r0, &l2.r1, &l2.r2, &result.C0.B0, &result.C0.B1, &result.C1.B1) + result.C0.B0 = prodLines[0] + result.C0.B1 = prodLines[1] + result.C0.B2 = prodLines[2] + result.C1.B1 = prodLines[3] + result.C1.B2 = prodLines[4] + } - // i == len(loopCounter) - 2 - for k := 0; k < n; k++ { - qProj[k].DoubleStep(&l1) - // line eval + // k >= 1 + for k := 1; k < n; k++ { + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] l1.r1.MulByElement(&l1.r1, &p[k].X) l1.r2.MulByElement(&l1.r2, &p[k].Y) - qProj[k].AddMixedStep(&l2, &q[k]) - // line eval + // qProj[k] ← qProj[k]+Q[k] and + // l2 the line ℓ passing qProj[k] and Q[k] + qProj[k].addMixedStep(&l2, &q[k]) + // line evaluation at P[k] l2.r1.MulByElement(&l2.r1, &p[k].X) l2.r2.MulByElement(&l2.r2, &p[k].Y) // ℓ × ℓ - lines.Mul014By014(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) + prodLines = fptower.Mul014By014(&l2.r0, &l2.r1, &l2.r2, &l1.r0, &l1.r1, &l1.r2) // (ℓ × ℓ) × result - result.Mul(&result, &lines) + result.MulBy01245(&prodLines) } - for i := len(loopCounter) - 3; i >= 0; i-- { + // i <= 61 + for i := len(loopCounter) - 3; i >= 1; i-- { + // mutualize the square among n Miller loops // (∏ᵢfᵢ)² result.Square(&result) for k := 0; k < n; k++ { - qProj[k].DoubleStep(&l1) - // line eval + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] l1.r1.MulByElement(&l1.r1, &p[k].X) l1.r2.MulByElement(&l1.r2, &p[k].Y) if loopCounter[i] == 0 { + // ℓ × res result.MulBy014(&l1.r0, &l1.r1, &l1.r2) } else { - qProj[k].AddMixedStep(&l2, &q[k]) - // line eval + // qProj[k] ← qProj[k]+Q[k] and + // l2 the line ℓ passing qProj[k] and Q[k] + qProj[k].addMixedStep(&l2, &q[k]) + // line evaluation at P[k] l2.r1.MulByElement(&l2.r1, &p[k].X) l2.r2.MulByElement(&l2.r2, &p[k].Y) // ℓ × ℓ - lines.Mul014By014(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) + prodLines = fptower.Mul014By014(&l2.r0, &l2.r1, &l2.r2, &l1.r0, &l1.r1, &l1.r2) // (ℓ × ℓ) × result - result.Mul(&result, &lines) + result.MulBy01245(&prodLines) } } } + // i = 0, separately to avoid a point doubling + // loopCounter[0] = 0 + result.Square(&result) + for k := 0; k < n; k++ { + // l1 the tangent ℓ passing 2qProj[k] + qProj[k].tangentLine(&l1) + // line evaluation at P[k] + l1.r1.MulByElement(&l1.r1, &p[k].X) + l1.r2.MulByElement(&l1.r2, &p[k].Y) + // ℓ × result + result.MulBy014(&l1.r0, &l1.r1, &l1.r2) + } + // negative x₀ result.Conjugate(&result) return result, nil } -// DoubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop +// doubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g2Proj) DoubleStep(l *lineEvaluation) { +func (p *g2Proj) doubleStep(l *lineEvaluation) { // get some Element from our pool var t1, A, B, C, D, E, EE, F, G, H, I, J, K fptower.E2 @@ -226,9 +278,9 @@ func (p *g2Proj) DoubleStep(l *lineEvaluation) { } -// AddMixedStep point addition in Mixed Homogenous projective and Affine coordinates +// addMixedStep point addition in Mixed Homogenous projective and Affine coordinates // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g2Proj) AddMixedStep(l *lineEvaluation, a *G2Affine) { +func (p *g2Proj) addMixedStep(l *lineEvaluation, a *G2Affine) { // get some Element from our pool var Y2Z1, X2Z1, O, L, C, D, E, F, G, H, t0, t1, t2, J fptower.E2 @@ -262,3 +314,28 @@ func (p *g2Proj) AddMixedStep(l *lineEvaluation, a *G2Affine) { l.r1.Neg(&O) l.r2.Set(&L) } + +// tangentCompute computes the tangent through [2]p in Homogenous projective coordinates. +// It does not compute the resulting point [2]p. +func (p *g2Proj) tangentLine(l *lineEvaluation) { + + // get some Element from our pool + var t1, B, C, D, E, H, I, J fptower.E2 + B.Square(&p.y) + C.Square(&p.z) + D.Double(&C). + Add(&D, &C) + E.MulBybTwistCurveCoeff(&D) + H.Add(&p.y, &p.z). + Square(&H) + t1.Add(&B, &C) + H.Sub(&H, &t1) + I.Sub(&E, &B) + J.Square(&p.x) + + // Line evaluation + l.r0.Set(&I) + l.r1.Double(&J). + Add(&l.r1, &J) + l.r2.Neg(&H) +} diff --git a/ecc/bls24-315/bls24-315.go b/ecc/bls24-315/bls24-315.go index ade22cdb51..9fc4554649 100644 --- a/ecc/bls24-315/bls24-315.go +++ b/ecc/bls24-315/bls24-315.go @@ -41,7 +41,8 @@ import ( // ID bls315 ID const ID = ecc.BLS24_315 -// bCurveCoeff b coeff of the curve Y²=X³+b +// aCurveCoeff is the a coefficients of the curve Y²=X³+ax+b +var aCurveCoeff fp.Element var bCurveCoeff fp.Element // twist @@ -101,7 +102,7 @@ type E12 = fptower.E12 type E24 = fptower.E24 func init() { - + aCurveCoeff.SetUint64(0) bCurveCoeff.SetUint64(1) // D-twist twist.B1.SetOne() @@ -161,3 +162,8 @@ func Generators() (g1Jac G1Jac, g2Jac G2Jac, g1Aff G1Affine, g2Aff G2Affine) { g2Jac = g2Gen return } + +// CurveCoefficients returns the a, b coefficients of the curve equation. +func CurveCoefficients() (a, b fp.Element) { + return aCurveCoeff, bCurveCoeff +} diff --git a/ecc/bls24-315/ecdsa/ecdsa.go b/ecc/bls24-315/ecdsa/ecdsa.go index e1309b2f36..ce29aaaef2 100644 --- a/ecc/bls24-315/ecdsa/ecdsa.go +++ b/ecc/bls24-315/ecdsa/ecdsa.go @@ -22,7 +22,6 @@ import ( "crypto/rand" "crypto/sha512" "crypto/subtle" - "errors" "hash" "io" "math/big" @@ -33,8 +32,6 @@ import ( "github.com/consensys/gnark-crypto/signature" ) -var errInvalidSig = errors.New("invalid signature") - const ( sizeFr = fr.Bytes sizeFp = fp.Bytes @@ -213,6 +210,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) kInv.ModInverse(k, order) P.X.BigInt(r) + r.Mod(r, order) if r.Sign() != 0 { break diff --git a/ecc/bls24-315/fp/element.go b/ecc/bls24-315/fp/element.go index 520464ac2c..234f87bb42 100644 --- a/ecc/bls24-315/fp/element.go +++ b/ecc/bls24-315/fp/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -765,12 +766,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -780,7 +781,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bls24-315/fr/element.go b/ecc/bls24-315/fr/element.go index feabc5beda..240dc5d080 100644 --- a/ecc/bls24-315/fr/element.go +++ b/ecc/bls24-315/fr/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -692,12 +693,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -707,7 +708,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bls24-315/fr/fft/domain.go b/ecc/bls24-315/fr/fft/domain.go index f4d3e77810..39f447b33c 100644 --- a/ecc/bls24-315/fr/fft/domain.go +++ b/ecc/bls24-315/fr/fft/domain.go @@ -63,30 +63,27 @@ type Domain struct { // NewDomain returns a subgroup with a power of 2 cardinality // cardinality >= m -func NewDomain(m uint64) *Domain { +// shift: when specified, it's the element by which the set of root of unity is shifted. +func NewDomain(m uint64, shift ...fr.Element) *Domain { domain := &Domain{} x := ecc.NextPowerOfTwo(m) domain.Cardinality = uint64(x) // generator of the largest 2-adic subgroup - var rootOfUnity fr.Element - rootOfUnity.SetString("1792993287828780812362846131493071959406149719416102105453370749552622525216") - const maxOrderRoot uint64 = 22 domain.FrMultiplicativeGen.SetUint64(7) + if len(shift) != 0 { + domain.FrMultiplicativeGen.Set(&shift[0]) + } domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen) - // find generator for Z/2^(log(m))Z - logx := uint64(bits.TrailingZeros64(x)) - if logx > maxOrderRoot { - panic(fmt.Sprintf("m (%d) is too big: the required root of unity does not exist", m)) + var err error + domain.Generator, err = Generator(m) + if err != nil { + panic(err) } - - // Generator = FinerGenerator^2 has order x - expo := uint64(1 << (maxOrderRoot - logx)) - domain.Generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x domain.GeneratorInv.Inverse(&domain.Generator) domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv) @@ -99,6 +96,28 @@ func NewDomain(m uint64) *Domain { return domain } +// Generator returns a generator for Z/2^(log(m))Z +// or an error if m is too big (required root of unity doesn't exist) +func Generator(m uint64) (fr.Element, error) { + x := ecc.NextPowerOfTwo(m) + + var rootOfUnity fr.Element + + rootOfUnity.SetString("1792993287828780812362846131493071959406149719416102105453370749552622525216") + const maxOrderRoot uint64 = 22 + + // find generator for Z/2^(log(m))Z + logx := uint64(bits.TrailingZeros64(x)) + if logx > maxOrderRoot { + return fr.Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m) + } + + expo := uint64(1 << (maxOrderRoot - logx)) + var generator fr.Element + generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x + return generator, nil +} + func (d *Domain) reverseCosetTables() { d.CosetTableReversed = make([]fr.Element, d.Cardinality) d.CosetTableInvReversed = make([]fr.Element, d.Cardinality) diff --git a/ecc/bls24-315/fr/fft/fft.go b/ecc/bls24-315/fr/fft/fft.go index 08cb0a9db1..529095fc7d 100644 --- a/ecc/bls24-315/fr/fft/fft.go +++ b/ecc/bls24-315/fr/fft/fft.go @@ -18,7 +18,6 @@ package fft import ( "math/bits" - "runtime" "github.com/consensys/gnark-crypto/ecc" "github.com/consensys/gnark-crypto/internal/parallel" @@ -40,24 +39,18 @@ const butterflyThreshold = 16 // FFT computes (recursively) the discrete Fourier transform of a and stores the result in a // if decimation == DIT (decimation in time), the input must be in bit-reversed order // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order -// if coset if set, the FFT(a) returns the evaluation of a on a coset. -func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) { +func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option) { - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } + opt := options(opts...) // if coset != 0, scale by coset table - if _coset { + if opt.coset { scale := func(cosetTable []fr.Element) { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &cosetTable[i]) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableReversed) @@ -69,16 +62,16 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.Twiddles, 0, maxSplits, nil) + difFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.Twiddles, 0, maxSplits, nil) + ditFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } @@ -89,37 +82,31 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order // coset sets the shift of the fft (0 = no shift, standard fft) // len(a) must be a power of 2, and w must be a len(a)th root of unity in field F. -func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset ...bool) { - - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } +func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...Option) { + opt := options(opts...) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } // scale by CardinalityInv - if !_coset { + if !opt.coset { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) return } @@ -129,7 +116,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. a[i].Mul(&a[i], &cosetTable[i]). Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableInv) @@ -141,7 +128,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. } -func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -159,7 +146,7 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for i := start; i < end; i++ { fr.Butterfly(&a[i], &a[i+m]) @@ -182,17 +169,17 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon nextStage := stage + 1 if stage < maxSplits { chDone := make(chan struct{}, 1) - go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone) - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone, nbTasks) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - difFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + difFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } } -func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -210,12 +197,12 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon if stage < maxSplits { // that's the only time we fire go routines chDone := make(chan struct{}, 1) - go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone) - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone, nbTasks) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } @@ -223,7 +210,7 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for k := start; k < end; k++ { a[k+m].Mul(&a[k+m], &twiddles[stage][k]) diff --git a/ecc/bls24-315/fr/fft/fft_test.go b/ecc/bls24-315/fr/fft/fft_test.go index e855948083..933db53f06 100644 --- a/ecc/bls24-315/fr/fft/fft_test.go +++ b/ecc/bls24-315/fr/fft/fft_test.go @@ -52,7 +52,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIF) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -79,7 +79,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIF, OnCoset()) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -108,7 +108,7 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFT(pol, DIT) sample := domainWithPrecompute.Generator sample.Exp(sample, big.NewInt(int64(ithpower))) @@ -134,8 +134,8 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) - domainWithPrecompute.FFTInverse(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIT) + domainWithPrecompute.FFTInverse(pol, DIF) BitReverse(pol) check := true @@ -163,8 +163,8 @@ func TestFFT(t *testing.T) { for i := 1; i <= nbCosets; i++ { BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, true) - domainWithPrecompute.FFTInverse(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) BitReverse(pol) for i := 0; i < len(pol); i++ { @@ -188,8 +188,8 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, false) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFTInverse(pol, DIF) + domainWithPrecompute.FFT(pol, DIT) check := true for i := 0; i < len(pol); i++ { @@ -211,14 +211,26 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, true) - domainWithPrecompute.FFT(pol, DIT, true) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) - check := true for i := 0; i < len(pol); i++ { - check = check && (pol[i] == backupPol[i]) + if !(pol[i].Equal(&backupPol[i])) { + return false + } } - return check + + // compute with nbTasks == 1 + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset(), WithNbTasks(1)) + domainWithPrecompute.FFT(pol, DIT, OnCoset(), WithNbTasks(1)) + + for i := 0; i < len(pol); i++ { + if !(pol[i].Equal(&backupPol[i])) { + return false + } + } + + return true }, )) @@ -265,14 +277,14 @@ func BenchmarkFFT(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, false) + domain.FFT(pol[:sizeDomain], DIT) } }) b.Run("fft 2**"+strconv.Itoa(i)+"bits (coset)", func(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, true) + domain.FFT(pol[:sizeDomain], DIT, OnCoset()) } }) } @@ -292,7 +304,7 @@ func BenchmarkFFTDITCosetReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIT, true) + domain.FFT(pol, DIT, OnCoset()) } } @@ -309,7 +321,7 @@ func BenchmarkFFTDIFReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIF, false) + domain.FFT(pol, DIF) } } diff --git a/ecc/bls24-315/fr/fft/options.go b/ecc/bls24-315/fr/fft/options.go new file mode 100644 index 0000000000..603b76f299 --- /dev/null +++ b/ecc/bls24-315/fr/fft/options.go @@ -0,0 +1,61 @@ +// Copyright 2020 ConsenSys Software Inc. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +// Code generated by consensys/gnark-crypto DO NOT EDIT + +package fft + +import "runtime" + +// Option defines option for altering the behavior of FFT methods. +// See the descriptions of functions returning instances of this type for +// particular options. +type Option func(*fftConfig) + +type fftConfig struct { + coset bool + nbTasks int +} + +// OnCoset if provided, FFT(a) returns the evaluation of a on a coset. +func OnCoset() Option { + return func(opt *fftConfig) { + opt.coset = true + } +} + +// WithNbTasks sets the max number of task (go routine) to spawn. Must be between 1 and 512. +func WithNbTasks(nbTasks int) Option { + if nbTasks < 1 { + nbTasks = 1 + } else if nbTasks > 512 { + nbTasks = 512 + } + return func(opt *fftConfig) { + opt.nbTasks = nbTasks + } +} + +// default options +func options(opts ...Option) fftConfig { + // apply options + opt := fftConfig{ + coset: false, + nbTasks: runtime.NumCPU(), + } + for _, option := range opts { + option(&opt) + } + return opt +} diff --git a/ecc/bls24-315/fr/iop/polynomial.go b/ecc/bls24-315/fr/iop/polynomial.go index 0828d251e0..ec6fd8d5eb 100644 --- a/ecc/bls24-315/fr/iop/polynomial.go +++ b/ecc/bls24-315/fr/iop/polynomial.go @@ -146,11 +146,13 @@ func (p *Polynomial) Evaluate(x fr.Element) fr.Element { return p.polynomial.evaluate(x) } - // TODO find a way to retrieve the root properly instead of re generating the fft domain - d := fft.NewDomain(uint64(p.size)) var g fr.Element if p.shift <= 5 { - g = smallExp(d.Generator, p.shift) + gen, err := fft.Generator(uint64(p.size)) + if err != nil { + panic(err) + } + g = smallExp(gen, p.shift) x.Mul(&x, &g) return p.polynomial.evaluate(x) } @@ -288,11 +290,11 @@ func (p *Polynomial) ToLagrange(d *fft.Domain) *Polynomial { return p case lagrangeCosetRegular: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIT) case lagrangeCosetBitReverse: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIF) default: panic("unknown ID") @@ -317,10 +319,10 @@ func (p *Polynomial) ToCanonical(d *fft.Domain) *Polynomial { d.FFTInverse((*p.coefficients), fft.DIT) case lagrangeCosetRegular: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetBitReverse: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) default: panic("unknown ID") } @@ -342,18 +344,18 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial { switch id { case canonicalRegular: p.Layout = BitReverse - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case canonicalBitReverse: p.Layout = Regular - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeRegular: p.Layout = Regular d.FFTInverse((*p.coefficients), fft.DIF) - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeBitReverse: p.Layout = BitReverse d.FFTInverse((*p.coefficients), fft.DIT) - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetRegular, lagrangeCosetBitReverse: return p default: diff --git a/ecc/bls24-315/fr/iop/polynomial_test.go b/ecc/bls24-315/fr/iop/polynomial_test.go index fc43b7f9f0..06ab8ed36e 100644 --- a/ecc/bls24-315/fr/iop/polynomial_test.go +++ b/ecc/bls24-315/fr/iop/polynomial_test.go @@ -240,7 +240,7 @@ func fromLagrange4(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = Regular d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) return r } @@ -250,7 +250,7 @@ func fromLagrange5(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = BitReverse d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) fft.BitReverse(r.Coefficients()) return r } @@ -438,7 +438,7 @@ func fromCanonical4(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = Regular - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -448,7 +448,7 @@ func fromCanonical5(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = BitReverse - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -566,7 +566,7 @@ func fromLagrangeCoset0(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -576,7 +576,7 @@ func fromLagrangeCoset1(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -585,7 +585,7 @@ func fromLagrangeCoset2(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) return _p } @@ -595,7 +595,7 @@ func fromLagrangeCoset3(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) fft.BitReverse(_p.Coefficients()) return _p diff --git a/ecc/bls24-315/fr/iop/ratios.go b/ecc/bls24-315/fr/iop/ratios.go index 74af061df0..e4249d012e 100644 --- a/ecc/bls24-315/fr/iop/ratios.go +++ b/ecc/bls24-315/fr/iop/ratios.go @@ -18,7 +18,10 @@ package iop import ( "errors" + "math/big" "math/bits" + "runtime" + "sync" "github.com/consensys/gnark-crypto/internal/parallel" @@ -213,16 +216,38 @@ func BuildRatioCopyConstraint( } }) - for i := 0; i < n-1; i++ { - coeffs[i+1].Mul(&coeffs[i+1], &coeffs[i]) - t[i+1].Mul(&t[i+1], &t[i]) + chCoeffs := make(chan struct{}, 1) + go func() { + for i := 2; i < n; i++ { + // ignoring coeffs[0] + coeffs[i].Mul(&coeffs[i], &coeffs[i-1]) + } + close(chCoeffs) + }() + + for i := 2; i < n; i++ { + // ignoring t[0] + t[i].Mul(&t[i], &t[i-1]) } + <-chCoeffs - t = fr.BatchInvert(t) - for i := 1; i < n; i++ { - coeffs[i].Mul(&coeffs[i], &t[i]) + // rough ratio inverse to mul; see if it makes sense to parallelize the batch inverse. + const ratioInvMul = 1000 / 17 + nbTasks := runtime.NumCPU() + if ratio := n / ratioInvMul; ratio < nbTasks { + nbTasks = ratio } + parallel.Execute(n-1, func(start, end int) { + // ignoring t[0] and coeff[0] + start++ + end++ + tInv := fr.BatchInvert(t[start:end]) + for i := start; i < end; i++ { + coeffs[i].Mul(&coeffs[i], &tInv[i-start]) + } + }, nbTasks) + res := NewPolynomial(&coeffs, expectedForm) // at this stage the result is in Lagrange form, Regular layout putInExpectedFormFromLagrangeRegular(res, domain, expectedForm) @@ -245,7 +270,7 @@ func putInExpectedFormFromLagrangeRegular(p *Polynomial, domain *fft.Domain, exp if expectedForm.Basis == LagrangeCoset { domain.FFTInverse(p.Coefficients(), fft.DIF) - domain.FFT(p.Coefficients(), fft.DIT, true) + domain.FFT(p.Coefficients(), fft.DIT, fft.OnCoset()) if expectedForm.Layout == BitReverse { fft.BitReverse(p.Coefficients()) } @@ -308,16 +333,42 @@ func getSupportIdentityPermutation(nbCopies int, domain *fft.Domain) []fr.Elemen res := make([]fr.Element, uint64(nbCopies)*domain.Cardinality) sizePoly := int(domain.Cardinality) - res[0].SetOne() - for i := 0; i < sizePoly-1; i++ { + // len(domain.Twiddle) == sizePoly / 2 + copy(res, domain.Twiddles[0]) + // remaining ones. + for i := (sizePoly / 2) - 1; i < sizePoly-1; i++ { res[i+1].Mul(&res[i], &domain.Generator) } + if nbCopies <= 1 { + return res + } + var wg sync.WaitGroup + wg.Add(nbCopies - 1) for i := 1; i < nbCopies; i++ { - copy(res[i*sizePoly:], res[(i-1)*sizePoly:i*int(domain.Cardinality)]) - for j := 0; j < sizePoly; j++ { - res[i*sizePoly+j].Mul(&res[i*sizePoly+j], &domain.FrMultiplicativeGen) + i := i + + var coset fr.Element + if i == 1 { + coset = domain.FrMultiplicativeGen + } else { + if len(domain.CosetTable) > i { + coset = domain.CosetTable[i] + } else { + coset.Exp(domain.FrMultiplicativeGen, big.NewInt(int64(i))) + } } + + go func() { + parallel.Execute(sizePoly, func(start, end int) { + for j := start; j < end; j++ { + res[i*sizePoly+j].Mul(&res[j], &coset) + } + }, (runtime.NumCPU()/(nbCopies-1))+1) + wg.Done() + }() } + wg.Wait() + return res } diff --git a/ecc/bls24-315/fr/kzg/kzg.go b/ecc/bls24-315/fr/kzg/kzg.go index 108163d55d..9dfbc64313 100644 --- a/ecc/bls24-315/fr/kzg/kzg.go +++ b/ecc/bls24-315/fr/kzg/kzg.go @@ -26,6 +26,8 @@ import ( "github.com/consensys/gnark-crypto/ecc/bls24-315" "github.com/consensys/gnark-crypto/ecc/bls24-315/fr" "github.com/consensys/gnark-crypto/fiat-shamir" + + "github.com/consensys/gnark-crypto/internal/parallel" ) var ( @@ -275,14 +277,21 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr // gamma n in parallel, before reducing into foldedPolynomials foldedPolynomials := make([]fr.Element, largestPoly) copy(foldedPolynomials, polynomials[0]) - acc := gamma - var pj fr.Element + gammas := make([]fr.Element, len(polynomials)) + gammas[0] = gamma for i := 1; i < len(polynomials); i++ { - for j := 0; j < len(polynomials[i]); j++ { - pj.Mul(&polynomials[i][j], &acc) - foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) - } - acc.Mul(&acc, &gamma) + gammas[i].Mul(&gammas[i-1], &gamma) + } + + for i := 1; i < len(polynomials); i++ { + i := i + parallel.Execute(len(polynomials[i]), func(start, end int) { + var pj fr.Element + for j := start; j < end; j++ { + pj.Mul(&polynomials[i][j], &gammas[i-1]) + foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) + } + }) } // compute H diff --git a/ecc/bls24-315/fr/permutation/permutation.go b/ecc/bls24-315/fr/permutation/permutation.go index 639876678b..e7612e717d 100644 --- a/ecc/bls24-315/fr/permutation/permutation.go +++ b/ecc/bls24-315/fr/permutation/permutation.go @@ -191,15 +191,15 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } lz := make([]fr.Element, s) copy(lz, cz) - d.FFT(lz, fft.DIF, true) + d.FFT(lz, fft.DIF, fft.OnCoset()) // compute the first part of the numerator lt1 := make([]fr.Element, s) lt2 := make([]fr.Element, s) copy(lt1, ct1) copy(lt2, ct2) - d.FFT(lt1, fft.DIF, true) - d.FFT(lt2, fft.DIF, true) + d.FFT(lt1, fft.DIF, fft.OnCoset()) + d.FFT(lt2, fft.DIF, fft.OnCoset()) lsNumFirstPart := evaluateFirstPartNumReverse(lt1, lt2, lz, epsilon) // compute second part of the numerator @@ -222,7 +222,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } // get the quotient and commit it - d.FFTInverse(lsNum, fft.DIT, true) + d.FFTInverse(lsNum, fft.DIT, fft.OnCoset()) proof.q, err = kzg.Commit(lsNum, srs) if err != nil { return proof, err diff --git a/ecc/bls24-315/fr/plookup/vector.go b/ecc/bls24-315/fr/plookup/vector.go index 056138410c..c24632ae02 100644 --- a/ecc/bls24-315/fr/plookup/vector.go +++ b/ecc/bls24-315/fr/plookup/vector.go @@ -340,7 +340,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element Mul(&res[_i], &numLn[i%2]) } - domainBig.FFTInverse(res, fft.DIT, true) + domainBig.FFTInverse(res, fft.DIT, fft.OnCoset()) return res } @@ -476,11 +476,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) copy(_lh2, ch2) copy(_lt, ct) copy(_lf, cf) - domainBig.FFT(_lz, fft.DIF, true) - domainBig.FFT(_lh1, fft.DIF, true) - domainBig.FFT(_lh2, fft.DIF, true) - domainBig.FFT(_lt, fft.DIF, true) - domainBig.FFT(_lf, fft.DIF, true) + domainBig.FFT(_lz, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh1, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh2, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lt, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lf, fft.DIF, fft.OnCoset()) // compute h lh := evaluateNumBitReversed(_lz, _lh1, _lh2, _lt, _lf, beta, gamma, domainBig) diff --git a/ecc/bls24-315/internal/fptower/e24_pairing.go b/ecc/bls24-315/internal/fptower/e24_pairing.go index 9f175ca940..aa4e3b14b9 100644 --- a/ecc/bls24-315/internal/fptower/e24_pairing.go +++ b/ecc/bls24-315/internal/fptower/e24_pairing.go @@ -53,3 +53,53 @@ func (z *E24) MulBy034(c0, c3, c4 *E4) *E24 { return z } + +// Mul034By034 multiplication of sparse element (c0,0,0,c3,c4,0) by sparse element (d0,0,0,d3,d4,0) +func Mul034By034(d0, d3, d4, c0, c3, c4 *E4) [5]E4 { + var z00, tmp, x0, x3, x4, x04, x03, x34 E4 + x0.Mul(c0, d0) + x3.Mul(c3, d3) + x4.Mul(c4, d4) + tmp.Add(c0, c4) + x04.Add(d0, d4). + Mul(&x04, &tmp). + Sub(&x04, &x0). + Sub(&x04, &x4) + tmp.Add(c0, c3) + x03.Add(d0, d3). + Mul(&x03, &tmp). + Sub(&x03, &x0). + Sub(&x03, &x3) + tmp.Add(c3, c4) + x34.Add(d3, d4). + Mul(&x34, &tmp). + Sub(&x34, &x3). + Sub(&x34, &x4) + + z00.MulByNonResidue(&x4). + Add(&z00, &x0) + + return [5]E4{z00, x3, x34, x03, x04} +} + +// MulBy01234 multiplies z by an E12 sparse element of the form (x0, x1, x2, x3, x4, 0) +func (z *E24) MulBy01234(x *[5]E4) *E24 { + var c1, a, b, c, z0, z1 E12 + c0 := &E12{C0: x[0], C1: x[1], C2: x[2]} + c1.C0 = x[3] + c1.C1 = x[4] + a.Add(&z.D0, &z.D1) + b.Add(c0, &c1) + a.Mul(&a, &b) + b.Mul(&z.D0, c0) + c.Set(&z.D1).MulBy01(&x[3], &x[4]) + z1.Sub(&a, &b) + z1.Sub(&z1, &c) + z0.MulByNonResidue(&c) + z0.Add(&z0, &b) + + z.D0 = z0 + z.D1 = z1 + + return z +} diff --git a/ecc/bls24-315/marshal.go b/ecc/bls24-315/marshal.go index 79fbab8103..10e20cefed 100644 --- a/ecc/bls24-315/marshal.go +++ b/ecc/bls24-315/marshal.go @@ -50,6 +50,8 @@ const ( // SizeOfGT represents the size in bytes that a GT element need in binary form const SizeOfGT = fptower.SizeOfGT +var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding") + // Encoder writes bls24-315 object values to an output stream type Encoder struct { w io.Writer @@ -365,6 +367,19 @@ func NoSubgroupChecks() func(*Decoder) { } } +// isZeroed checks that the provided bytes are at 0 +func isZeroed(firstByte byte, buf []byte) bool { + if firstByte != 0 { + return false + } + for _, b := range buf { + if b != 0 { + return false + } + } + return true +} + func (enc *Encoder) encode(v interface{}) (err error) { rv := reflect.ValueOf(v) if v == nil || (rv.Kind() == reflect.Ptr && rv.IsNil()) { @@ -674,13 +689,19 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineUncompressed, nil @@ -796,9 +817,12 @@ func (p *G1Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } @@ -933,13 +957,19 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineUncompressed, nil @@ -1087,9 +1117,12 @@ func (p *G2Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } diff --git a/ecc/bls24-315/pairing.go b/ecc/bls24-315/pairing.go index 5e1bf1fe3c..1ef5569e13 100644 --- a/ecc/bls24-315/pairing.go +++ b/ecc/bls24-315/pairing.go @@ -144,54 +144,126 @@ func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { var result GT result.SetOne() + var l1, l2 lineEvaluation + var prodLines [5]fptower.E4 + + // Compute ∏ᵢ { fᵢ_{x₀,Q}(P) } + if n >= 1 { + // i = 31, separately to avoid an E12 Square + // (Square(res) = 1² = 1) + // loopCounter[31] = 0 + // k = 0, separately to avoid MulBy014 (res × ℓ) + // (assign line to res) + + // qProj[0] ← 2qProj[0] and l1 the tangent ℓ passing 2qProj[0] qProj[0].doubleStep(&l1) + qProj[0].doubleStep(&l1) + // line evaluation at P[0] (assign) + result.D0.C0.MulByElement(&l1.r0, &p[0].Y) + result.D1.C0.MulByElement(&l1.r1, &p[0].X) + result.D1.C1.Set(&l1.r2) + } - var l lineEvaluation + if n >= 2 { + // k = 1, separately to avoid MulBy014 (res × ℓ) + // (res is also a line at this point, so we use Mul014By014 ℓ × ℓ) + + // qProj[1] ← 2qProj[1] and l1 the tangent ℓ passing 2qProj[1] + qProj[1].doubleStep(&l1) + // line evaluation at P[1] + l1.r0.MulByElement(&l1.r0, &p[1].Y) + l1.r1.MulByElement(&l1.r1, &p[1].X) + // ℓ × res + prodLines = fptower.Mul034By034(&l1.r0, &l1.r1, &l1.r2, &result.D0.C0, &result.D1.C0, &result.D1.C1) + result.D0.C0 = prodLines[0] + result.D0.C1 = prodLines[1] + result.D0.C2 = prodLines[2] + result.D1.C0 = prodLines[3] + result.D1.C1 = prodLines[4] + } - // len(loopCounter) - 2 - for k := 0; k < n; k++ { - qProj[k].DoubleStep(&l) - // line evaluation - l.r0.MulByElement(&l.r0, &p[k].Y) - l.r1.MulByElement(&l.r1, &p[k].X) - result.MulBy034(&l.r0, &l.r1, &l.r2) + // k >= 2 + for k := 2; k < n; k++ { + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] + l1.r0.MulByElement(&l1.r0, &p[k].Y) + l1.r1.MulByElement(&l1.r1, &p[k].X) + // ℓ × res + result.MulBy034(&l1.r0, &l1.r1, &l1.r2) } - for i := len(loopCounter) - 3; i >= 0; i-- { + // i <= 30 + for i := len(loopCounter) - 3; i >= 1; i-- { // (∏ᵢfᵢ)² + // mutualize the square among n Miller loops result.Square(&result) for k := 0; k < n; k++ { - qProj[k].DoubleStep(&l) - // line evaluation - l.r0.MulByElement(&l.r0, &p[k].Y) - l.r1.MulByElement(&l.r1, &p[k].X) - result.MulBy034(&l.r0, &l.r1, &l.r2) - - if loopCounter[i] == 1 { - qProj[k].AddMixedStep(&l, &q[k]) - // line evaluation - l.r0.MulByElement(&l.r0, &p[k].Y) - l.r1.MulByElement(&l.r1, &p[k].X) - result.MulBy034(&l.r0, &l.r1, &l.r2) - + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] + l1.r0.MulByElement(&l1.r0, &p[k].Y) + l1.r1.MulByElement(&l1.r1, &p[k].X) + + if loopCounter[i] == 0 { + // ℓ × result + result.MulBy034(&l1.r0, &l1.r1, &l1.r2) + } else if loopCounter[i] == 1 { + // qProj[k] ← qProj[k]+Q[k] and + // l2 the line ℓ passing qProj[k] and Q[k] + qProj[k].addMixedStep(&l2, &q[k]) + // line evaluation at P[k] + l2.r0.MulByElement(&l2.r0, &p[k].Y) + l2.r1.MulByElement(&l2.r1, &p[k].X) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) + // (ℓ × ℓ) × result + result.MulBy01234(&prodLines) } else if loopCounter[i] == -1 { - qProj[k].AddMixedStep(&l, &qNeg[k]) - // line evaluation - l.r0.MulByElement(&l.r0, &p[k].Y) - l.r1.MulByElement(&l.r1, &p[k].X) - result.MulBy034(&l.r0, &l.r1, &l.r2) + // qProj[k] ← qProj[k]-Q[k] and + // l2 the line ℓ passing qProj[k] and -Q[k] + qProj[k].addMixedStep(&l2, &qNeg[k]) + // line evaluation at P[k] + l2.r0.MulByElement(&l2.r0, &p[k].Y) + l2.r1.MulByElement(&l2.r1, &p[k].X) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) + // (ℓ × ℓ) × result + result.MulBy01234(&prodLines) } } } + // i = 0, separately to avoid a point addition + // loopCounter[0] = 1 + result.Square(&result) + for k := 0; k < n; k++ { + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] + l1.r0.MulByElement(&l1.r0, &p[k].Y) + l1.r1.MulByElement(&l1.r1, &p[k].X) + + // l2 the line passing qProj[k] and Q + qProj[k].lineCompute(&l2, &qNeg[k]) + // line evaluation at P[k] + l2.r0.MulByElement(&l2.r0, &p[k].Y) + l2.r1.MulByElement(&l2.r1, &p[k].X) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) + } + + // negative x₀ result.Conjugate(&result) return result, nil } -// DoubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop +// doubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g2Proj) DoubleStep(evaluations *lineEvaluation) { +func (p *g2Proj) doubleStep(evaluations *lineEvaluation) { // get some Element from our pool var t1, A, B, C, D, E, EE, F, G, H, I, J, K fptower.E4 @@ -230,9 +302,9 @@ func (p *g2Proj) DoubleStep(evaluations *lineEvaluation) { evaluations.r2.Set(&I) } -// AddMixedStep point addition in Mixed Homogenous projective and Affine coordinates +// addMixedStep point addition in Mixed Homogenous projective and Affine coordinates // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g2Proj) AddMixedStep(evaluations *lineEvaluation, a *G2Affine) { +func (p *g2Proj) addMixedStep(evaluations *lineEvaluation, a *G2Affine) { // get some Element from our pool var Y2Z1, X2Z1, O, L, C, D, E, F, G, H, t0, t1, t2, J fptower.E4 @@ -266,3 +338,23 @@ func (p *g2Proj) AddMixedStep(evaluations *lineEvaluation, a *G2Affine) { evaluations.r1.Neg(&O) evaluations.r2.Set(&J) } + +// lineCompute computes the line through p in Homogenous projective coordinates +// and a in affine coordinates. It does not compute the resulting point p+a. +func (p *g2Proj) lineCompute(evaluations *lineEvaluation, a *G2Affine) { + + // get some Element from our pool + var Y2Z1, X2Z1, O, L, t2, J fptower.E4 + Y2Z1.Mul(&a.Y, &p.z) + O.Sub(&p.y, &Y2Z1) + X2Z1.Mul(&a.X, &p.z) + L.Sub(&p.x, &X2Z1) + t2.Mul(&L, &a.Y) + J.Mul(&a.X, &O). + Sub(&J, &t2) + + // Line evaluation + evaluations.r0.Set(&L) + evaluations.r1.Neg(&O) + evaluations.r2.Set(&J) +} diff --git a/ecc/bls24-317/bls24-317.go b/ecc/bls24-317/bls24-317.go index 9d2eb9c533..00589b875a 100644 --- a/ecc/bls24-317/bls24-317.go +++ b/ecc/bls24-317/bls24-317.go @@ -41,7 +41,8 @@ import ( // ID bls317 ID const ID = ecc.BLS24_317 -// bCurveCoeff b coeff of the curve Y²=X³+b +// aCurveCoeff is the a coefficients of the curve Y²=X³+ax+b +var aCurveCoeff fp.Element var bCurveCoeff fp.Element // twist @@ -87,7 +88,7 @@ var endo struct { var xGen big.Int func init() { - + aCurveCoeff.SetUint64(0) bCurveCoeff.SetUint64(4) // M-twist twist.B1.SetOne() @@ -149,3 +150,8 @@ func Generators() (g1Jac G1Jac, g2Jac G2Jac, g1Aff G1Affine, g2Aff G2Affine) { g2Jac = g2Gen return } + +// CurveCoefficients returns the a, b coefficients of the curve equation. +func CurveCoefficients() (a, b fp.Element) { + return aCurveCoeff, bCurveCoeff +} diff --git a/ecc/bls24-317/ecdsa/ecdsa.go b/ecc/bls24-317/ecdsa/ecdsa.go index dfcbab66cb..19560eec47 100644 --- a/ecc/bls24-317/ecdsa/ecdsa.go +++ b/ecc/bls24-317/ecdsa/ecdsa.go @@ -22,7 +22,6 @@ import ( "crypto/rand" "crypto/sha512" "crypto/subtle" - "errors" "hash" "io" "math/big" @@ -33,8 +32,6 @@ import ( "github.com/consensys/gnark-crypto/signature" ) -var errInvalidSig = errors.New("invalid signature") - const ( sizeFr = fr.Bytes sizeFp = fp.Bytes @@ -213,6 +210,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) kInv.ModInverse(k, order) P.X.BigInt(r) + r.Mod(r, order) if r.Sign() != 0 { break diff --git a/ecc/bls24-317/fp/element.go b/ecc/bls24-317/fp/element.go index c8a9f46caa..89cafe1a22 100644 --- a/ecc/bls24-317/fp/element.go +++ b/ecc/bls24-317/fp/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -765,12 +766,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -780,7 +781,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bls24-317/fr/element.go b/ecc/bls24-317/fr/element.go index bfa8c1c9ab..7077feff68 100644 --- a/ecc/bls24-317/fr/element.go +++ b/ecc/bls24-317/fr/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -692,12 +693,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -707,7 +708,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bls24-317/fr/fft/domain.go b/ecc/bls24-317/fr/fft/domain.go index 64b3459bf8..11a7bcab9c 100644 --- a/ecc/bls24-317/fr/fft/domain.go +++ b/ecc/bls24-317/fr/fft/domain.go @@ -63,30 +63,27 @@ type Domain struct { // NewDomain returns a subgroup with a power of 2 cardinality // cardinality >= m -func NewDomain(m uint64) *Domain { +// shift: when specified, it's the element by which the set of root of unity is shifted. +func NewDomain(m uint64, shift ...fr.Element) *Domain { domain := &Domain{} x := ecc.NextPowerOfTwo(m) domain.Cardinality = uint64(x) // generator of the largest 2-adic subgroup - var rootOfUnity fr.Element - rootOfUnity.SetString("16532287748948254263922689505213135976137839535221842169193829039521719560631") - const maxOrderRoot uint64 = 60 domain.FrMultiplicativeGen.SetUint64(7) + if len(shift) != 0 { + domain.FrMultiplicativeGen.Set(&shift[0]) + } domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen) - // find generator for Z/2^(log(m))Z - logx := uint64(bits.TrailingZeros64(x)) - if logx > maxOrderRoot { - panic(fmt.Sprintf("m (%d) is too big: the required root of unity does not exist", m)) + var err error + domain.Generator, err = Generator(m) + if err != nil { + panic(err) } - - // Generator = FinerGenerator^2 has order x - expo := uint64(1 << (maxOrderRoot - logx)) - domain.Generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x domain.GeneratorInv.Inverse(&domain.Generator) domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv) @@ -99,6 +96,28 @@ func NewDomain(m uint64) *Domain { return domain } +// Generator returns a generator for Z/2^(log(m))Z +// or an error if m is too big (required root of unity doesn't exist) +func Generator(m uint64) (fr.Element, error) { + x := ecc.NextPowerOfTwo(m) + + var rootOfUnity fr.Element + + rootOfUnity.SetString("16532287748948254263922689505213135976137839535221842169193829039521719560631") + const maxOrderRoot uint64 = 60 + + // find generator for Z/2^(log(m))Z + logx := uint64(bits.TrailingZeros64(x)) + if logx > maxOrderRoot { + return fr.Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m) + } + + expo := uint64(1 << (maxOrderRoot - logx)) + var generator fr.Element + generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x + return generator, nil +} + func (d *Domain) reverseCosetTables() { d.CosetTableReversed = make([]fr.Element, d.Cardinality) d.CosetTableInvReversed = make([]fr.Element, d.Cardinality) diff --git a/ecc/bls24-317/fr/fft/fft.go b/ecc/bls24-317/fr/fft/fft.go index c521aff873..f0dfe7647d 100644 --- a/ecc/bls24-317/fr/fft/fft.go +++ b/ecc/bls24-317/fr/fft/fft.go @@ -18,7 +18,6 @@ package fft import ( "math/bits" - "runtime" "github.com/consensys/gnark-crypto/ecc" "github.com/consensys/gnark-crypto/internal/parallel" @@ -40,24 +39,18 @@ const butterflyThreshold = 16 // FFT computes (recursively) the discrete Fourier transform of a and stores the result in a // if decimation == DIT (decimation in time), the input must be in bit-reversed order // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order -// if coset if set, the FFT(a) returns the evaluation of a on a coset. -func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) { +func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option) { - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } + opt := options(opts...) // if coset != 0, scale by coset table - if _coset { + if opt.coset { scale := func(cosetTable []fr.Element) { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &cosetTable[i]) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableReversed) @@ -69,16 +62,16 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.Twiddles, 0, maxSplits, nil) + difFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.Twiddles, 0, maxSplits, nil) + ditFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } @@ -89,37 +82,31 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order // coset sets the shift of the fft (0 = no shift, standard fft) // len(a) must be a power of 2, and w must be a len(a)th root of unity in field F. -func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset ...bool) { - - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } +func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...Option) { + opt := options(opts...) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } // scale by CardinalityInv - if !_coset { + if !opt.coset { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) return } @@ -129,7 +116,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. a[i].Mul(&a[i], &cosetTable[i]). Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableInv) @@ -141,7 +128,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. } -func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -159,7 +146,7 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for i := start; i < end; i++ { fr.Butterfly(&a[i], &a[i+m]) @@ -182,17 +169,17 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon nextStage := stage + 1 if stage < maxSplits { chDone := make(chan struct{}, 1) - go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone) - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone, nbTasks) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - difFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + difFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } } -func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -210,12 +197,12 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon if stage < maxSplits { // that's the only time we fire go routines chDone := make(chan struct{}, 1) - go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone) - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone, nbTasks) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } @@ -223,7 +210,7 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for k := start; k < end; k++ { a[k+m].Mul(&a[k+m], &twiddles[stage][k]) diff --git a/ecc/bls24-317/fr/fft/fft_test.go b/ecc/bls24-317/fr/fft/fft_test.go index 8e477ba0af..9c98d3e08b 100644 --- a/ecc/bls24-317/fr/fft/fft_test.go +++ b/ecc/bls24-317/fr/fft/fft_test.go @@ -52,7 +52,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIF) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -79,7 +79,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIF, OnCoset()) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -108,7 +108,7 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFT(pol, DIT) sample := domainWithPrecompute.Generator sample.Exp(sample, big.NewInt(int64(ithpower))) @@ -134,8 +134,8 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) - domainWithPrecompute.FFTInverse(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIT) + domainWithPrecompute.FFTInverse(pol, DIF) BitReverse(pol) check := true @@ -163,8 +163,8 @@ func TestFFT(t *testing.T) { for i := 1; i <= nbCosets; i++ { BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, true) - domainWithPrecompute.FFTInverse(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) BitReverse(pol) for i := 0; i < len(pol); i++ { @@ -188,8 +188,8 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, false) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFTInverse(pol, DIF) + domainWithPrecompute.FFT(pol, DIT) check := true for i := 0; i < len(pol); i++ { @@ -211,14 +211,26 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, true) - domainWithPrecompute.FFT(pol, DIT, true) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) - check := true for i := 0; i < len(pol); i++ { - check = check && (pol[i] == backupPol[i]) + if !(pol[i].Equal(&backupPol[i])) { + return false + } } - return check + + // compute with nbTasks == 1 + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset(), WithNbTasks(1)) + domainWithPrecompute.FFT(pol, DIT, OnCoset(), WithNbTasks(1)) + + for i := 0; i < len(pol); i++ { + if !(pol[i].Equal(&backupPol[i])) { + return false + } + } + + return true }, )) @@ -265,14 +277,14 @@ func BenchmarkFFT(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, false) + domain.FFT(pol[:sizeDomain], DIT) } }) b.Run("fft 2**"+strconv.Itoa(i)+"bits (coset)", func(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, true) + domain.FFT(pol[:sizeDomain], DIT, OnCoset()) } }) } @@ -292,7 +304,7 @@ func BenchmarkFFTDITCosetReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIT, true) + domain.FFT(pol, DIT, OnCoset()) } } @@ -309,7 +321,7 @@ func BenchmarkFFTDIFReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIF, false) + domain.FFT(pol, DIF) } } diff --git a/ecc/bls24-317/fr/fft/options.go b/ecc/bls24-317/fr/fft/options.go new file mode 100644 index 0000000000..603b76f299 --- /dev/null +++ b/ecc/bls24-317/fr/fft/options.go @@ -0,0 +1,61 @@ +// Copyright 2020 ConsenSys Software Inc. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +// Code generated by consensys/gnark-crypto DO NOT EDIT + +package fft + +import "runtime" + +// Option defines option for altering the behavior of FFT methods. +// See the descriptions of functions returning instances of this type for +// particular options. +type Option func(*fftConfig) + +type fftConfig struct { + coset bool + nbTasks int +} + +// OnCoset if provided, FFT(a) returns the evaluation of a on a coset. +func OnCoset() Option { + return func(opt *fftConfig) { + opt.coset = true + } +} + +// WithNbTasks sets the max number of task (go routine) to spawn. Must be between 1 and 512. +func WithNbTasks(nbTasks int) Option { + if nbTasks < 1 { + nbTasks = 1 + } else if nbTasks > 512 { + nbTasks = 512 + } + return func(opt *fftConfig) { + opt.nbTasks = nbTasks + } +} + +// default options +func options(opts ...Option) fftConfig { + // apply options + opt := fftConfig{ + coset: false, + nbTasks: runtime.NumCPU(), + } + for _, option := range opts { + option(&opt) + } + return opt +} diff --git a/ecc/bls24-317/fr/iop/polynomial.go b/ecc/bls24-317/fr/iop/polynomial.go index 7f30e369af..43732836db 100644 --- a/ecc/bls24-317/fr/iop/polynomial.go +++ b/ecc/bls24-317/fr/iop/polynomial.go @@ -146,11 +146,13 @@ func (p *Polynomial) Evaluate(x fr.Element) fr.Element { return p.polynomial.evaluate(x) } - // TODO find a way to retrieve the root properly instead of re generating the fft domain - d := fft.NewDomain(uint64(p.size)) var g fr.Element if p.shift <= 5 { - g = smallExp(d.Generator, p.shift) + gen, err := fft.Generator(uint64(p.size)) + if err != nil { + panic(err) + } + g = smallExp(gen, p.shift) x.Mul(&x, &g) return p.polynomial.evaluate(x) } @@ -288,11 +290,11 @@ func (p *Polynomial) ToLagrange(d *fft.Domain) *Polynomial { return p case lagrangeCosetRegular: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIT) case lagrangeCosetBitReverse: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIF) default: panic("unknown ID") @@ -317,10 +319,10 @@ func (p *Polynomial) ToCanonical(d *fft.Domain) *Polynomial { d.FFTInverse((*p.coefficients), fft.DIT) case lagrangeCosetRegular: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetBitReverse: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) default: panic("unknown ID") } @@ -342,18 +344,18 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial { switch id { case canonicalRegular: p.Layout = BitReverse - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case canonicalBitReverse: p.Layout = Regular - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeRegular: p.Layout = Regular d.FFTInverse((*p.coefficients), fft.DIF) - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeBitReverse: p.Layout = BitReverse d.FFTInverse((*p.coefficients), fft.DIT) - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetRegular, lagrangeCosetBitReverse: return p default: diff --git a/ecc/bls24-317/fr/iop/polynomial_test.go b/ecc/bls24-317/fr/iop/polynomial_test.go index 9ae3a4fd2e..dda6d39d80 100644 --- a/ecc/bls24-317/fr/iop/polynomial_test.go +++ b/ecc/bls24-317/fr/iop/polynomial_test.go @@ -240,7 +240,7 @@ func fromLagrange4(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = Regular d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) return r } @@ -250,7 +250,7 @@ func fromLagrange5(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = BitReverse d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) fft.BitReverse(r.Coefficients()) return r } @@ -438,7 +438,7 @@ func fromCanonical4(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = Regular - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -448,7 +448,7 @@ func fromCanonical5(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = BitReverse - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -566,7 +566,7 @@ func fromLagrangeCoset0(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -576,7 +576,7 @@ func fromLagrangeCoset1(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -585,7 +585,7 @@ func fromLagrangeCoset2(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) return _p } @@ -595,7 +595,7 @@ func fromLagrangeCoset3(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) fft.BitReverse(_p.Coefficients()) return _p diff --git a/ecc/bls24-317/fr/iop/ratios.go b/ecc/bls24-317/fr/iop/ratios.go index 28121fbb5c..beb4c94ba6 100644 --- a/ecc/bls24-317/fr/iop/ratios.go +++ b/ecc/bls24-317/fr/iop/ratios.go @@ -18,7 +18,10 @@ package iop import ( "errors" + "math/big" "math/bits" + "runtime" + "sync" "github.com/consensys/gnark-crypto/internal/parallel" @@ -213,16 +216,38 @@ func BuildRatioCopyConstraint( } }) - for i := 0; i < n-1; i++ { - coeffs[i+1].Mul(&coeffs[i+1], &coeffs[i]) - t[i+1].Mul(&t[i+1], &t[i]) + chCoeffs := make(chan struct{}, 1) + go func() { + for i := 2; i < n; i++ { + // ignoring coeffs[0] + coeffs[i].Mul(&coeffs[i], &coeffs[i-1]) + } + close(chCoeffs) + }() + + for i := 2; i < n; i++ { + // ignoring t[0] + t[i].Mul(&t[i], &t[i-1]) } + <-chCoeffs - t = fr.BatchInvert(t) - for i := 1; i < n; i++ { - coeffs[i].Mul(&coeffs[i], &t[i]) + // rough ratio inverse to mul; see if it makes sense to parallelize the batch inverse. + const ratioInvMul = 1000 / 17 + nbTasks := runtime.NumCPU() + if ratio := n / ratioInvMul; ratio < nbTasks { + nbTasks = ratio } + parallel.Execute(n-1, func(start, end int) { + // ignoring t[0] and coeff[0] + start++ + end++ + tInv := fr.BatchInvert(t[start:end]) + for i := start; i < end; i++ { + coeffs[i].Mul(&coeffs[i], &tInv[i-start]) + } + }, nbTasks) + res := NewPolynomial(&coeffs, expectedForm) // at this stage the result is in Lagrange form, Regular layout putInExpectedFormFromLagrangeRegular(res, domain, expectedForm) @@ -245,7 +270,7 @@ func putInExpectedFormFromLagrangeRegular(p *Polynomial, domain *fft.Domain, exp if expectedForm.Basis == LagrangeCoset { domain.FFTInverse(p.Coefficients(), fft.DIF) - domain.FFT(p.Coefficients(), fft.DIT, true) + domain.FFT(p.Coefficients(), fft.DIT, fft.OnCoset()) if expectedForm.Layout == BitReverse { fft.BitReverse(p.Coefficients()) } @@ -308,16 +333,42 @@ func getSupportIdentityPermutation(nbCopies int, domain *fft.Domain) []fr.Elemen res := make([]fr.Element, uint64(nbCopies)*domain.Cardinality) sizePoly := int(domain.Cardinality) - res[0].SetOne() - for i := 0; i < sizePoly-1; i++ { + // len(domain.Twiddle) == sizePoly / 2 + copy(res, domain.Twiddles[0]) + // remaining ones. + for i := (sizePoly / 2) - 1; i < sizePoly-1; i++ { res[i+1].Mul(&res[i], &domain.Generator) } + if nbCopies <= 1 { + return res + } + var wg sync.WaitGroup + wg.Add(nbCopies - 1) for i := 1; i < nbCopies; i++ { - copy(res[i*sizePoly:], res[(i-1)*sizePoly:i*int(domain.Cardinality)]) - for j := 0; j < sizePoly; j++ { - res[i*sizePoly+j].Mul(&res[i*sizePoly+j], &domain.FrMultiplicativeGen) + i := i + + var coset fr.Element + if i == 1 { + coset = domain.FrMultiplicativeGen + } else { + if len(domain.CosetTable) > i { + coset = domain.CosetTable[i] + } else { + coset.Exp(domain.FrMultiplicativeGen, big.NewInt(int64(i))) + } } + + go func() { + parallel.Execute(sizePoly, func(start, end int) { + for j := start; j < end; j++ { + res[i*sizePoly+j].Mul(&res[j], &coset) + } + }, (runtime.NumCPU()/(nbCopies-1))+1) + wg.Done() + }() } + wg.Wait() + return res } diff --git a/ecc/bls24-317/fr/kzg/kzg.go b/ecc/bls24-317/fr/kzg/kzg.go index be8cbadbd7..39d229288a 100644 --- a/ecc/bls24-317/fr/kzg/kzg.go +++ b/ecc/bls24-317/fr/kzg/kzg.go @@ -26,6 +26,8 @@ import ( "github.com/consensys/gnark-crypto/ecc/bls24-317" "github.com/consensys/gnark-crypto/ecc/bls24-317/fr" "github.com/consensys/gnark-crypto/fiat-shamir" + + "github.com/consensys/gnark-crypto/internal/parallel" ) var ( @@ -275,14 +277,21 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr // gamma n in parallel, before reducing into foldedPolynomials foldedPolynomials := make([]fr.Element, largestPoly) copy(foldedPolynomials, polynomials[0]) - acc := gamma - var pj fr.Element + gammas := make([]fr.Element, len(polynomials)) + gammas[0] = gamma for i := 1; i < len(polynomials); i++ { - for j := 0; j < len(polynomials[i]); j++ { - pj.Mul(&polynomials[i][j], &acc) - foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) - } - acc.Mul(&acc, &gamma) + gammas[i].Mul(&gammas[i-1], &gamma) + } + + for i := 1; i < len(polynomials); i++ { + i := i + parallel.Execute(len(polynomials[i]), func(start, end int) { + var pj fr.Element + for j := start; j < end; j++ { + pj.Mul(&polynomials[i][j], &gammas[i-1]) + foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) + } + }) } // compute H diff --git a/ecc/bls24-317/fr/permutation/permutation.go b/ecc/bls24-317/fr/permutation/permutation.go index 50245e48a7..7dab3039f7 100644 --- a/ecc/bls24-317/fr/permutation/permutation.go +++ b/ecc/bls24-317/fr/permutation/permutation.go @@ -191,15 +191,15 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } lz := make([]fr.Element, s) copy(lz, cz) - d.FFT(lz, fft.DIF, true) + d.FFT(lz, fft.DIF, fft.OnCoset()) // compute the first part of the numerator lt1 := make([]fr.Element, s) lt2 := make([]fr.Element, s) copy(lt1, ct1) copy(lt2, ct2) - d.FFT(lt1, fft.DIF, true) - d.FFT(lt2, fft.DIF, true) + d.FFT(lt1, fft.DIF, fft.OnCoset()) + d.FFT(lt2, fft.DIF, fft.OnCoset()) lsNumFirstPart := evaluateFirstPartNumReverse(lt1, lt2, lz, epsilon) // compute second part of the numerator @@ -222,7 +222,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } // get the quotient and commit it - d.FFTInverse(lsNum, fft.DIT, true) + d.FFTInverse(lsNum, fft.DIT, fft.OnCoset()) proof.q, err = kzg.Commit(lsNum, srs) if err != nil { return proof, err diff --git a/ecc/bls24-317/fr/plookup/vector.go b/ecc/bls24-317/fr/plookup/vector.go index 8bbdefb623..38ae005997 100644 --- a/ecc/bls24-317/fr/plookup/vector.go +++ b/ecc/bls24-317/fr/plookup/vector.go @@ -340,7 +340,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element Mul(&res[_i], &numLn[i%2]) } - domainBig.FFTInverse(res, fft.DIT, true) + domainBig.FFTInverse(res, fft.DIT, fft.OnCoset()) return res } @@ -476,11 +476,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) copy(_lh2, ch2) copy(_lt, ct) copy(_lf, cf) - domainBig.FFT(_lz, fft.DIF, true) - domainBig.FFT(_lh1, fft.DIF, true) - domainBig.FFT(_lh2, fft.DIF, true) - domainBig.FFT(_lt, fft.DIF, true) - domainBig.FFT(_lf, fft.DIF, true) + domainBig.FFT(_lz, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh1, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh2, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lt, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lf, fft.DIF, fft.OnCoset()) // compute h lh := evaluateNumBitReversed(_lz, _lh1, _lh2, _lt, _lf, beta, gamma, domainBig) diff --git a/ecc/bls24-317/internal/fptower/e12.go b/ecc/bls24-317/internal/fptower/e12.go index f1f296d741..9f41f03a39 100644 --- a/ecc/bls24-317/internal/fptower/e12.go +++ b/ecc/bls24-317/internal/fptower/e12.go @@ -291,6 +291,34 @@ func (z *E12) Conjugate(x *E12) *E12 { return z } +// MulBy12 multiplication by sparse element (0,b1,b2) +func (x *E12) MulBy12(b1, b2 *E4) *E12 { + var t1, t2, c0, tmp, c1, c2 E4 + t1.Mul(&x.C1, b1) + t2.Mul(&x.C2, b2) + c0.Add(&x.C1, &x.C2) + tmp.Add(b1, b2) + c0.Mul(&c0, &tmp) + c0.Sub(&c0, &t1) + c0.Sub(&c0, &t2) + c0.MulByNonResidue(&c0) + c1.Add(&x.C0, &x.C1) + c1.Mul(&c1, b1) + c1.Sub(&c1, &t1) + tmp.MulByNonResidue(&t2) + c1.Add(&c1, &tmp) + tmp.Add(&x.C0, &x.C2) + c2.Mul(b2, &tmp) + c2.Sub(&c2, &t2) + c2.Add(&c2, &t1) + + x.C0 = c0 + x.C1 = c1 + x.C2 = c2 + + return x +} + // MulBy01 multiplication by sparse element (c0,c1,0) func (z *E12) MulBy01(c0, c1 *E4) *E12 { diff --git a/ecc/bls24-317/internal/fptower/e24_pairing.go b/ecc/bls24-317/internal/fptower/e24_pairing.go index 20a953107e..4fe79d6cfe 100644 --- a/ecc/bls24-317/internal/fptower/e24_pairing.go +++ b/ecc/bls24-317/internal/fptower/e24_pairing.go @@ -12,9 +12,9 @@ func (z *E24) nSquareCompressed(n int) { } } -// Expt set z to x^t in E24 and return z (t is the seed of the curve) -// t = 3640754176 -func (z *E24) Expt(x *E24) *E24 { +// ExptHalf set z to x^(t/2) in E24 and return z (t is the seed of the curve) +// t/2 = 1820377088 +func (z *E24) ExptHalf(x *E24) *E24 { // Expt computation is derived from the addition chain: // // _10 = 2*1 @@ -23,9 +23,9 @@ func (z *E24) Expt(x *E24) *E24 { // _11000000 = _11000 << 3 // _11011000 = _11000 + _11000000 // _11011001 = 1 + _11011000 - // return (_11011001 << 9 + _11) << 15 + // return (_11011001 << 9 + _11) << 14 // - // Operations: 31 squares 4 multiplies + // Operations: 30 squares 4 multiplies // // Generated by github.com/mmcloughlin/addchain v0.4.0. @@ -60,7 +60,7 @@ func (z *E24) Expt(x *E24) *E24 { result.Mul(&result, &t0) // Step 35: result = x^0xd9018000 - result.nSquareCompressed(15) + result.nSquareCompressed(14) result.DecompressKarabina(&result) z.Set(&result) @@ -68,6 +68,14 @@ func (z *E24) Expt(x *E24) *E24 { return z } +// Expt set z to x^t in E24 and return z (t is the seed of the curve) +// t = 3640754176 +func (z *E24) Expt(x *E24) *E24 { + var result E24 + result.ExptHalf(x) + return z.CyclotomicSquare(&result) +} + // MulBy014 multiplication by sparse element (c0, c1, 0, 0, c4, 0) func (z *E24) MulBy014(c0, c1, c4 *E4) *E24 { @@ -90,3 +98,53 @@ func (z *E24) MulBy014(c0, c1, c4 *E4) *E24 { return z } + +// Mul014By014 multiplication of sparse element (c0,c1,0,0,c4,0) by sparse element (d0,d1,0,0,d4,0) +func Mul014By014(d0, d1, d4, c0, c1, c4 *E4) [5]E4 { + var z00, tmp, x0, x1, x4, x04, x01, x14 E4 + x0.Mul(c0, d0) + x1.Mul(c1, d1) + x4.Mul(c4, d4) + tmp.Add(c0, c4) + x04.Add(d0, d4). + Mul(&x04, &tmp). + Sub(&x04, &x0). + Sub(&x04, &x4) + tmp.Add(c0, c1) + x01.Add(d0, d1). + Mul(&x01, &tmp). + Sub(&x01, &x0). + Sub(&x01, &x1) + tmp.Add(c1, c4) + x14.Add(d1, d4). + Mul(&x14, &tmp). + Sub(&x14, &x1). + Sub(&x14, &x4) + + z00.MulByNonResidue(&x4). + Add(&z00, &x0) + + return [5]E4{z00, x01, x1, x04, x14} +} + +// MulBy01245 multiplies z by an E24 sparse element of the form (x0, x1, x2, 0, x4, x5) +func (z *E24) MulBy01245(x *[5]E4) *E24 { + var c1, a, b, c, z0, z1 E12 + c0 := &E12{C0: x[0], C1: x[1], C2: x[2]} + c1.C1 = x[3] + c1.C2 = x[4] + a.Add(&z.D0, &z.D1) + b.Add(c0, &c1) + a.Mul(&a, &b) + b.Mul(&z.D0, c0) + c.Set(&z.D1).MulBy12(&x[3], &x[4]) + z1.Sub(&a, &b) + z1.Sub(&z1, &c) + z0.MulByNonResidue(&c) + z0.Add(&z0, &b) + + z.D0 = z0 + z.D1 = z1 + + return z +} diff --git a/ecc/bls24-317/marshal.go b/ecc/bls24-317/marshal.go index 8f50f8e176..d353ba8e39 100644 --- a/ecc/bls24-317/marshal.go +++ b/ecc/bls24-317/marshal.go @@ -50,6 +50,8 @@ const ( // SizeOfGT represents the size in bytes that a GT element need in binary form const SizeOfGT = fptower.SizeOfGT +var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding") + // Encoder writes bls24-317 object values to an output stream type Encoder struct { w io.Writer @@ -365,6 +367,19 @@ func NoSubgroupChecks() func(*Decoder) { } } +// isZeroed checks that the provided bytes are at 0 +func isZeroed(firstByte byte, buf []byte) bool { + if firstByte != 0 { + return false + } + for _, b := range buf { + if b != 0 { + return false + } + } + return true +} + func (enc *Encoder) encode(v interface{}) (err error) { rv := reflect.ValueOf(v) if v == nil || (rv.Kind() == reflect.Ptr && rv.IsNil()) { @@ -674,13 +689,19 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineUncompressed, nil @@ -796,9 +817,12 @@ func (p *G1Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } @@ -933,13 +957,19 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineUncompressed, nil @@ -1087,9 +1117,12 @@ func (p *G2Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } diff --git a/ecc/bls24-317/pairing.go b/ecc/bls24-317/pairing.go index 1d4cb27300..c82e7e63fc 100644 --- a/ecc/bls24-317/pairing.go +++ b/ecc/bls24-317/pairing.go @@ -84,7 +84,7 @@ func FinalExponentiation(z *GT, _z ...*GT) GT { // https://eprint.iacr.org/2020/875.pdf // 3(p⁸ - p⁴ +1)/r = (x₀-1)² * (x₀+p) * (x₀²+p²) * (x₀⁴+p⁴-1) + 3 t[0].CyclotomicSquare(&result) - t[1].Expt(&result) + t[1].ExptHalf(&t[0]) t[2].InverseUnitary(&result) t[1].Mul(&t[1], &t[2]) t[2].Expt(&t[1]) @@ -98,10 +98,14 @@ func FinalExponentiation(z *GT, _z ...*GT) GT { t[2].Expt(&t[0]) t[0].FrobeniusSquare(&t[1]) t[2].Mul(&t[0], &t[2]) - t[1].Expt(&t[2]) - t[1].Expt(&t[1]) - t[1].Expt(&t[1]) - t[1].Expt(&t[1]) + t[1].ExptHalf(&t[2]) + t[1].ExptHalf(&t[1]) + t[1].ExptHalf(&t[1]) + t[1].ExptHalf(&t[1]) + for s := 0; s < 4; s++ { + t[1].CyclotomicSquareCompressed(&t[1]) + } + t[1].DecompressKarabina(&t[1]) t[0].FrobeniusQuad(&t[2]) t[0].Mul(&t[0], &t[1]) t[2].InverseUnitary(&t[2]) @@ -112,7 +116,7 @@ func FinalExponentiation(z *GT, _z ...*GT) GT { } // MillerLoop computes the multi-Miller loop -// ∏ᵢ MillerLoop(Pᵢ, Qᵢ) +// ∏ᵢ MillerLoop(Pᵢ, Qᵢ) = ∏ᵢ { fᵢ_{x,Qᵢ}(Pᵢ) } func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { // check input size match n := len(P) @@ -144,52 +148,115 @@ func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { var result GT result.SetOne() + var l1, l2 lineEvaluation + var prodLines [5]fptower.E4 + + // Compute ∏ᵢ { fᵢ_{x₀,Q}(P) } + if n >= 1 { + // i = 31, separately to avoid an E12 Square + // (Square(res) = 1² = 1) + // loopCounter[31] = 0 + // k = 0, separately to avoid MulBy014 (res × ℓ) + // (assign line to res) + + // qProj[0] ← 2qProj[0] and l1 the tangent ℓ passing 2qProj[0] + qProj[0].doubleStep(&l1) + // line evaluation at P[0] (assign) + result.D0.C0.Set(&l1.r0) + result.D0.C1.MulByElement(&l1.r1, &p[0].X) + result.D1.C1.MulByElement(&l1.r2, &p[0].Y) + } - var l lineEvaluation + if n >= 2 { + // k = 1, separately to avoid MulBy014 (res × ℓ) + // (res is also a line at this point, so we use Mul014By014 ℓ × ℓ) + + // qProj[1] ← 2qProj[1] and l1 the tangent ℓ passing 2qProj[1] + qProj[1].doubleStep(&l1) + // line evaluation at P[1] + l1.r1.MulByElement(&l1.r1, &p[1].X) + l1.r2.MulByElement(&l1.r2, &p[1].Y) + // ℓ × res + prodLines = fptower.Mul014By014(&l1.r0, &l1.r1, &l1.r2, &result.D0.C0, &result.D0.C1, &result.D1.C1) + result.D0.C0 = prodLines[0] + result.D0.C1 = prodLines[1] + result.D0.C2 = prodLines[2] + result.D1.C1 = prodLines[3] + result.D1.C2 = prodLines[4] + } - // i == len(loopCounter) - 2 - for k := 0; k < n; k++ { - qProj[k].DoubleStep(&l) - // line evaluation - l.r1.MulByElement(&l.r1, &p[k].X) - l.r2.MulByElement(&l.r2, &p[k].Y) - result.MulBy014(&l.r0, &l.r1, &l.r2) + // k >= 2 + for k := 2; k < n; k++ { + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] + l1.r1.MulByElement(&l1.r1, &p[k].X) + l1.r2.MulByElement(&l1.r2, &p[k].Y) + // ℓ × res + result.MulBy014(&l1.r0, &l1.r1, &l1.r2) } - for i := len(loopCounter) - 3; i >= 0; i-- { + // i <= 30 + for i := len(loopCounter) - 3; i >= 1; i-- { + // mutualize the square among n Miller loops // (∏ᵢfᵢ)² result.Square(&result) for k := 0; k < n; k++ { - qProj[k].DoubleStep(&l) - // line evaluation - l.r1.MulByElement(&l.r1, &p[k].X) - l.r2.MulByElement(&l.r2, &p[k].Y) - result.MulBy014(&l.r0, &l.r1, &l.r2) + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] + l1.r1.MulByElement(&l1.r1, &p[k].X) + l1.r2.MulByElement(&l1.r2, &p[k].Y) if loopCounter[i] == 1 { - qProj[k].AddMixedStep(&l, &q[k]) - // line evaluation - l.r1.MulByElement(&l.r1, &p[k].X) - l.r2.MulByElement(&l.r2, &p[k].Y) - result.MulBy014(&l.r0, &l.r1, &l.r2) - + // qProj[k] ← qProj[k]+Q[k] and + // l2 the line ℓ passing qProj[k] and Q[k] + qProj[k].addMixedStep(&l2, &q[k]) + // line evaluation at P[k] + l2.r1.MulByElement(&l2.r1, &p[k].X) + l2.r2.MulByElement(&l2.r2, &p[k].Y) + // ℓ × ℓ + prodLines = fptower.Mul014By014(&l2.r0, &l2.r1, &l2.r2, &l1.r0, &l1.r1, &l1.r2) + // (ℓ × ℓ) × result + result.MulBy01245(&prodLines) } else if loopCounter[i] == -1 { - qProj[k].AddMixedStep(&l, &qNeg[k]) - // line evaluation - l.r1.MulByElement(&l.r1, &p[k].X) - l.r2.MulByElement(&l.r2, &p[k].Y) - result.MulBy014(&l.r0, &l.r1, &l.r2) + // qProj[k] ← qProj[k]-Q[k] and + // l2 the line ℓ passing qProj[k] and -Q[k] + qProj[k].addMixedStep(&l2, &qNeg[k]) + // line evaluation at P[k] + l2.r1.MulByElement(&l2.r1, &p[k].X) + l2.r2.MulByElement(&l2.r2, &p[k].Y) + // ℓ × ℓ + prodLines = fptower.Mul014By014(&l2.r0, &l2.r1, &l2.r2, &l1.r0, &l1.r1, &l1.r2) + // (ℓ × ℓ) × result + result.MulBy01245(&prodLines) + } else { + // ℓ × result + result.MulBy014(&l1.r0, &l1.r1, &l1.r2) } } } + // i = 0, separately to avoid a point doubling + // loopCounter[0] = 0 + result.Square(&result) + for k := 0; k < n; k++ { + // l1 the tangent ℓ passing 2qProj[k] + qProj[k].tangentLine(&l1) + // line evaluation at P[k] + l1.r1.MulByElement(&l1.r1, &p[k].X) + l1.r2.MulByElement(&l1.r2, &p[k].Y) + // ℓ × result + result.MulBy014(&l1.r0, &l1.r1, &l1.r2) + } + return result, nil } -// DoubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop +// doubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g2Proj) DoubleStep(evaluations *lineEvaluation) { +func (p *g2Proj) doubleStep(evaluations *lineEvaluation) { // get some Element from our pool var t1, A, B, C, D, E, EE, F, G, H, I, J, K fptower.E4 @@ -228,9 +295,9 @@ func (p *g2Proj) DoubleStep(evaluations *lineEvaluation) { evaluations.r2.Neg(&H) } -// AddMixedStep point addition in Mixed Homogenous projective and Affine coordinates +// addMixedStep point addition in Mixed Homogenous projective and Affine coordinates // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g2Proj) AddMixedStep(evaluations *lineEvaluation, a *G2Affine) { +func (p *g2Proj) addMixedStep(evaluations *lineEvaluation, a *G2Affine) { // get some Element from our pool var Y2Z1, X2Z1, O, L, C, D, E, F, G, H, t0, t1, t2, J fptower.E4 @@ -264,3 +331,28 @@ func (p *g2Proj) AddMixedStep(evaluations *lineEvaluation, a *G2Affine) { evaluations.r1.Neg(&O) evaluations.r2.Set(&L) } + +// tangentCompute computes the tangent through [2]p in Homogenous projective coordinates. +// It does not compute the resulting point [2]p. +func (p *g2Proj) tangentLine(l *lineEvaluation) { + + // get some Element from our pool + var t1, B, C, D, E, H, I, J fptower.E4 + B.Square(&p.y) + C.Square(&p.z) + D.Double(&C). + Add(&D, &C) + E.MulBybTwistCurveCoeff(&D) + H.Add(&p.y, &p.z). + Square(&H) + t1.Add(&B, &C) + H.Sub(&H, &t1) + I.Sub(&E, &B) + J.Square(&p.x) + + // Line evaluation + l.r0.Set(&I) + l.r1.Double(&J). + Add(&l.r1, &J) + l.r2.Neg(&H) +} diff --git a/ecc/bn254/bn254.go b/ecc/bn254/bn254.go index 9763843179..f6f2990ca3 100644 --- a/ecc/bn254/bn254.go +++ b/ecc/bn254/bn254.go @@ -54,7 +54,8 @@ import ( // ID bn254 ID const ID = ecc.BN254 -// bCurveCoeff b coeff of the curve Y²=X³+b +// aCurveCoeff is the a coefficients of the curve Y²=X³+ax+b +var aCurveCoeff fp.Element var bCurveCoeff fp.Element // twist @@ -99,8 +100,19 @@ var endo struct { // seed x₀ of the curve var xGen big.Int -func init() { +// expose the tower -- github.com/consensys/gnark uses it in a gnark circuit + +// 𝔽p² +type E2 = fptower.E2 + +// 𝔽p⁶ +type E6 = fptower.E6 + +// 𝔽p¹² +type E12 = fptower.E12 +func init() { + aCurveCoeff.SetUint64(0) bCurveCoeff.SetUint64(3) // D-twist twist.A0.SetUint64(9) @@ -154,3 +166,8 @@ func Generators() (g1Jac G1Jac, g2Jac G2Jac, g1Aff G1Affine, g2Aff G2Affine) { g2Jac = g2Gen return } + +// CurveCoefficients returns the a, b coefficients of the curve equation. +func CurveCoefficients() (a, b fp.Element) { + return aCurveCoeff, bCurveCoeff +} diff --git a/ecc/bn254/ecdsa/ecdsa.go b/ecc/bn254/ecdsa/ecdsa.go index 8593d6a721..9bd86a8470 100644 --- a/ecc/bn254/ecdsa/ecdsa.go +++ b/ecc/bn254/ecdsa/ecdsa.go @@ -33,8 +33,6 @@ import ( "github.com/consensys/gnark-crypto/signature" ) -var errInvalidSig = errors.New("invalid signature") - const ( sizeFr = fr.Bytes sizeFp = fp.Bytes @@ -110,6 +108,54 @@ func HashToInt(hash []byte) *big.Int { return ret } +// RecoverP recovers the value P (prover commitment) when creating a signature. +// It uses the recovery information v and part of the decomposed signature r. It +// is used internally for recovering the public key. +func RecoverP(v uint, r *big.Int) (*bn254.G1Affine, error) { + if r.Cmp(fr.Modulus()) >= 0 { + return nil, errors.New("r is larger than modulus") + } + if r.Cmp(big.NewInt(0)) <= 0 { + return nil, errors.New("r is negative") + } + x := new(big.Int).Set(r) + // if x is r or r+N + xChoice := (v & 2) >> 1 + // if y is y or -y + yChoice := v & 1 + // decompose limbs into big.Int value + // conditional +n based on xChoice + kn := big.NewInt(int64(xChoice)) + kn.Mul(kn, fr.Modulus()) + x.Add(x, kn) + // y^2 = x^3+ax+b + a, b := bn254.CurveCoefficients() + y := new(big.Int).Exp(x, big.NewInt(3), fp.Modulus()) + if !a.IsZero() { + y.Add(y, new(big.Int).Mul(a.BigInt(new(big.Int)), x)) + } + y.Add(y, b.BigInt(new(big.Int))) + y.Mod(y, fp.Modulus()) + // y = sqrt(y^2) + if y.ModSqrt(y, fp.Modulus()) == nil { + return nil, errors.New("no square root") + } + // y2 is -y + y2 := new(big.Int).Sub(fp.Modulus(), y) + // if yChoice == 0, return min(y, y2), else max(y, y2) + if (y.Cmp(y2) < 0) == (yChoice == 0) { + return &bn254.G1Affine{ + X: *new(fp.Element).SetBigInt(x), + Y: *new(fp.Element).SetBigInt(y), + }, nil + } else { + return &bn254.G1Affine{ + X: *new(fp.Element).SetBigInt(x), + Y: *new(fp.Element).SetBigInt(y2), + }, nil + } +} + type zr struct{} // Read replaces the contents of dst with zeros. It is safe for concurrent use. @@ -185,27 +231,31 @@ func (privKey *PrivateKey) Public() signature.PublicKey { return &pub } -// Sign performs the ECDSA signature +// SignForRecover performs the ECDSA signature and returns public key recovery information // // k ← 𝔽r (random) // P = k ⋅ g1Gen // r = x_P (mod order) // s = k⁻¹ . (m + sk ⋅ r) -// signature = {r, s} +// v = (div(x_P, order)<<1) || y_P[-1] // // SEC 1, Version 2.0, Section 4.1.3 -func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) { - scalar, r, s, kInv := new(big.Int), new(big.Int), new(big.Int), new(big.Int) +func (privKey *PrivateKey) SignForRecover(message []byte, hFunc hash.Hash) (v uint, r, s *big.Int, err error) { + halfp := new(big.Int).Sub(fp.Modulus(), big.NewInt(1)) + halfp.Div(halfp, big.NewInt(2)) + r, s = new(big.Int), new(big.Int) + + scalar, kInv := new(big.Int), new(big.Int) scalar.SetBytes(privKey.scalar[:sizeFr]) for { for { csprng, err := nonce(privKey, message) if err != nil { - return nil, err + return 0, nil, nil, err } k, err := randFieldElement(csprng) if err != nil { - return nil, err + return 0, nil, nil, err } var P bn254.G1Affine @@ -213,6 +263,13 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) kInv.ModInverse(k, order) P.X.BigInt(r) + // set how many times we overflow the scalar field + v |= (uint(new(big.Int).Div(r, order).Uint64())) << 1 + // set if y is small or big + if P.Y.BigInt(new(big.Int)).Cmp(halfp) >= 0 { + v |= 1 + } + r.Mod(r, order) if r.Sign() != 0 { break @@ -228,7 +285,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) hFunc.Reset() _, err := hFunc.Write(dataToHash[:]) if err != nil { - return nil, err + return 0, nil, nil, err } hramBin := hFunc.Sum(nil) m = HashToInt(hramBin) @@ -244,6 +301,23 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) } } + return v, r, s, nil +} + +// Sign performs the ECDSA signature +// +// k ← 𝔽r (random) +// P = k ⋅ g1Gen +// r = x_P (mod order) +// s = k⁻¹ . (m + sk ⋅ r) +// signature = {r, s} +// +// SEC 1, Version 2.0, Section 4.1.3 +func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) { + _, r, s, err := privKey.SignForRecover(message, hFunc) + if err != nil { + return nil, err + } var sig Signature r.FillBytes(sig.R[:sizeFr]) s.FillBytes(sig.S[:sizeFr]) diff --git a/ecc/bn254/ecdsa/ecdsa_test.go b/ecc/bn254/ecdsa/ecdsa_test.go index 5c6fa1f567..53a5d9d760 100644 --- a/ecc/bn254/ecdsa/ecdsa_test.go +++ b/ecc/bn254/ecdsa/ecdsa_test.go @@ -62,6 +62,31 @@ func TestECDSA(t *testing.T) { properties.TestingRun(t, gopter.ConsoleReporter(false)) } +func TestRecoverPublicKey(t *testing.T) { + t.Parallel() + parameters := gopter.DefaultTestParameters() + properties := gopter.NewProperties(parameters) + properties.Property("[BN254] test public key recover", prop.ForAll( + func() bool { + sk, err := GenerateKey(rand.Reader) + if err != nil { + return false + } + pk := sk.PublicKey + msg := []byte("test") + v, r, s, err := sk.SignForRecover(msg, nil) + if err != nil { + return false + } + var recovered PublicKey + if err = recovered.RecoverFrom(msg, v, r, s); err != nil { + return false + } + return pk.Equal(&recovered) + }, + )) + properties.TestingRun(t, gopter.ConsoleReporter(false)) +} // ------------------------------------------------------------ // benches @@ -88,3 +113,20 @@ func BenchmarkVerifyECDSA(b *testing.B) { privKey.PublicKey.Verify(sig, msg, nil) } } +func BenchmarkRecoverPublicKey(b *testing.B) { + sk, err := GenerateKey(rand.Reader) + if err != nil { + b.Fatal(err) + } + msg := []byte("bench") + v, r, s, err := sk.SignForRecover(msg, sha256.New()) + if err != nil { + b.Fatal(err) + } + for i := 0; i < b.N; i++ { + var recovered PublicKey + if err = recovered.RecoverFrom(msg, v, r, s); err != nil { + b.Fatal(err) + } + } +} diff --git a/ecc/bn254/ecdsa/marshal.go b/ecc/bn254/ecdsa/marshal.go index 72d74c5cb1..5561e6e0b1 100644 --- a/ecc/bn254/ecdsa/marshal.go +++ b/ecc/bn254/ecdsa/marshal.go @@ -19,6 +19,10 @@ package ecdsa import ( "crypto/subtle" "io" + "math/big" + + "github.com/consensys/gnark-crypto/ecc/bn254" + "github.com/consensys/gnark-crypto/ecc/bn254/fr" ) // Bytes returns the binary representation of the public key @@ -52,6 +56,28 @@ func (pk *PublicKey) SetBytes(buf []byte) (int, error) { return n, nil } +// RecoverFrom recovers the public key from the message msg, recovery +// information v and decompose signature {r,s}. If recovery succeeded, the +// methods sets the current public key to the recovered value. Otherwise returns +// error and leaves current public key unchanged. +func (pk *PublicKey) RecoverFrom(msg []byte, v uint, r, s *big.Int) error { + P, err := RecoverP(v, r) + if err != nil { + return err + } + z := HashToInt(msg) + rinv := new(big.Int).ModInverse(r, fr.Modulus()) + u1 := new(big.Int).Mul(z, rinv) + u1.Neg(u1) + u1.Mod(u1, fr.Modulus()) + u2 := new(big.Int).Mul(s, rinv) + u2.Mod(u2, fr.Modulus()) + var Q bn254.G1Jac + Q.JointScalarMultiplicationBase(P, u1, u2) + pk.A.FromJacobian(&Q) + return nil +} + // Bytes returns the binary representation of pk, // as byte array publicKey||scalar // where publicKey is as publicKey.Bytes(), and diff --git a/ecc/bn254/fp/element.go b/ecc/bn254/fp/element.go index 52fb5e8952..5671c99003 100644 --- a/ecc/bn254/fp/element.go +++ b/ecc/bn254/fp/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -692,12 +693,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -707,7 +708,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bn254/fr/element.go b/ecc/bn254/fr/element.go index fe3090935d..2f7e7bf1b9 100644 --- a/ecc/bn254/fr/element.go +++ b/ecc/bn254/fr/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -692,12 +693,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -707,7 +708,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bn254/fr/fft/domain.go b/ecc/bn254/fr/fft/domain.go index 3a94fcfacc..c9d0a63dd9 100644 --- a/ecc/bn254/fr/fft/domain.go +++ b/ecc/bn254/fr/fft/domain.go @@ -63,30 +63,27 @@ type Domain struct { // NewDomain returns a subgroup with a power of 2 cardinality // cardinality >= m -func NewDomain(m uint64) *Domain { +// shift: when specified, it's the element by which the set of root of unity is shifted. +func NewDomain(m uint64, shift ...fr.Element) *Domain { domain := &Domain{} x := ecc.NextPowerOfTwo(m) domain.Cardinality = uint64(x) // generator of the largest 2-adic subgroup - var rootOfUnity fr.Element - rootOfUnity.SetString("19103219067921713944291392827692070036145651957329286315305642004821462161904") - const maxOrderRoot uint64 = 28 domain.FrMultiplicativeGen.SetUint64(5) + if len(shift) != 0 { + domain.FrMultiplicativeGen.Set(&shift[0]) + } domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen) - // find generator for Z/2^(log(m))Z - logx := uint64(bits.TrailingZeros64(x)) - if logx > maxOrderRoot { - panic(fmt.Sprintf("m (%d) is too big: the required root of unity does not exist", m)) + var err error + domain.Generator, err = Generator(m) + if err != nil { + panic(err) } - - // Generator = FinerGenerator^2 has order x - expo := uint64(1 << (maxOrderRoot - logx)) - domain.Generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x domain.GeneratorInv.Inverse(&domain.Generator) domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv) @@ -99,6 +96,28 @@ func NewDomain(m uint64) *Domain { return domain } +// Generator returns a generator for Z/2^(log(m))Z +// or an error if m is too big (required root of unity doesn't exist) +func Generator(m uint64) (fr.Element, error) { + x := ecc.NextPowerOfTwo(m) + + var rootOfUnity fr.Element + + rootOfUnity.SetString("19103219067921713944291392827692070036145651957329286315305642004821462161904") + const maxOrderRoot uint64 = 28 + + // find generator for Z/2^(log(m))Z + logx := uint64(bits.TrailingZeros64(x)) + if logx > maxOrderRoot { + return fr.Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m) + } + + expo := uint64(1 << (maxOrderRoot - logx)) + var generator fr.Element + generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x + return generator, nil +} + func (d *Domain) reverseCosetTables() { d.CosetTableReversed = make([]fr.Element, d.Cardinality) d.CosetTableInvReversed = make([]fr.Element, d.Cardinality) diff --git a/ecc/bn254/fr/fft/fft.go b/ecc/bn254/fr/fft/fft.go index 4d4557dcb5..0c87fe37e1 100644 --- a/ecc/bn254/fr/fft/fft.go +++ b/ecc/bn254/fr/fft/fft.go @@ -18,7 +18,6 @@ package fft import ( "math/bits" - "runtime" "github.com/consensys/gnark-crypto/ecc" "github.com/consensys/gnark-crypto/internal/parallel" @@ -40,24 +39,18 @@ const butterflyThreshold = 16 // FFT computes (recursively) the discrete Fourier transform of a and stores the result in a // if decimation == DIT (decimation in time), the input must be in bit-reversed order // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order -// if coset if set, the FFT(a) returns the evaluation of a on a coset. -func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) { +func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option) { - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } + opt := options(opts...) // if coset != 0, scale by coset table - if _coset { + if opt.coset { scale := func(cosetTable []fr.Element) { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &cosetTable[i]) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableReversed) @@ -69,16 +62,16 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.Twiddles, 0, maxSplits, nil) + difFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.Twiddles, 0, maxSplits, nil) + ditFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } @@ -89,37 +82,31 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order // coset sets the shift of the fft (0 = no shift, standard fft) // len(a) must be a power of 2, and w must be a len(a)th root of unity in field F. -func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset ...bool) { - - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } +func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...Option) { + opt := options(opts...) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } // scale by CardinalityInv - if !_coset { + if !opt.coset { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) return } @@ -129,7 +116,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. a[i].Mul(&a[i], &cosetTable[i]). Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableInv) @@ -141,7 +128,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. } -func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -159,7 +146,7 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for i := start; i < end; i++ { fr.Butterfly(&a[i], &a[i+m]) @@ -182,17 +169,17 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon nextStage := stage + 1 if stage < maxSplits { chDone := make(chan struct{}, 1) - go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone) - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone, nbTasks) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - difFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + difFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } } -func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -210,12 +197,12 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon if stage < maxSplits { // that's the only time we fire go routines chDone := make(chan struct{}, 1) - go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone) - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone, nbTasks) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } @@ -223,7 +210,7 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for k := start; k < end; k++ { a[k+m].Mul(&a[k+m], &twiddles[stage][k]) diff --git a/ecc/bn254/fr/fft/fft_test.go b/ecc/bn254/fr/fft/fft_test.go index 59e3db45b9..668f361f6b 100644 --- a/ecc/bn254/fr/fft/fft_test.go +++ b/ecc/bn254/fr/fft/fft_test.go @@ -52,7 +52,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIF) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -79,7 +79,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIF, OnCoset()) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -108,7 +108,7 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFT(pol, DIT) sample := domainWithPrecompute.Generator sample.Exp(sample, big.NewInt(int64(ithpower))) @@ -134,8 +134,8 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) - domainWithPrecompute.FFTInverse(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIT) + domainWithPrecompute.FFTInverse(pol, DIF) BitReverse(pol) check := true @@ -163,8 +163,8 @@ func TestFFT(t *testing.T) { for i := 1; i <= nbCosets; i++ { BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, true) - domainWithPrecompute.FFTInverse(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) BitReverse(pol) for i := 0; i < len(pol); i++ { @@ -188,8 +188,8 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, false) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFTInverse(pol, DIF) + domainWithPrecompute.FFT(pol, DIT) check := true for i := 0; i < len(pol); i++ { @@ -211,14 +211,26 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, true) - domainWithPrecompute.FFT(pol, DIT, true) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) - check := true for i := 0; i < len(pol); i++ { - check = check && (pol[i] == backupPol[i]) + if !(pol[i].Equal(&backupPol[i])) { + return false + } } - return check + + // compute with nbTasks == 1 + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset(), WithNbTasks(1)) + domainWithPrecompute.FFT(pol, DIT, OnCoset(), WithNbTasks(1)) + + for i := 0; i < len(pol); i++ { + if !(pol[i].Equal(&backupPol[i])) { + return false + } + } + + return true }, )) @@ -265,14 +277,14 @@ func BenchmarkFFT(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, false) + domain.FFT(pol[:sizeDomain], DIT) } }) b.Run("fft 2**"+strconv.Itoa(i)+"bits (coset)", func(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, true) + domain.FFT(pol[:sizeDomain], DIT, OnCoset()) } }) } @@ -292,7 +304,7 @@ func BenchmarkFFTDITCosetReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIT, true) + domain.FFT(pol, DIT, OnCoset()) } } @@ -309,7 +321,7 @@ func BenchmarkFFTDIFReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIF, false) + domain.FFT(pol, DIF) } } diff --git a/ecc/bn254/fr/fft/options.go b/ecc/bn254/fr/fft/options.go new file mode 100644 index 0000000000..603b76f299 --- /dev/null +++ b/ecc/bn254/fr/fft/options.go @@ -0,0 +1,61 @@ +// Copyright 2020 ConsenSys Software Inc. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +// Code generated by consensys/gnark-crypto DO NOT EDIT + +package fft + +import "runtime" + +// Option defines option for altering the behavior of FFT methods. +// See the descriptions of functions returning instances of this type for +// particular options. +type Option func(*fftConfig) + +type fftConfig struct { + coset bool + nbTasks int +} + +// OnCoset if provided, FFT(a) returns the evaluation of a on a coset. +func OnCoset() Option { + return func(opt *fftConfig) { + opt.coset = true + } +} + +// WithNbTasks sets the max number of task (go routine) to spawn. Must be between 1 and 512. +func WithNbTasks(nbTasks int) Option { + if nbTasks < 1 { + nbTasks = 1 + } else if nbTasks > 512 { + nbTasks = 512 + } + return func(opt *fftConfig) { + opt.nbTasks = nbTasks + } +} + +// default options +func options(opts ...Option) fftConfig { + // apply options + opt := fftConfig{ + coset: false, + nbTasks: runtime.NumCPU(), + } + for _, option := range opts { + option(&opt) + } + return opt +} diff --git a/ecc/bn254/fr/iop/polynomial.go b/ecc/bn254/fr/iop/polynomial.go index 0fe473f184..e00471a49d 100644 --- a/ecc/bn254/fr/iop/polynomial.go +++ b/ecc/bn254/fr/iop/polynomial.go @@ -146,11 +146,13 @@ func (p *Polynomial) Evaluate(x fr.Element) fr.Element { return p.polynomial.evaluate(x) } - // TODO find a way to retrieve the root properly instead of re generating the fft domain - d := fft.NewDomain(uint64(p.size)) var g fr.Element if p.shift <= 5 { - g = smallExp(d.Generator, p.shift) + gen, err := fft.Generator(uint64(p.size)) + if err != nil { + panic(err) + } + g = smallExp(gen, p.shift) x.Mul(&x, &g) return p.polynomial.evaluate(x) } @@ -288,11 +290,11 @@ func (p *Polynomial) ToLagrange(d *fft.Domain) *Polynomial { return p case lagrangeCosetRegular: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIT) case lagrangeCosetBitReverse: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIF) default: panic("unknown ID") @@ -317,10 +319,10 @@ func (p *Polynomial) ToCanonical(d *fft.Domain) *Polynomial { d.FFTInverse((*p.coefficients), fft.DIT) case lagrangeCosetRegular: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetBitReverse: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) default: panic("unknown ID") } @@ -342,18 +344,18 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial { switch id { case canonicalRegular: p.Layout = BitReverse - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case canonicalBitReverse: p.Layout = Regular - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeRegular: p.Layout = Regular d.FFTInverse((*p.coefficients), fft.DIF) - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeBitReverse: p.Layout = BitReverse d.FFTInverse((*p.coefficients), fft.DIT) - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetRegular, lagrangeCosetBitReverse: return p default: diff --git a/ecc/bn254/fr/iop/polynomial_test.go b/ecc/bn254/fr/iop/polynomial_test.go index 6ba60bf1a9..afc59102ed 100644 --- a/ecc/bn254/fr/iop/polynomial_test.go +++ b/ecc/bn254/fr/iop/polynomial_test.go @@ -240,7 +240,7 @@ func fromLagrange4(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = Regular d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) return r } @@ -250,7 +250,7 @@ func fromLagrange5(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = BitReverse d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) fft.BitReverse(r.Coefficients()) return r } @@ -438,7 +438,7 @@ func fromCanonical4(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = Regular - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -448,7 +448,7 @@ func fromCanonical5(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = BitReverse - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -566,7 +566,7 @@ func fromLagrangeCoset0(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -576,7 +576,7 @@ func fromLagrangeCoset1(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -585,7 +585,7 @@ func fromLagrangeCoset2(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) return _p } @@ -595,7 +595,7 @@ func fromLagrangeCoset3(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) fft.BitReverse(_p.Coefficients()) return _p diff --git a/ecc/bn254/fr/iop/ratios.go b/ecc/bn254/fr/iop/ratios.go index e22fd0706d..e2be872fba 100644 --- a/ecc/bn254/fr/iop/ratios.go +++ b/ecc/bn254/fr/iop/ratios.go @@ -18,7 +18,10 @@ package iop import ( "errors" + "math/big" "math/bits" + "runtime" + "sync" "github.com/consensys/gnark-crypto/internal/parallel" @@ -213,16 +216,38 @@ func BuildRatioCopyConstraint( } }) - for i := 0; i < n-1; i++ { - coeffs[i+1].Mul(&coeffs[i+1], &coeffs[i]) - t[i+1].Mul(&t[i+1], &t[i]) + chCoeffs := make(chan struct{}, 1) + go func() { + for i := 2; i < n; i++ { + // ignoring coeffs[0] + coeffs[i].Mul(&coeffs[i], &coeffs[i-1]) + } + close(chCoeffs) + }() + + for i := 2; i < n; i++ { + // ignoring t[0] + t[i].Mul(&t[i], &t[i-1]) } + <-chCoeffs - t = fr.BatchInvert(t) - for i := 1; i < n; i++ { - coeffs[i].Mul(&coeffs[i], &t[i]) + // rough ratio inverse to mul; see if it makes sense to parallelize the batch inverse. + const ratioInvMul = 1000 / 17 + nbTasks := runtime.NumCPU() + if ratio := n / ratioInvMul; ratio < nbTasks { + nbTasks = ratio } + parallel.Execute(n-1, func(start, end int) { + // ignoring t[0] and coeff[0] + start++ + end++ + tInv := fr.BatchInvert(t[start:end]) + for i := start; i < end; i++ { + coeffs[i].Mul(&coeffs[i], &tInv[i-start]) + } + }, nbTasks) + res := NewPolynomial(&coeffs, expectedForm) // at this stage the result is in Lagrange form, Regular layout putInExpectedFormFromLagrangeRegular(res, domain, expectedForm) @@ -245,7 +270,7 @@ func putInExpectedFormFromLagrangeRegular(p *Polynomial, domain *fft.Domain, exp if expectedForm.Basis == LagrangeCoset { domain.FFTInverse(p.Coefficients(), fft.DIF) - domain.FFT(p.Coefficients(), fft.DIT, true) + domain.FFT(p.Coefficients(), fft.DIT, fft.OnCoset()) if expectedForm.Layout == BitReverse { fft.BitReverse(p.Coefficients()) } @@ -308,16 +333,42 @@ func getSupportIdentityPermutation(nbCopies int, domain *fft.Domain) []fr.Elemen res := make([]fr.Element, uint64(nbCopies)*domain.Cardinality) sizePoly := int(domain.Cardinality) - res[0].SetOne() - for i := 0; i < sizePoly-1; i++ { + // len(domain.Twiddle) == sizePoly / 2 + copy(res, domain.Twiddles[0]) + // remaining ones. + for i := (sizePoly / 2) - 1; i < sizePoly-1; i++ { res[i+1].Mul(&res[i], &domain.Generator) } + if nbCopies <= 1 { + return res + } + var wg sync.WaitGroup + wg.Add(nbCopies - 1) for i := 1; i < nbCopies; i++ { - copy(res[i*sizePoly:], res[(i-1)*sizePoly:i*int(domain.Cardinality)]) - for j := 0; j < sizePoly; j++ { - res[i*sizePoly+j].Mul(&res[i*sizePoly+j], &domain.FrMultiplicativeGen) + i := i + + var coset fr.Element + if i == 1 { + coset = domain.FrMultiplicativeGen + } else { + if len(domain.CosetTable) > i { + coset = domain.CosetTable[i] + } else { + coset.Exp(domain.FrMultiplicativeGen, big.NewInt(int64(i))) + } } + + go func() { + parallel.Execute(sizePoly, func(start, end int) { + for j := start; j < end; j++ { + res[i*sizePoly+j].Mul(&res[j], &coset) + } + }, (runtime.NumCPU()/(nbCopies-1))+1) + wg.Done() + }() } + wg.Wait() + return res } diff --git a/ecc/bn254/fr/kzg/kzg.go b/ecc/bn254/fr/kzg/kzg.go index c0d1d26381..3a90e10fd4 100644 --- a/ecc/bn254/fr/kzg/kzg.go +++ b/ecc/bn254/fr/kzg/kzg.go @@ -26,6 +26,8 @@ import ( "github.com/consensys/gnark-crypto/ecc/bn254" "github.com/consensys/gnark-crypto/ecc/bn254/fr" "github.com/consensys/gnark-crypto/fiat-shamir" + + "github.com/consensys/gnark-crypto/internal/parallel" ) var ( @@ -275,14 +277,21 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr // gamma n in parallel, before reducing into foldedPolynomials foldedPolynomials := make([]fr.Element, largestPoly) copy(foldedPolynomials, polynomials[0]) - acc := gamma - var pj fr.Element + gammas := make([]fr.Element, len(polynomials)) + gammas[0] = gamma for i := 1; i < len(polynomials); i++ { - for j := 0; j < len(polynomials[i]); j++ { - pj.Mul(&polynomials[i][j], &acc) - foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) - } - acc.Mul(&acc, &gamma) + gammas[i].Mul(&gammas[i-1], &gamma) + } + + for i := 1; i < len(polynomials); i++ { + i := i + parallel.Execute(len(polynomials[i]), func(start, end int) { + var pj fr.Element + for j := start; j < end; j++ { + pj.Mul(&polynomials[i][j], &gammas[i-1]) + foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) + } + }) } // compute H diff --git a/ecc/bn254/fr/permutation/permutation.go b/ecc/bn254/fr/permutation/permutation.go index 0777420c56..c5f96ea8e5 100644 --- a/ecc/bn254/fr/permutation/permutation.go +++ b/ecc/bn254/fr/permutation/permutation.go @@ -191,15 +191,15 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } lz := make([]fr.Element, s) copy(lz, cz) - d.FFT(lz, fft.DIF, true) + d.FFT(lz, fft.DIF, fft.OnCoset()) // compute the first part of the numerator lt1 := make([]fr.Element, s) lt2 := make([]fr.Element, s) copy(lt1, ct1) copy(lt2, ct2) - d.FFT(lt1, fft.DIF, true) - d.FFT(lt2, fft.DIF, true) + d.FFT(lt1, fft.DIF, fft.OnCoset()) + d.FFT(lt2, fft.DIF, fft.OnCoset()) lsNumFirstPart := evaluateFirstPartNumReverse(lt1, lt2, lz, epsilon) // compute second part of the numerator @@ -222,7 +222,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } // get the quotient and commit it - d.FFTInverse(lsNum, fft.DIT, true) + d.FFTInverse(lsNum, fft.DIT, fft.OnCoset()) proof.q, err = kzg.Commit(lsNum, srs) if err != nil { return proof, err diff --git a/ecc/bn254/fr/plookup/vector.go b/ecc/bn254/fr/plookup/vector.go index bd9f7634f4..0971c04707 100644 --- a/ecc/bn254/fr/plookup/vector.go +++ b/ecc/bn254/fr/plookup/vector.go @@ -340,7 +340,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element Mul(&res[_i], &numLn[i%2]) } - domainBig.FFTInverse(res, fft.DIT, true) + domainBig.FFTInverse(res, fft.DIT, fft.OnCoset()) return res } @@ -476,11 +476,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) copy(_lh2, ch2) copy(_lt, ct) copy(_lf, cf) - domainBig.FFT(_lz, fft.DIF, true) - domainBig.FFT(_lh1, fft.DIF, true) - domainBig.FFT(_lh2, fft.DIF, true) - domainBig.FFT(_lt, fft.DIF, true) - domainBig.FFT(_lf, fft.DIF, true) + domainBig.FFT(_lz, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh1, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh2, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lt, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lf, fft.DIF, fft.OnCoset()) // compute h lh := evaluateNumBitReversed(_lz, _lh1, _lh2, _lt, _lf, beta, gamma, domainBig) diff --git a/ecc/bn254/fr/sis/sis.go b/ecc/bn254/fr/sis/sis.go new file mode 100644 index 0000000000..79114f23c5 --- /dev/null +++ b/ecc/bn254/fr/sis/sis.go @@ -0,0 +1,314 @@ +// Copyright 2023 ConsenSys Software Inc. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +package sis + +import ( + "bytes" + "encoding/binary" + "errors" + "hash" + "math/big" + "math/bits" + + "github.com/bits-and-blooms/bitset" + "github.com/consensys/gnark-crypto/ecc/bn254/fr" + "github.com/consensys/gnark-crypto/ecc/bn254/fr/fft" + "github.com/consensys/gnark-crypto/internal/parallel" + "golang.org/x/crypto/blake2b" +) + +var ( + ErrNotAPowerOfTwo = errors.New("d must be a power of 2") +) + +// Ring-SIS instance +type RSis struct { + + // buffer storing the data to hash + buffer bytes.Buffer + + // Vectors in ℤ_{p}/Xⁿ+1 + // A[i] is the i-th polynomial. + // Ag the evaluation form of the polynomials in A on the coset √(g) * + A [][]fr.Element + Ag [][]fr.Element + + // LogTwoBound (Inifinty norm) of the vector to hash. It means that each component in m + // is < 2^B, where m is the vector to hash (the hash being A*m). + // cf https://hackmd.io/7OODKWQZRRW9RxM5BaXtIw , B >= 3. + LogTwoBound int + + // domain for the polynomial multiplication + Domain *fft.Domain + + // d, the degree of X^{d}+1 + Degree int + + // in bytes, represents the maximum number of bytes the .Write(...) will handle; + // ( maximum number of bytes to sum ) + capacity int + maxNbElementsToHash int + + // allocate memory once per instance (used in Sum()) + bufM, bufRes fr.Vector + bufMValues *bitset.BitSet +} + +// NewRSis creates an instance of RSis. +// seed: seed for the randomness for generating A. +// logTwoDegree: if d := logTwoDegree, the ring will be ℤ_{p}[X]/Xᵈ-1, where X^{2ᵈ} is the 2ᵈ⁺¹-th cyclotomic polynomial +// logTwoBound: the bound of the vector to hash (using the infinity norm). +// maxNbElementsToHash: maximum number of field elements the instance handles +// used to derived n, the number of polynomials in A, and max size of instance's internal buffer. +func NewRSis(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (*RSis, error) { + + if logTwoBound > 64 { + return nil, errors.New("logTwoBound too large") + } + if bits.UintSize == 32 { + return nil, errors.New("unsupported architecture; need 64bit target") + } + + degree := 1 << logTwoDegree + capacity := maxNbElementsToHash * fr.Bytes + + // n: number of polynomials in A + // len(m) == degree * n + // with each element in m being logTwoBounds bits from the instance buffer. + // that is, to fill m, we need [degree * n * logTwoBound] bits of data + // capacity == [degree * n * logTwoBound] / 8 + // n == (capacity*8)/(degree*logTwoBound) + + n := capacity * 8 / logTwoBound // number of coefficients + if n%degree == 0 { + n /= degree + } else { + n /= degree // number of polynomials + n++ + } + + // domains (shift is √{gen} ) + var shift fr.Element + shift.SetString("19103219067921713944291392827692070036145651957329286315305642004821462161904") // -> 2²⁸-th root of unity of bn254 + e := int64(1 << (28 - (logTwoDegree + 1))) + shift.Exp(shift, big.NewInt(e)) + + r := &RSis{ + LogTwoBound: logTwoBound, + capacity: capacity, + Degree: degree, + Domain: fft.NewDomain(uint64(degree), shift), + A: make([][]fr.Element, n), + Ag: make([][]fr.Element, n), + bufM: make(fr.Vector, degree*n), + bufRes: make(fr.Vector, degree), + bufMValues: bitset.New(uint(n)), + maxNbElementsToHash: maxNbElementsToHash, + } + + // filling A + a := make([]fr.Element, n*r.Degree) + ag := make([]fr.Element, n*r.Degree) + + parallel.Execute(n, func(start, end int) { + var buf bytes.Buffer + for i := start; i < end; i++ { + rstart, rend := i*r.Degree, (i+1)*r.Degree + r.A[i] = a[rstart:rend:rend] + r.Ag[i] = ag[rstart:rend:rend] + for j := 0; j < r.Degree; j++ { + r.A[i][j] = genRandom(seed, int64(i), int64(j), &buf) + } + + // fill Ag the evaluation form of the polynomials in A on the coset √(g) * + copy(r.Ag[i], r.A[i]) + r.Domain.FFT(r.Ag[i], fft.DIF, fft.OnCoset()) + } + }) + // TODO @gbotrel add nbtasks here; whiile in tests it's more convenient to paralellize + // in tensor-commitment we may not want to do that. + + return r, nil +} + +func (r *RSis) Write(p []byte) (n int, err error) { + r.buffer.Write(p) + return len(p), nil +} + +// Sum appends the current hash to b and returns the resulting slice. +// It does not change the underlying hash state. +// The instance buffer is interpreted as a sequence of coefficients of size r.Bound bits long. +// The function returns the hash of the polynomial as a a sequence []fr.Elements, interpreted as []bytes, +// corresponding to sum_i A[i]*m Mod X^{d}+1 +func (r *RSis) Sum(b []byte) []byte { + buf := r.buffer.Bytes() + if len(buf) > r.capacity { + panic("buffer too large") + } + + // clear the buffers of the instance. + defer func() { + r.bufMValues.ClearAll() + for i := 0; i < len(r.bufM); i++ { + r.bufM[i].SetZero() + } + for i := 0; i < len(r.bufRes); i++ { + r.bufRes[i].SetZero() + } + }() + + // bitwise decomposition of the buffer, in order to build m (the vector to hash) + // as a list of polynomials, whose coefficients are less than r.B bits long. + // Say buf=[0xbe,0x0f]. As a stream of bits it is interpreted like this: + // 10111110 00001111. BitAt(0)=1 (=leftmost bit), bitAt(1)=0 (=second leftmost bit), etc. + nbBits := len(buf) * 8 + bitAt := func(i int) uint8 { + k := i / 8 + if k >= len(buf) { + return 0 + } + b := buf[k] + j := i % 8 + return b >> (7 - j) & 1 + } + + // now we can construct m. The input to hash consists of the polynomials + // m[k*r.Degree:(k+1)*r.Degree] + m := r.bufM + + // mark blocks m[i*r.Degree : (i+1)*r.Degree] != [0...0] + mValues := r.bufMValues + + // we process the input buffer by blocks of r.LogTwoBound bits + // each of these block (<< 64bits) are interpreted as a coefficient + mPos := 0 + for i := 0; i < nbBits; mPos++ { + for j := 0; j < r.LogTwoBound; j++ { + // r.LogTwoBound < 64; we just use the first word of our element here, + // and set the bits from LSB to MSB. + m[mPos][0] |= uint64(bitAt(i) << j) + i++ + } + if m[mPos][0] == 0 { + continue + } + mValues.Set(uint(mPos / r.Degree)) + } + + // we can hash now. + res := r.bufRes + + // method 1: fft + for i := 0; i < len(r.Ag); i++ { + if !mValues.Test(uint(i)) { + // means m[i*r.Degree : (i+1)*r.Degree] == [0...0] + // we can skip this, FFT(0) = 0 + continue + } + k := m[i*r.Degree : (i+1)*r.Degree] + r.Domain.FFT(k, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1)) + mulModAcc(res, r.Ag[i], k) + } + r.Domain.FFTInverse(res, fft.DIT, fft.OnCoset(), fft.WithNbTasks(1)) // -> reduces mod Xᵈ+1 + + resBytes, err := res.MarshalBinary() + if err != nil { + panic(err) + } + + return append(b, resBytes[4:]...) // first 4 bytes are uint32(len(res)) +} + +// Reset resets the Hash to its initial state. +func (r *RSis) Reset() { + r.buffer.Reset() +} + +// Size returns the number of bytes Sum will return. +func (r *RSis) Size() int { + + // The size in bits is the size in bits of a polynomial in A. + degree := len(r.A[0]) + totalSize := degree * fr.Modulus().BitLen() / 8 + + return totalSize +} + +// BlockSize returns the hash's underlying block size. +// The Write method must be able to accept any amount +// of data, but it may operate more efficiently if all writes +// are a multiple of the block size. +func (r *RSis) BlockSize() int { + return 0 +} + +// Construct a hasher generator. It takes as input the same parameters +// as `NewRingSIS` and outputs a function which returns fresh hasher +// everytime it is called +func NewRingSISMaker(seed int64, logTwoDegree, logTwoBound, maxNbElementsToHash int) (func() hash.Hash, error) { + return func() hash.Hash { + h, err := NewRSis(seed, logTwoDegree, logTwoBound, maxNbElementsToHash) + if err != nil { + panic(err) + } + return h + }, nil + +} + +func genRandom(seed, i, j int64, buf *bytes.Buffer) fr.Element { + + buf.Reset() + buf.WriteString("SIS") + binary.Write(buf, binary.BigEndian, seed) + binary.Write(buf, binary.BigEndian, i) + binary.Write(buf, binary.BigEndian, j) + + digest := blake2b.Sum256(buf.Bytes()) + + var res fr.Element + res.SetBytes(digest[:]) + + return res +} + +// mulMod computes p * q in ℤ_{p}[X]/Xᵈ+1. +// Is assumed that pLagrangeShifted and qLagrangeShifted are of the corret sizes +// and that they are in evaluation form on √(g) * +// The result is not FFTinversed. The fft inverse is done once every +// multiplications are done. +func mulMod(pLagrangeCosetBitReversed, qLagrangeCosetBitReversed []fr.Element) []fr.Element { + + res := make([]fr.Element, len(pLagrangeCosetBitReversed)) + for i := 0; i < len(pLagrangeCosetBitReversed); i++ { + res[i].Mul(&pLagrangeCosetBitReversed[i], &qLagrangeCosetBitReversed[i]) + } + + // NOT fft inv for now, wait until every part of the keys have been multiplied + // r.Domain.FFTInverse(res, fft.DIT, true) + + return res + +} + +// mulMod + accumulate in res. +func mulModAcc(res []fr.Element, pLagrangeCosetBitReversed, qLagrangeCosetBitReversed []fr.Element) { + var t fr.Element + for i := 0; i < len(pLagrangeCosetBitReversed); i++ { + t.Mul(&pLagrangeCosetBitReversed[i], &qLagrangeCosetBitReversed[i]) + res[i].Add(&res[i], &t) + } +} diff --git a/ecc/bn254/fr/sis/sis.sage b/ecc/bn254/fr/sis/sis.sage new file mode 100644 index 0000000000..48e438ba48 --- /dev/null +++ b/ecc/bn254/fr/sis/sis.sage @@ -0,0 +1,249 @@ +## "sage sis.sage" will generate test_cases.json +## tested with a fresh sage install on macOS (Feb 2023) + +import json + +# BN254 Fr +r = 21888242871839275222246405745257275088548364400416034343698204186575808495617 +frByteSize = 32 +gfr = GF(r) +Fr = GF(r) +Fr. = Fr[] +rz = IntegerRing() + +# Montgomery constant +rr = Fr(2**256) + +# utils + + +def buildPoly(a): + """ Builds a poly from the array a + + Args: + a an array + + Returns: + a[0]+a[1]*X + .. + a[n]*X**n + """ + + res = Fr(0) + for i, v in enumerate(a): + res += Fr(v)*x**i + return res + + +def bitAt(i, b): + """ + Args: + i: index of the bit to retrieve + b: array of bytes + + Returns: + the i-th bit of b, when it is written b[0] || b[1] || ... + """ + k = i//8 + if k >= len(b): + return 0 + j = i % 8 + return (b[k] >> (7-j)) & 1 + + +def toBytes(m, s): + """ + + Args: + m: a bit int + s: the expected number of bytes of the result. If s is bigger than the + number of bytes in m, the remaining bytes are set to zero. + + Returns: + the byte representation of m as a byte array, as + in gnark-crypto. + """ + _m = rz(m) + res = s*[0] + mask = 255 + for i in range(s): + res[s-1-i] = _m & 255 + _m = _m >> 8 + return res + + +def splitCoeffs(b, logTwoBound): + """ + Args: + b: an array of bytes + logTwoBound: number of bits of the bound + + Returns: + an array of coeffs, each coeff being the i-th chunk of logTwoBounds bits of b. + """ + nbBits = len(b)*8 + res = [] + i = 0 + while i < nbBits: + e = 0 + for j in range(logTwoBound): + e += bitAt(i, b) << j + i += 1 + res.append(e) + # careful Montgomery constant... + return [Fr(e)*rr**-1 for e in res] + + +def polyRand(seed, n): + """ Generates a pseudo random polynomial of size n from seed. + + Args: + seed: seed for the pseudo random gen + n: degree of the polynomial + """ + seed = gfr(seed) + a = n*[0] + for i in range(n): + a[i] = seed**2 + seed = a[i] + return buildPoly(a) + + +# SIS +class SIS: + def __init__(self, seed, logTwoDegree, logTwoBound, maxNbElementsToHash): + """ + Args: + seed + logTwoDegree: + logTwoBound: bound of SIS + maxNbElementsToHash + """ + capacity = maxNbElementsToHash * frByteSize + degree = 1 << logTwoDegree + + n = capacity * 8 / logTwoBound # number of coefficients + if n % degree == 0: # check how sage / python rounds the int div. + n = n / degree + else: + n = n / degree + n = n + 1 + + n = int(n) + + self.logTwoBound = logTwoBound + self.degree = degree + self.size = n + self.key = n * [0] + for i in range(n): + self.key[i] = polyRand(seed, self.degree) + seed += 1 + + def hash(self, inputs): + """ + Args: + inputs is a vector of Fr elements + + Returns: + the sis hash of m. + """ + b = [] + for i in inputs: + b.extend(toBytes(i, 32)) + + return self.hash_bytes(b) + + def hash_bytes(self, b): + """ + Args: + b is a list of bytes to hash + + Returns: + the sis hash of m. + """ + # step 1: build the polynomials from m + c = splitCoeffs(b, self.logTwoBound) + mp = [buildPoly(c[self.degree*i:self.degree*(i+1)]) + for i in range(self.size)] + + # step 2: compute sum_i mp[i]*key[i] mod X^n+1 + modulo = x**self.degree+1 + res = 0 + for i in range(self.size): + res += self.key[i]*mp[i] + res = res % modulo + return res + + +def vectorToString(v): + # v is a vector of field elements + # we return a list of strings in base10 + r = [] + for e in v: + r.append("0x"+rz(e).hex()) + return r + + +def SISParams(seed, logTwoDegree, logTwoBound, maxNbElementsToHash): + p = {} + p['seed'] = int(seed) + p['logTwoDegree'] = int(logTwoDegree) + p['logTwoBound'] = int(logTwoBound) + p['maxNbElementsToHash'] = int(maxNbElementsToHash) + return p + +params = [ + SISParams(5, 2, 3, 10), + SISParams(5, 4, 3, 10), + SISParams(5, 4, 4, 10), + SISParams(5, 5, 4, 10), + SISParams(5, 6, 5, 10), + SISParams(5, 10, 6, 10), + SISParams(5, 11, 7, 10), + SISParams(5, 12, 7, 10), +] + +inputs = [ + [Fr(21888242871839275222246405745257275088548364400416034343698204186575808495614)], + [Fr(1)], + [Fr(42),Fr(8000)], + [Fr(1),Fr(2), Fr(0),Fr(21888242871839275222246405745257275088548364400416034343698204186575808495616)], + [Fr(1), Fr(0)], + [Fr(0), Fr(1)], + [Fr(0)], + [Fr(0),Fr(0),Fr(0),Fr(0)], + [Fr(0),Fr(0),Fr(8000),Fr(0)], +] + +# sprinkle some random elements +for i in range(10): + line = [] + for j in range(i): + line.append(gfr.random_element()) + inputs.append(line) + +testCases = {} +testCases['inputs'] = [] +testCases['entries'] = [] + + +for i, v in enumerate(inputs): + testCases['inputs'].append(vectorToString(v)) + + +for p in params: + entry = {} + entry['params'] = p + entry['expected'] = [] + + print("generating test cases with SIS params " + json.dumps(p)) + instance = SIS(p['seed'], p['logTwoDegree'], p['logTwoBound'], p['maxNbElementsToHash']) + for i, v in enumerate(inputs): + # hash the vector + hResult = instance.hash(v) + entry['expected'].append(vectorToString(hResult)) + + testCases['entries'].append(entry) + + +testCases_json = json.dumps(testCases, indent=4) +with open("test_cases.json", "w") as outfile: + outfile.write(testCases_json) diff --git a/ecc/bn254/fr/sis/sis_test.go b/ecc/bn254/fr/sis/sis_test.go new file mode 100644 index 0000000000..ed08ad407b --- /dev/null +++ b/ecc/bn254/fr/sis/sis_test.go @@ -0,0 +1,387 @@ +// Copyright 2023 ConsenSys Software Inc. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +package sis + +import ( + "bytes" + "encoding/binary" + "encoding/json" + "fmt" + "io" + "io/ioutil" + "math/bits" + "testing" + "time" + + "github.com/consensys/gnark-crypto/ecc/bn254/fr" + "github.com/consensys/gnark-crypto/ecc/bn254/fr/fft" + "github.com/stretchr/testify/require" +) + +type sisParams struct { + logTwoBound, logTwoDegree int +} + +var params128Bits []sisParams = []sisParams{ + {logTwoBound: 2, logTwoDegree: 3}, + {logTwoBound: 4, logTwoDegree: 4}, + {logTwoBound: 6, logTwoDegree: 5}, + {logTwoBound: 10, logTwoDegree: 6}, + {logTwoBound: 16, logTwoDegree: 7}, + {logTwoBound: 32, logTwoDegree: 8}, +} + +type TestCases struct { + Inputs [][]fr.Element `json:"inputs"` + Entries []struct { + Params struct { + Seed int64 `json:"seed"` + LogTwoDegree int `json:"logTwoDegree"` + LogTwoBound int `json:"logTwoBound"` + MaxNbElementsToHash int `json:"maxNbElementsToHash"` + } `json:"params"` + Expected [][]fr.Element `json:"expected"` + } `json:"entries"` +} + +func TestReference(t *testing.T) { + if bits.UintSize == 32 { + t.Skip("skipping this test in 32bit.") + } + assert := require.New(t) + + // read the test case file + var testCases TestCases + data, err := ioutil.ReadFile("test_cases.json") + assert.NoError(err, "reading test cases failed") + err = json.Unmarshal(data, &testCases) + assert.NoError(err, "reading test cases failed") + + for _, testCase := range testCases.Entries { + // create the SIS instance + sis, err := NewRSis(testCase.Params.Seed, testCase.Params.LogTwoDegree, testCase.Params.LogTwoBound, testCase.Params.MaxNbElementsToHash) + assert.NoError(err) + + // key generation same than in sage + makeKeyDeterminitic(t, sis, testCase.Params.Seed) + + for i, in := range testCases.Inputs { + sis.Reset() + + // hash test case entry input and compare with expected (computed by sage) + got, err := sis.Hash(in) + assert.NoError(err) + if len(testCase.Expected[i]) == 0 { + for _, e := range got { + assert.True(e.IsZero(), "mismatch between reference test and computed value") + } + } else { + assert.EqualValues(testCase.Expected[i], got, "mismatch between reference test and computed value") + } + + // ensure max nb elements to hash has no incidence on result. + if len(in) < testCase.Params.MaxNbElementsToHash { + sis2, err := NewRSis(testCase.Params.Seed, testCase.Params.LogTwoDegree, testCase.Params.LogTwoBound, len(in)) + assert.NoError(err) + makeKeyDeterminitic(t, sis2, testCase.Params.Seed) + + got2, err := sis2.Hash(in) + assert.NoError(err) + if len(testCase.Expected[i]) == 0 { + for _, e := range got2 { + assert.True(e.IsZero(), "mismatch between reference test and computed value") + } + } else { + assert.EqualValues(got, got2, "max nb elements to hash change SIS result") + } + } + + } + } + +} + +func TestMulMod(t *testing.T) { + + size := 4 + + p := make([]fr.Element, size) + p[0].SetString("2389") + p[1].SetString("987192") + p[2].SetString("623") + p[3].SetString("91") + + q := make([]fr.Element, size) + q[0].SetString("76755") + q[1].SetString("232893720") + q[2].SetString("989273") + q[3].SetString("675273") + + // creation of the domain + var shift fr.Element + shift.SetString("19540430494807482326159819597004422086093766032135589407132600596362845576832") + domain := fft.NewDomain(uint64(size), shift) + + // mul mod + domain.FFT(p, fft.DIF, fft.OnCoset()) + domain.FFT(q, fft.DIF, fft.OnCoset()) + r := mulMod(p, q) + domain.FFTInverse(r, fft.DIT, fft.OnCoset()) + + // expected result + expectedr := make([]fr.Element, 4) + expectedr[0].SetString("21888242871839275222246405745257275088548364400416034343698204185887558114297") + expectedr[1].SetString("631644300118") + expectedr[2].SetString("229913166975959") + expectedr[3].SetString("1123315390878") + + for i := 0; i < 4; i++ { + if !expectedr[i].Equal(&r[i]) { + t.Fatal("product failed") + } + } + +} + +func makeKeyDeterminitic(t *testing.T, sis *RSis, _seed int64) { + t.Helper() + // generate the key deterministically, the same way + // we do in sage to generate the test vectors. + + polyRand := func(seed fr.Element, deg int) []fr.Element { + res := make([]fr.Element, deg) + for i := 0; i < deg; i++ { + res[i].Square(&seed) + seed.Set(&res[i]) + } + return res + } + + var seed, one fr.Element + one.SetOne() + seed.SetInt64(_seed) + for i := 0; i < len(sis.A); i++ { + sis.A[i] = polyRand(seed, sis.Degree) + copy(sis.Ag[i], sis.A[i]) + sis.Domain.FFT(sis.Ag[i], fft.DIF, fft.OnCoset()) + seed.Add(&seed, &one) + } +} + +const ( + LATENCY_MUL_FIELD_NS int = 18 + LATENCY_ADD_FIELD_NS int = 4 +) + +// Estimate the theoretical performances that are achievable using ring-SIS +// operations. The time is obtained by counting the number of additions and +// multiplications occurring in the computation. This does not account for the +// possibilities to use SIMD instructions or for cache-locality issues. Thus, it +// does not represents a maximum even though it returns a good idea of what is +// achievable . This returns performances in term of ns/field. This also does not +// account for the time taken for "limb-splitting" the input. +func estimateSisTheory(p sisParams) float64 { + + // Since the FFT occurs over a coset, we need to multiply all the coefficients + // of the input by some coset factors (for an entire polynomial) + timeCosetShift := (1 << p.logTwoDegree) * LATENCY_MUL_FIELD_NS + + // The two additions are from the butterfly, and the multiplication represents + // the one by the twiddle. (for an entire polynomial) + timeFFT := (1 << p.logTwoDegree) * p.logTwoDegree * (2*LATENCY_ADD_FIELD_NS + LATENCY_MUL_FIELD_NS) + + // Time taken to multiply by the key and accumulate (for an entire polynomial) + timeMulAddKey := (1 << p.logTwoDegree) * (LATENCY_MUL_FIELD_NS + LATENCY_ADD_FIELD_NS) + + // Total computation time for an entire polynomial + totalTimePoly := timeCosetShift + timeFFT + timeMulAddKey + + // Convert this into a time per input field + r := totalTimePoly * fr.Bits / p.logTwoBound / (1 << p.logTwoDegree) + return float64(r) +} + +func BenchmarkSIS(b *testing.B) { + + // max nb field elements to hash + const nbInputs = 1 << 16 + + // Assign the input with random bytes. In practice, theses bytes encodes + // a string of field element. It would be more meaningful to take a slice + // of field element directly because otherwise the conversion time is not + // accounted for in the benchmark. + inputs := make(fr.Vector, nbInputs) + for i := 0; i < len(inputs); i++ { + inputs[i].SetRandom() + } + + for _, param := range params128Bits { + for n := 1 << 10; n <= nbInputs; n <<= 1 { + in := inputs[:n] + benchmarkSIS(b, in, false, param.logTwoBound, param.logTwoDegree, estimateSisTheory(param)) + } + + } +} + +func benchmarkSIS(b *testing.B, input []fr.Element, sparse bool, logTwoBound, logTwoDegree int, theoritical float64) { + b.Helper() + + n := len(input) + + benchName := "ring-sis/" + if sparse { + benchName += "sparse/" + } + benchName += fmt.Sprintf("inputs=%v/log2-bound=%v/log2-degree=%v", n, logTwoBound, logTwoDegree) + + b.Run(benchName, func(b *testing.B) { + instance, err := NewRSis(0, logTwoDegree, logTwoBound, n) + if err != nil { + b.Fatal(err) + } + + // We introduce a custom metric which is the time per field element + // Since the benchmark object allows to report extra meta but does + // not allow accessing them. We measure the time ourself. + + startTime := time.Now() + b.ResetTimer() + for i := 0; i < b.N; i++ { + _, err = instance.Hash(input) + if err != nil { + b.Fatal(err) + } + } + b.StopTimer() + + totalDuration := time.Since(startTime) + nsPerField := totalDuration.Nanoseconds() / int64(b.N) / int64(n) + + b.ReportMetric(float64(nsPerField), "ns/field") + + b.ReportMetric(theoritical, "ns/field(theory)") + + }) +} + +// Hash interprets the input vector as a sequence of coefficients of size r.LogTwoBound bits long, +// and return the hash of the polynomial corresponding to the sum sum_i A[i]*m Mod X^{d}+1 +// +// It is equivalent to calling r.Write(element.Marshal()); outBytes = r.Sum(nil); +// ! note @gbotrel: this is a place holder, may not make sense +func (r *RSis) Hash(v []fr.Element) ([]fr.Element, error) { + if len(v) > r.maxNbElementsToHash { + return nil, fmt.Errorf("can't hash more than %d elements with params provided in constructor", r.maxNbElementsToHash) + } + + r.Reset() + for _, e := range v { + r.Write(e.Marshal()) + } + sum := r.Sum(nil) + var rlen [4]byte + binary.BigEndian.PutUint32(rlen[:], uint32(len(sum)/fr.Bytes)) + reader := io.MultiReader(bytes.NewReader(rlen[:]), bytes.NewReader(sum)) + var result fr.Vector + _, err := result.ReadFrom(reader) + if err != nil { + return nil, err + } + return result, nil +} + +// Hash version without mem copy +// // Hash interprets the input vector as a sequence of coefficients of size r.LogTwoBound bits long, +// // and return the hash of the polynomial corresponding to the sum sum_i A[i]*m Mod X^{d}+1 +// // +// // It is equivalent to calling r.Write(element.Marshal()); outBytes = r.Sum(nil); +// func (r *RSis) Hash(v []fr.Element) ([]fr.Element, error) { +// if len(v) > r.maxNbElementsToHash { +// return nil, fmt.Errorf("can't hash more than %d elements with params provided in constructor", r.maxNbElementsToHash) +// } + +// // clear the buffers of the instance. +// defer func() { +// r.bufMValues.ClearAll() +// for i := 0; i < len(r.bufM); i++ { +// r.bufM[i].SetZero() +// } +// }() + +// // bitwise decomposition of the buffer, in order to build m (the vector to hash) +// // as a list of polynomials, whose coefficients are less than r.B bits long. + +// bitAt := func(v []fr.Element, i int) uint8 { +// // v --> slice of bits +// // return bit at position i +// const n = fr.Bytes * 8 // nb bits per element +// nbBits := len(v) * n + +// if i >= nbBits { +// return 0 +// } + +// eIndex := i / n +// i %= n + +// // we want bit i of v[eIndex] +// j := i / 64 +// return uint8(v[eIndex][j] >> (i % 64) & 1) + +// } + +// // now we can construct m. The input to hash consists of the polynomials +// // m[k*r.Degree:(k+1)*r.Degree] +// m := r.bufM + +// // mark blocks m[i*r.Degree : (i+1)*r.Degree] != [0...0] +// mValues := r.bufMValues + +// // we process the input buffer by blocks of r.LogTwoBound bits +// // each of these block (<< 64bits) are interpreted as a coefficient +// mPos := 0 +// nbBits := len(v) * fr.Bytes * 8 +// for i := 0; i < nbBits; mPos++ { +// for j := 0; j < r.LogTwoBound; j++ { +// // r.LogTwoBound < 64; we just use the first word of our element here, +// // and set the bits from LSB to MSB. +// m[mPos][0] |= uint64(bitAt(v, i) << j) +// i++ +// } +// if m[mPos][0] == 0 { +// continue +// } +// mValues.Set(uint(mPos / r.Degree)) +// } + +// // we can hash now. +// res := make(fr.Vector, r.Degree) + +// // method 1: fft +// for i := 0; i < len(r.Ag); i++ { +// if !mValues.Test(uint(i)) { +// // means m[i*r.Degree : (i+1)*r.Degree] == [0...0] +// // we can skip this, FFT(0) = 0 +// continue +// } +// k := m[i*r.Degree : (i+1)*r.Degree] +// r.Domain.FFT(k, fft.DIF, fft.OnCoset(), fft.WithNbTasks(1)) +// mulModAcc(res, r.Ag[i], k) +// } +// r.Domain.FFTInverse(res, fft.DIT, fft.OnCoset(), fft.WithNbTasks(1)) // -> reduces mod Xᵈ+1 + +// return res, nil +// } diff --git a/ecc/bn254/fr/sis/test_cases.json b/ecc/bn254/fr/sis/test_cases.json new file mode 100644 index 0000000000..d9670587a1 --- /dev/null +++ b/ecc/bn254/fr/sis/test_cases.json @@ -0,0 +1,117269 @@ +{ + "inputs": [ + [ + "0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593effffffe" + ], + [ + "0x1" + ], + [ + "0x2a", + "0x1f40" + ], + [ + "0x1", + "0x2", + "0x0", + "0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000000" + ], + [ + "0x1", + "0x0" + ], + [ + "0x0", + "0x1" + ], + [ + "0x0" + ], + [ + "0x0", + "0x0", + "0x0", + "0x0" + ], + [ + "0x0", + "0x0", + "0x1f40", + "0x0" + ], + [], + [ + "0x1953dbbb634990faadd67e97e5e6c8e3cbabdfd3f7ed8ca5040715fe43bbe68" + ], + [ + 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distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +package tensorcommitment + +import ( + "bytes" + "errors" + "hash" + "math/big" + + "github.com/consensys/gnark-crypto/ecc/bn254/fr" + "github.com/consensys/gnark-crypto/ecc/bn254/fr/fft" + "github.com/consensys/gnark-crypto/internal/parallel" +) + +var ( + ErrWrongSize = errors.New("polynomial is too large") + ErrNotSquare = errors.New("the size of the polynomial must be a square") + ErrProofFailedHash = errors.New("hash of one of the columns is wrong") + ErrProofFailedEncoding = errors.New("inconsistency with the code word") + ErrProofFailedOob = errors.New("the entry is out of bound") + ErrMaxNbColumns = errors.New("the state is full") + ErrCommitmentNotDone = errors.New("the proof cannot be built before the computation of the digest") +) + +// commitment (TODO Merkle tree for that...) +// The i-th entry is the hash of the i-th columns of P, +// where P is written as a matrix √(m) x √(m) +// (m = len(P)), and the ij-th entry of M is p[m*j + i]. +type Digest [][]byte + +// Proof that a commitment is correct +// cf https://eprint.iacr.org/2021/1043.pdf page 10 +type Proof struct { + + // list of entries of ̂{u} to query (see https://eprint.iacr.org/2021/1043.pdf for notations) + EntryList []int + + // columns on against which the linear combination is checked + // (the i-th entry is the EntryList[i]-th column) + Columns [][]fr.Element + + // Linear combination of the rows of the polynomial P written as a square matrix + LinearCombination []fr.Element + + // small domain, to retrieve the canonical form of the linear combination + Domain *fft.Domain + + // root of unity of the big domain + Generator fr.Element +} + +// TcParams stores the public parameters of the tensor commitment +type TcParams struct { + // NbColumns number of columns of the matrix storing the polynomials. The total size of + // the polynomials which are committed is NbColumns x NbRows. + // The Number of columns is a power of 2, it corresponds to the original size of the codewords + // of the Reed Solomon code. + NbColumns int + + // NbRows number of rows of the matrix storing the polynomials. If a polynomial p is appended + // whose size if not 0 mod NbRows, it is padded as p' so that len(p')=0 mod NbRows. + NbRows int + + // Domains[1] used for the Reed Solomon encoding + Domains [2]*fft.Domain + + // Rho⁻¹, rate of the RS code ( > 1) + Rho int + + // Function that returns a fresh hasher. The returned hash function is used for hashing the + // columns. We use this and not directly a hasher for threadsafety hasher. Indeed, if different + // thread share the same hasher, they will end up mixing hash inputs that should remain separate. + MakeHash func() hash.Hash +} + +// TensorCommitment stores the data to use a tensor commitment +type TensorCommitment struct { + // The public parameters of the tensor commitment + params *TcParams + + // State contains the polynomials that have been appended so far. + // when we append a polynomial p, it is stored in the state like this: + // state[i][j] = p[j*nbRows + i]: + // p[0] | p[nbRows] | p[2*nbRows] ... + // p[1] | p[nbRows+1] | p[2*nbRows+1] + // p[2] | p[nbRows+2] | p[2*nbRows+2] + // .. + // p[nbRows-1] | p[2*nbRows-1] | p[3*nbRows-1] .. + State [][]fr.Element + + // same content as state, but the polynomials are displayed as a matrix + // and the rows are encoded. + // encodedState = encodeRows(M_0 || .. || M_n) + // where M_i is the i-th polynomial layed out as a matrix, that is + // M_i_jk = p_i[i*m+j] where m = \sqrt(len(p)). + EncodedState [][]fr.Element + + // boolean telling if the commitment has already been done. + // The method BuildProof cannot be called before Commit(), + // because it would allow to build a proof before giving the commitment + // to a verifier, making the worklow not secure. + isCommitted bool + + // number of columns which have already been hashed (atomic) + NbColumnsHashed int + + // counts the number of time `Append` was called (atomic). + NbAppendsSoFar int +} + +// NewTensorCommitment retunrs a new TensorCommitment +// * ρ rate of the code ( > 1) +// * size size of the polynomial to be committed. The size of the commitment is +// then ρ * √(m) where m² = size +func NewTCParams(codeRate, NbColumns, NbRows int, makeHash func() hash.Hash) (*TcParams, error) { + var res TcParams + + // domain[0]: domain to perform the FFT^-1, of size capacity * sqrt + // domain[1]: domain to perform FFT, of size rho * capacity * sqrt + res.Domains[0] = fft.NewDomain(uint64(NbColumns)) + res.Domains[1] = fft.NewDomain(uint64(codeRate * NbColumns)) + + // size of the matrix + res.NbColumns = int(res.Domains[0].Cardinality) + res.NbRows = NbRows + + // rate + res.Rho = codeRate + + // Hash function + res.MakeHash = makeHash + + return &res, nil +} + +// Initializes an instance of tensor commitment that we can use start +// appending value into it +func NewTensorCommitment(params *TcParams) *TensorCommitment { + var res TensorCommitment + + // create the state. It's the matrix containing the polynomials, the ij-th + // entry of the matrix is state[i][j]. The polynomials are split and stacked + // columns per column. + res.State = make([][]fr.Element, params.NbRows) + for i := 0; i < params.NbRows; i++ { + res.State[i] = make([]fr.Element, params.NbColumns) + } + + // nothing has been committed... + res.isCommitted = false + res.params = params + return &res +} + +// Append appends p to the state. +// when we append a polynomial p, it is stored in the state like this: +// state[i][j] = p[j*nbRows + i]: +// p[0] | p[nbRows] | p[2*nbRows] ... +// p[1] | p[nbRows+1] | p[2*nbRows+1] +// p[2] | p[nbRows+2] | p[2*nbRows+2] +// .. +// p[nbRows-1] | p[2*nbRows-1] | p[3*nbRows-1] .. +// If p doesn't fill a full submatrix it is padded with zeroes. +func (tc *TensorCommitment) Append(ps ...[]fr.Element) ([][]byte, error) { + + nbColumnsTakenByPs := make([]int, len(ps)) + totalNumberOfColumnsTakenByPs := 0 + // Short-hand to avoid writing `tc.params.NbRows` all over the places + numRows := tc.params.NbRows + + /* + Precomputes the number of columns that will be taken by each colums + */ + for iPol, p := range ps { + // check if there is some room for p + nbColumnsTakenByP := len(p) / numRows + // Note, Alex. Really, if you want to not handle the padding and just + // panic whenever you receive "incomplete" columns this would be fine. + if len(p)%numRows != 0 { + // If the division has a remainder. Add an extra column + // Implicitly, it will be padded + nbColumnsTakenByP += 1 + } + + nbColumnsTakenByPs[iPol] = nbColumnsTakenByP + totalNumberOfColumnsTakenByPs += nbColumnsTakenByP + } + + // Position at which we need to start inserting columns in the state + currentColumnToFill := int(tc.NbColumnsHashed) + + // Check that we are not inserting more columns that we can handle + if currentColumnToFill+totalNumberOfColumnsTakenByPs > tc.params.NbColumns { + return nil, ErrMaxNbColumns + } + + // Update the internal state variables to keep track of how many poly + // have been appended so far and how many columns. + tc.NbAppendsSoFar += len(ps) + tc.NbColumnsHashed += totalNumberOfColumnsTakenByPs + + backupCurrentColumnToFill := currentColumnToFill + + // put p in the state + for iPol, p := range ps { + + pIsPadded := false + if len(p)%numRows != 0 { + pIsPadded = true + } + + // Number of column taken by P, ignoring the last one if it is padded + nbFullColumnsTakenByP := nbColumnsTakenByPs[iPol] + if pIsPadded { + nbFullColumnsTakenByP-- + } + + // Insert the "full columns" in the state + for i := 0; i < nbFullColumnsTakenByP; i++ { + for j := 0; j < numRows; j++ { + tc.State[j][currentColumnToFill+i] = p[i*numRows+j] + } + } + + // Insert the padded column in the state if any + currentColumnToFill += nbFullColumnsTakenByP + if pIsPadded { + offsetP := len(p) - len(p)%numRows + for j := offsetP; j < len(p); j++ { + tc.State[j-offsetP][currentColumnToFill] = p[j] + } + currentColumnToFill += 1 + } + } + + // Preallocate the result, and as well a buffer for the columns to hash + res := make([][]byte, totalNumberOfColumnsTakenByPs) + + parallel.Execute(totalNumberOfColumnsTakenByPs, func(start, stop int) { + hasher := tc.params.MakeHash() + for i := start; i < stop; i++ { + hasher.Reset() + for j := 0; j < tc.params.NbRows; j++ { + hasher.Write(tc.State[j][i+backupCurrentColumnToFill].Marshal()) + } + res[i] = hasher.Sum(nil) + } + }) + + return res, nil +} + +// Commit to p. The commitment procedure is the following: +// * Encode the rows of the state to get M' +// * Hash the columns of M' +func (tc *TensorCommitment) Commit() (Digest, error) { + + // we encode the rows of p using Reed Solomon + // encodedState[i][:] = i-th line of M. It is of size domain[1].Cardinality + tc.EncodedState = make([][]fr.Element, tc.params.NbRows) + for i := 0; i < tc.params.NbRows; i++ { // we fill encodedState line by line + tc.EncodedState[i] = make([]fr.Element, tc.params.Domains[1].Cardinality) // size = NbRows*rho*capacity + for j := 0; j < tc.params.NbColumns; j++ { // for each polynomial + tc.EncodedState[i][j].Set(&tc.State[i][j]) + } + tc.params.Domains[0].FFTInverse(tc.EncodedState[i][:tc.params.Domains[0].Cardinality], fft.DIF) + fft.BitReverse(tc.EncodedState[i][:tc.params.Domains[0].Cardinality]) + tc.params.Domains[1].FFT(tc.EncodedState[i], fft.DIF) + fft.BitReverse(tc.EncodedState[i]) + } + + // now we hash each columns of _p + res := make([][]byte, tc.params.Domains[1].Cardinality) + + parallel.Execute(int(tc.params.Domains[1].Cardinality), func(start, stop int) { + hasher := tc.params.MakeHash() + for i := start; i < stop; i++ { + hasher.Reset() + for j := 0; j < tc.params.NbRows; j++ { + hasher.Write(tc.EncodedState[j][i].Marshal()) + } + res[i] = hasher.Sum(nil) + } + }) + + // records that the ccommitment has been built + tc.isCommitted = true + + return res, nil + +} + +// BuildProofAtOnceForTest builds a proof to be tested against a previous commitment of a list of +// polynomials. +// * l the random linear coefficients used for the linear combination of size NbRows +// * entryList list of columns to hash +// l and entryList are supposed to be precomputed using Fiat Shamir +// +// The proof is the linear combination (using l) of the encoded rows of p written +// as a matrix. Only the entries contained in entryList are kept. +func (tc *TensorCommitment) BuildProofAtOnceForTest(l []fr.Element, entryList []int) (Proof, error) { + linComb, err := tc.ProverComputeLinComb(l) + if err != nil { + return Proof{}, err + } + + openedColumns, err := tc.ProverOpenColumns(entryList) + if err != nil { + return Proof{}, err + } + + return BuildProof(tc.params, linComb, entryList, openedColumns), nil +} + +// func printVector(v []fr.Element) { +// fmt.Printf("[") +// for i := 0; i < len(v); i++ { +// fmt.Printf("%s,", v[i].String()) +// } +// fmt.Printf("]\n") +// } + +// BuildProof builds a proof to be tested against a previous commitment of a list of +// polynomials. +// * l the random linear coefficients used for the linear combination of size NbRows +// * entryList list of columns to hash +// l and entryList are supposed to be precomputed using Fiat Shamir +// +// The proof is the linear combination (using l) of the encoded rows of p written +// as a matrix. Only the entries contained in entryList are kept. +func (tc *TensorCommitment) ProverComputeLinComb(l []fr.Element) ([]fr.Element, error) { + + // check that the digest has been computed + if !tc.isCommitted { + return []fr.Element{}, ErrCommitmentNotDone + } + + // since the digest has been computed, the encodedState is already stored. + // We use it to build the proof, without recomputing the ffts. + + // linear combination of the rows of the state + linComb := make([]fr.Element, tc.params.NbColumns) + for i := 0; i < tc.params.NbColumns; i++ { + var tmp fr.Element + for j := 0; j < tc.params.NbRows; j++ { + tmp.Mul(&tc.State[j][i], &l[j]) + linComb[i].Add(&linComb[i], &tmp) + } + } + + return linComb, nil +} + +func (tc *TensorCommitment) ProverOpenColumns(entryList []int) ([][]fr.Element, error) { + + // check that the digest has been computed + if !tc.isCommitted { + return [][]fr.Element{}, ErrCommitmentNotDone + } + + // columns of the state whose rows have been encoded, written as a matrix, + // corresponding to the indices in entryList (we will select the columns + // entryList[0], entryList[1], etc. + openedColumns := make([][]fr.Element, len(entryList)) + for i := 0; i < len(entryList); i++ { // for each column (corresponding to an elmt in entryList) + openedColumns[i] = make([]fr.Element, tc.params.NbRows) + for j := 0; j < tc.params.NbRows; j++ { + openedColumns[i][j] = tc.EncodedState[j][entryList[i]] + } + } + + return openedColumns, nil +} + +/* +Reconstruct the proof from the prover's outputs +*/ +func BuildProof(params *TcParams, linComb []fr.Element, entryList []int, openedCols [][]fr.Element) Proof { + + var res Proof + + // small domain to express the linear combination in canonical form + res.Domain = params.Domains[0] + + // generator g of the biggest domain, used to evaluate the canonical form of + // the linear combination at some powers of g. + res.Generator.Set(¶ms.Domains[1].Generator) + + res.Columns = openedCols + res.EntryList = entryList + res.LinearCombination = linComb + + return res +} + +// evalAtPower returns p(x**n) where p is interpreted as a polynomial +// p[0] + p[1]X + .. p[len(p)-1]xˡᵉⁿ⁽ᵖ⁾⁻¹ +func evalAtPower(p []fr.Element, x fr.Element, n int) fr.Element { + + var xexp fr.Element + xexp.Exp(x, big.NewInt(int64(n))) + + var res fr.Element + for i := 0; i < len(p); i++ { + res.Mul(&res, &xexp) + res.Add(&p[len(p)-1-i], &res) + } + + return res + +} + +// Verify a proof that digest is the hash of a polynomial given a proof +// proof: contains the linear combination of the non-encoded rows + the +// digest: hash of the polynomial +// l: random coefficients for the linear combination, chosen by the verifier +// h: hash function that is used for hashing the columns of the polynomial +// TODO make this function private and add a Verify function that derives +// the randomness using Fiat Shamir +// +// Note (alex), A more convenient API would be to expose two functions, +// one that does FS for you and what that let you do it for yourself. And likewise +// for the prover. +func Verify(proof Proof, digest Digest, l []fr.Element, h hash.Hash) error { + + // for each entry in the list -> it corresponds to the sampling + // set on which we probabilistically check that + // Encoded(linear_combination) = linear_combination(encoded) + for i := 0; i < len(proof.EntryList); i++ { + + // check that the hash of the columns correspond to what's in the digest + h.Reset() + for j := 0; j < len(proof.Columns[i]); j++ { + h.Write(proof.Columns[i][j].Marshal()) + } + s := h.Sum(nil) + if !bytes.Equal(s, digest[proof.EntryList[i]]) { + return ErrProofFailedHash + } + + if proof.EntryList[i] >= len(digest) { + return ErrProofFailedOob + } + + // linear combination of the i-th column, whose entries + // are the entryList[i]-th entries of the encoded lines + // of p + var linCombEncoded, tmp fr.Element + for j := 0; j < len(proof.Columns[i]); j++ { + + // linear combination of the encoded rows at column i + tmp.Mul(&proof.Columns[i][j], &l[j]) + linCombEncoded.Add(&linCombEncoded, &tmp) + } + + // entry i of the encoded linear combination + var encodedLinComb fr.Element + linCombCanonical := make([]fr.Element, proof.Domain.Cardinality) + copy(linCombCanonical, proof.LinearCombination) + proof.Domain.FFTInverse(linCombCanonical, fft.DIF) + fft.BitReverse(linCombCanonical) + encodedLinComb = evalAtPower(linCombCanonical, proof.Generator, proof.EntryList[i]) + + // compare both values + if !encodedLinComb.Equal(&linCombEncoded) { + return ErrProofFailedEncoding + + } + } + + return nil + +} diff --git a/ecc/bn254/fr/tensor-commitment/commitment_test.go b/ecc/bn254/fr/tensor-commitment/commitment_test.go new file mode 100644 index 0000000000..19e7be893b --- /dev/null +++ b/ecc/bn254/fr/tensor-commitment/commitment_test.go @@ -0,0 +1,520 @@ +// Copyright 2020 ConsenSys Software Inc. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +package tensorcommitment + +import ( + "bytes" + "hash" + "math/big" + "math/bits" + "strconv" + "testing" + + "github.com/consensys/gnark-crypto/ecc/bn254/fr" + "github.com/consensys/gnark-crypto/ecc/bn254/fr/sis" + "github.com/stretchr/testify/require" +) + +type DummyHash uint + +func (d DummyHash) Write(p []byte) (n int, err error) { + return 0, nil +} + +func (d DummyHash) Sum(b []byte) []byte { + return b +} + +func (d DummyHash) Reset() {} + +func (d DummyHash) Size() int { + return 0 +} + +func (d DummyHash) BlockSize() int { + return 0 +} + +func DummyHashMaker() hash.Hash { + var res DummyHash + return &res +} + +func TestAppend(t *testing.T) { + if bits.UintSize == 32 { + t.Skip("skipping this test in 32bit.") + } + + assert := require.New(t) + + // tensor commitment + const ( + rho = 4 + nbRows = 10 + nbColumns = 16 + ) + params, err := NewTCParams(rho, nbColumns, nbRows, DummyHashMaker) + assert.NoError(err) + + tc := NewTensorCommitment(params) + + { + // random Polynomial of size nbRows + p := make([]fr.Element, nbRows) + for i := 0; i < nbRows; i++ { + p[i].SetRandom() + } + _, err := tc.Append(p) + assert.NoError(err) + + // check if p corresponds to the first column of the state + for i := 0; i < nbRows; i++ { + assert.True(tc.State[i][0].Equal(&p[i]), "a column is not filled correctly") + } + + } + + // after a first polynomial has been filled + { + // random Polynomial of size nbRows + p := make([]fr.Element, nbRows) + for i := 0; i < nbRows; i++ { + p[i].SetRandom() + } + _, err := tc.Append(p) + assert.NoError(err) + + // check if p corresponds to the second column of the state + for i := 0; i < nbRows; i++ { + assert.True(tc.State[i][1].Equal(&p[i]), "a column is not filled correctly") + } + } + + // polynomial whose size is not a multiple of nbRows + { + // random Polynomial of size nbRows + offset := 4 + p := make([]fr.Element, nbRows+offset) + for i := 0; i < nbRows+offset; i++ { + p[i].SetRandom() + } + _, err := tc.Append(p) + assert.NoError(err) + + // check if p corresponds to the first column of the state + for i := 0; i < nbRows; i++ { + assert.True(tc.State[i][2].Equal(&p[i]), "a column is not filled correctly") + } + for i := 0; i < offset; i++ { + assert.True(tc.State[i][3].Equal(&p[i+nbRows]), "a column is not filled correctly") + } + } + + // same to see if the last column was correctly offset + { + // random Polynomial of size nbRows + offset := 4 + p := make([]fr.Element, nbRows+offset) + for i := 0; i < nbRows+offset; i++ { + p[i].SetRandom() + } + _, err := tc.Append(p) + assert.NoError(err) + + // check if p corresponds to the first column of the state + for i := 0; i < nbRows; i++ { + assert.True(tc.State[i][4].Equal(&p[i]), "a column is not filled correctly") + } + for i := 0; i < offset; i++ { + assert.True(tc.State[i][5].Equal(&p[i+nbRows]), "a column is not filled correctly") + } + } + +} + +func TestLinearCombination(t *testing.T) { + + rho := 4 + nbRows := 8 + nbColumns := 8 + params, err := NewTCParams(rho, nbColumns, nbRows, DummyHashMaker) + if err != nil { + t.Fatal(err) + } + tc := NewTensorCommitment(params) + + // build a random polynomial + p := make([]fr.Element, nbRows*nbColumns) + for i := 0; i < 64; i++ { + p[i].SetRandom() + } + + // we select all the entries for the test + entryList := make([]int, rho*nbColumns) + for i := 0; i < rho*nbColumns; i++ { + entryList[i] = i + } + + // append p and commit (otherwise the proof cannot be built) + tc.Append(p) + _, err = tc.Commit() + if err != nil { + t.Fatal(err) + } + + // at each trial, it's the i-th line which is selected + for i := 0; i < nbRows; i++ { + + // used for the random linear combination. + // it will act as a selector for the test: it selects the i-th + // row of p, when p is written as a matrix M_ij, where M_ij=p[i*m+j]. + // The i-th entry of l is 1, the others are 0. + l := make([]fr.Element, nbRows) + l[i].SetInt64(1) + + proof, err := tc.BuildProofAtOnceForTest(l, entryList) + if err != nil { + t.Fatal(err) + } + + // the i-th line of p is the one that is supposed to be selected + // (corresponding to the linear combination) + expected := make([]fr.Element, nbColumns) + for j := 0; j < nbColumns; j++ { + expected[j].Set(&p[j*nbRows+i]) + } + + for j := 0; j < nbColumns; j++ { + if !expected[j].Equal(&proof.LinearCombination[j]) { + t.Fatal("expected linear combination is incorrect") + } + } + + } +} + +// Test the verification of a correct proof using a mock hash +func TestCommitmentDummyHash(t *testing.T) { + + var rho, nbColumns, nbRows int + rho = 4 + nbColumns = 8 + nbRows = 8 + + var h DummyHash + params, err := NewTCParams(rho, nbColumns, nbRows, DummyHashMaker) + if err != nil { + t.Fatal(err) + } + tc := NewTensorCommitment(params) + + // random polynomial + p := make([]fr.Element, nbRows*nbColumns) + for i := 0; i < nbRows*nbColumns; i++ { + p[i].SetRandom() + } + + // coefficients for the linear combination + l := make([]fr.Element, nbRows) + for i := 0; i < nbRows; i++ { + l[i].SetRandom() + } + + // we select all the entries for the test + entryList := make([]int, rho*nbColumns) + for i := 0; i < rho*nbColumns; i++ { + entryList[i] = i + } + + // compute the digest... + _, err = tc.Append(p) + if err != nil { + t.Fatal(err) + } + digest, err := tc.Commit() + if err != nil { + t.Fatal(err) + } + + // build the proof... + proof, err := tc.BuildProofAtOnceForTest(l, entryList) + if err != nil { + t.Fatal(err) + } + + // verfiy that the proof is correct + err = Verify(proof, digest, l, h) + if err != nil { + t.Fatal(err) + } + +} + +// Test the opening using a dummy hash +func TestOpeningDummyHash(t *testing.T) { + + var rho, nbColumns, nbRows int + rho = 4 + nbColumns = 8 + nbRows = 8 + + params, err := NewTCParams(rho, nbColumns, nbRows, DummyHashMaker) + if err != nil { + t.Fatal(err) + } + tc := NewTensorCommitment(params) + + // random polynomial + p := make([]fr.Element, nbColumns*nbRows) + for i := 0; i < nbColumns*nbRows; i++ { + p[i].SetRandom() + } + + // the coefficients are (1,x,x^2,..,x^{n-1}) where x is the point + // at which the opening is done + var xm, x fr.Element + x.SetRandom() + hi := make([]fr.Element, nbColumns) // stores [1,x^{nbRows},..,x^{nbRows*nbColumns^-1}] + lo := make([]fr.Element, nbRows) // stores [1,x,..,x^{nbRows-1}] + lo[0].SetInt64(1) + hi[0].SetInt64(1) + xm.Exp(x, big.NewInt(int64(nbRows))) + for i := 1; i < nbColumns; i++ { + lo[i].Mul(&lo[i-1], &x) + hi[i].Mul(&hi[i-1], &xm) + } + + // create the digest before computing the proof + _, err = tc.Append(p) + if err != nil { + t.Fatal(err) + } + _, err = tc.Commit() + if err != nil { + t.Fatal(err) + } + + // build the proof + entryList := make([]int, rho*nbColumns) + for i := 0; i < rho*nbColumns; i++ { + entryList[i] = i + } + proof, err := tc.BuildProofAtOnceForTest(lo, entryList) + if err != nil { + t.Fatal(err) + } + + // finish the evalutation by computing + // [linearCombination] * [hi]^t + var eval, tmp fr.Element + for i := 0; i < nbColumns; i++ { + tmp.Mul(&proof.LinearCombination[i], &hi[i]) + eval.Add(&eval, &tmp) + } + + // compute the real evaluation of p at x manually + var expectedEval fr.Element + for i := 0; i < nbRows*nbColumns; i++ { + expectedEval.Mul(&expectedEval, &x) + expectedEval.Add(&expectedEval, &p[len(p)-i-1]) + } + + // the results coincide + if !expectedEval.Equal(&eval) { + t.Fatal("p(x) != [ lo ] x M x [ hi ]^t") + } + +} + +// Check the commitments are correctly formed when appending a polynomial +func TestAppendSis(t *testing.T) { + if bits.UintSize == 32 { + t.Skip("skipping this test in 32bit.") + } + const ( + rho = 4 + nbColumns = 8 + nbRows = 8 + logTwoDegree = 1 + logTwoBound = 4 + ) + + assert := require.New(t) + + // keySize := 256 + hMaker, err := sis.NewRingSISMaker(5, logTwoDegree, logTwoBound, 8) + assert.NoError(err) + + params, err := NewTCParams(rho, nbColumns, nbRows, hMaker) + assert.NoError(err) + + tc := NewTensorCommitment(params) + + // random polynomial (that does not fill the full matrix) + offset := 4 + p := make([]fr.Element, nbRows*nbColumns-offset) + for i := 0; i < nbRows*nbColumns-offset; i++ { + p[i].SetRandom() + } + + s, err := tc.Append(p) + assert.NoError(err) + + assert.Equal(nbColumns, len(s)) + + // check the hashes of the columns + h := hMaker() + for i := 0; i < nbColumns-1; i++ { + h.Reset() + for j := 0; j < nbRows; j++ { + h.Write(p[i*nbRows+j].Marshal()) + } + _s := h.Sum(nil) + assert.True(bytes.Equal(_s, s[i]), "error hash column when appending a polynomial for column", i) + } + + // last column + h.Reset() + for i := (nbColumns - 1) * nbRows; i < nbColumns*nbRows-offset; i++ { + h.Write(p[i].Marshal()) + } + var tmp fr.Element + for i := nbColumns*nbRows - offset; i < nbColumns*nbRows; i++ { + h.Write(tmp.Marshal()) + } + _s := h.Sum(nil) + assert.True(bytes.Equal(_s, s[nbColumns-1]), "error hash column when appending a polynomial") +} + +// Test the verification of a correct proof using SIS as hash +func TestCommitmentSis(t *testing.T) { + if bits.UintSize == 32 { + t.Skip("skipping this test in 32bit.") + } + var rho, nbColumns, nbRows int + rho = 4 + nbColumns = 8 + nbRows = 8 + + logTwoDegree := 1 + logTwoBound := 4 + hMaker, err := sis.NewRingSISMaker(5, logTwoDegree, logTwoBound, 8) + if err != nil { + t.Fatal(err) + } + + params, err := NewTCParams(rho, nbColumns, nbRows, hMaker) + if err != nil { + t.Fatal(err) + } + tc := NewTensorCommitment(params) + + // random polynomial + p := make([]fr.Element, nbRows*nbColumns) + for i := 0; i < nbRows*nbColumns; i++ { + p[i].SetRandom() + } + + // coefficients for the linear combination + l := make([]fr.Element, nbRows) + for i := 0; i < nbRows; i++ { + l[i].SetRandom() + } + + // compute the digest... + _, err = tc.Append(p) + if err != nil { + t.Fatal(err) + } + digest, err := tc.Commit() + if err != nil { + t.Fatal(err) + } + + // test 1: we select all the entries + { + entryList := make([]int, rho*nbColumns) + for i := 0; i < rho*nbColumns; i++ { + entryList[i] = i + } + + // build the proof... + proof, err := tc.BuildProofAtOnceForTest(l, entryList) + if err != nil { + t.Fatal(err) + } + + // verfiy that the proof is correct + err = Verify(proof, digest, l, hMaker()) + if err != nil { + t.Fatal(err) + } + } + // test 2: we select a subset of the entries + { + + entryList := make([]int, 2) + entryList[0] = 1 + entryList[1] = 4 + + // build the proof... + proof, err := tc.BuildProofAtOnceForTest(l, entryList) + if err != nil { + t.Fatal(err) + } + + // verfiy that the proof is correct + err = Verify(proof, digest, l, hMaker()) + if err != nil { + t.Fatal(err) + } + } +} + +// benches +func BenchmarkTensorCommitment(b *testing.B) { + + // prepare the tensor commitment + logTwoDegree := 4 + logTwoBound := 4 + rho := 4 + + for i := 0; i < 6; i++ { + + nbColumns := (1 << (3 + i)) + nbRows := nbColumns + + h, _ := sis.NewRingSISMaker(5, logTwoDegree, logTwoBound, nbRows) + params, _ := NewTCParams(rho, nbColumns, nbRows, h) + tc := NewTensorCommitment(params) + + // random polynomial + p := make([]fr.Element, nbRows*nbColumns) + for i := 0; i < nbRows*nbColumns; i++ { + p[i].SetRandom() + } + + // run the benchmark + b.Run("size poly"+strconv.Itoa(nbRows*nbColumns), func(b *testing.B) { + b.ResetTimer() + for i := 0; i < b.N; i++ { + tc.Append(p) + tc.Commit() + } + }) + + } + +} diff --git a/ecc/bn254/internal/fptower/e12_pairing.go b/ecc/bn254/internal/fptower/e12_pairing.go index a4abaf510d..78c94d2f61 100644 --- a/ecc/bn254/internal/fptower/e12_pairing.go +++ b/ecc/bn254/internal/fptower/e12_pairing.go @@ -153,8 +153,8 @@ func (z *E12) MulBy034(c0, c3, c4 *E2) *E12 { } // Mul034By034 multiplication of sparse element (c0,0,0,c3,c4,0) by sparse element (d0,0,0,d3,d4,0) -func (z *E12) Mul034by034(d0, d3, d4, c0, c3, c4 *E2) *E12 { - var tmp, x0, x3, x4, x04, x03, x34 E2 +func Mul034By034(d0, d3, d4, c0, c3, c4 *E2) [5]E2 { + var z00, tmp, x0, x3, x4, x04, x03, x34 E2 x0.Mul(c0, d0) x3.Mul(c3, d3) x4.Mul(c4, d4) @@ -174,13 +174,30 @@ func (z *E12) Mul034by034(d0, d3, d4, c0, c3, c4 *E2) *E12 { Sub(&x34, &x3). Sub(&x34, &x4) - z.C0.B0.MulByNonResidue(&x4). - Add(&z.C0.B0, &x0) - z.C0.B1.Set(&x3) - z.C0.B2.Set(&x34) - z.C1.B0.Set(&x03) - z.C1.B1.Set(&x04) - z.C1.B2.SetZero() + z00.MulByNonResidue(&x4). + Add(&z00, &x0) + + return [5]E2{z00, x3, x34, x03, x04} +} + +// MulBy01234 multiplies z by an E12 sparse element of the form (x0, x1, x2, x3, x4, 0) +func (z *E12) MulBy01234(x *[5]E2) *E12 { + var c1, a, b, c, z0, z1 E6 + c0 := &E6{B0: x[0], B1: x[1], B2: x[2]} + c1.B0 = x[3] + c1.B1 = x[4] + a.Add(&z.C0, &z.C1) + b.Add(c0, &c1) + a.Mul(&a, &b) + b.Mul(&z.C0, c0) + c.Set(&z.C1).MulBy01(&x[3], &x[4]) + z1.Sub(&a, &b) + z1.Sub(&z1, &c) + z0.MulByNonResidue(&c) + z0.Add(&z0, &b) + + z.C0 = z0 + z.C1 = z1 return z } diff --git a/ecc/bn254/internal/fptower/e6.go b/ecc/bn254/internal/fptower/e6.go index 8ae7216ec5..d4f80de958 100644 --- a/ecc/bn254/internal/fptower/e6.go +++ b/ecc/bn254/internal/fptower/e6.go @@ -126,6 +126,34 @@ func (z *E6) MulByE2(x *E6, y *E2) *E6 { return z } +// MulBy12 multiplication by sparse element (0,b1,b2) +func (x *E6) MulBy12(b1, b2 *E2) *E6 { + var t1, t2, c0, tmp, c1, c2 E2 + t1.Mul(&x.B1, b1) + t2.Mul(&x.B2, b2) + c0.Add(&x.B1, &x.B2) + tmp.Add(b1, b2) + c0.Mul(&c0, &tmp) + c0.Sub(&c0, &t1) + c0.Sub(&c0, &t2) + c0.MulByNonResidue(&c0) + c1.Add(&x.B0, &x.B1) + c1.Mul(&c1, b1) + c1.Sub(&c1, &t1) + tmp.MulByNonResidue(&t2) + c1.Add(&c1, &tmp) + tmp.Add(&x.B0, &x.B2) + c2.Mul(b2, &tmp) + c2.Sub(&c2, &t2) + c2.Add(&c2, &t1) + + x.B0 = c0 + x.B1 = c1 + x.B2 = c2 + + return x +} + // MulBy01 multiplication by sparse element (c0,c1,0) func (z *E6) MulBy01(c0, c1 *E2) *E6 { diff --git a/ecc/bn254/marshal.go b/ecc/bn254/marshal.go index f980f6f167..fe66b9a92d 100644 --- a/ecc/bn254/marshal.go +++ b/ecc/bn254/marshal.go @@ -44,6 +44,8 @@ const ( // SizeOfGT represents the size in bytes that a GT element need in binary form const SizeOfGT = fptower.SizeOfGT +var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding") + // Encoder writes bn254 object values to an output stream type Encoder struct { w io.Writer @@ -359,6 +361,19 @@ func NoSubgroupChecks() func(*Decoder) { } } +// isZeroed checks that the provided bytes are at 0 +func isZeroed(firstByte byte, buf []byte) bool { + if firstByte != 0 { + return false + } + for _, b := range buf { + if b != 0 { + return false + } + } + return true +} + func (enc *Encoder) encode(v interface{}) (err error) { rv := reflect.ValueOf(v) if v == nil || (rv.Kind() == reflect.Ptr && rv.IsNil()) { @@ -670,8 +685,11 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineCompressed, nil @@ -787,9 +805,12 @@ func (p *G1Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } @@ -854,7 +875,7 @@ func (p *G2Affine) Bytes() (res [SizeOfG2AffineCompressed]byte) { } // we store X and mask the most significant word with our metadata mask - // p.X.A1 | p.X.A0 + // p.X.A1 | p.X.A0 fp.BigEndian.PutElement((*[fp.Bytes]byte)(res[32:32+fp.Bytes]), p.X.A0) fp.BigEndian.PutElement((*[fp.Bytes]byte)(res[0:0+fp.Bytes]), p.X.A1) @@ -920,8 +941,11 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineCompressed, nil @@ -1051,9 +1075,12 @@ func (p *G2Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } diff --git a/ecc/bn254/pairing.go b/ecc/bn254/pairing.go index 53160c9be6..44a87ca612 100644 --- a/ecc/bn254/pairing.go +++ b/ecc/bn254/pairing.go @@ -58,7 +58,7 @@ func PairingCheck(P []G1Affine, Q []G2Affine) (bool, error) { // FinalExponentiation computes the exponentiation (∏ᵢ zᵢ)ᵈ // where d = (p¹²-1)/r = (p¹²-1)/Φ₁₂(p) ⋅ Φ₁₂(p)/r = (p⁶-1)(p²+1)(p⁴ - p² +1)/r // we use instead d=s ⋅ (p⁶-1)(p²+1)(p⁴ - p² +1)/r -// where s is the cofactor 2x₀(6x₀²+3x₀+1) (Fuentes et al.) +// where s is the cofactor 2x₀(6x₀²+3x₀+1) func FinalExponentiation(z *GT, _z ...*GT) GT { var result GT @@ -68,56 +68,50 @@ func FinalExponentiation(z *GT, _z ...*GT) GT { result.Mul(&result, e) } - var t [4]GT + var t [5]GT // Easy part // (p⁶-1)(p²+1) t[0].Conjugate(&result) result.Inverse(&result) t[0].Mul(&t[0], &result) - result.FrobeniusSquare(&t[0]). - Mul(&result, &t[0]) + result.FrobeniusSquare(&t[0]).Mul(&result, &t[0]) - // Hard part (up to permutation) - // 2x₀(6x₀²+3x₀+1)(p⁴-p²+1)/r + // Hard part (up to permutation) + // 2x₀(6x₀²+3x₀+1)(p⁴-p²+1)/r // Duquesne and Ghammam // https://eprint.iacr.org/2015/192.pdf - // Fuentes et al. variant (alg. 10) + // Fuentes et al. (alg. 6) t[0].Expt(&result). Conjugate(&t[0]) t[0].CyclotomicSquare(&t[0]) - t[2].Expt(&t[0]). - Conjugate(&t[2]) - t[1].CyclotomicSquare(&t[2]) - t[2].Mul(&t[2], &t[1]) - t[2].Mul(&t[2], &result) - t[1].Expt(&t[2]). - CyclotomicSquare(&t[1]). - Mul(&t[1], &t[2]). - Conjugate(&t[1]) - t[3].Conjugate(&t[1]) t[1].CyclotomicSquare(&t[0]) - t[1].Mul(&t[1], &result) - t[1].Conjugate(&t[1]) - t[1].Mul(&t[1], &t[3]) - t[0].Mul(&t[0], &t[1]) - t[2].Mul(&t[2], &t[1]) - t[3].FrobeniusSquare(&t[1]) + t[1].Mul(&t[0], &t[1]) + t[2].Expt(&t[1]) + t[2].Conjugate(&t[2]) + t[3].Conjugate(&t[1]) + t[1].Mul(&t[2], &t[3]) + t[3].CyclotomicSquare(&t[2]) + t[4].Expt(&t[3]) + t[4].Mul(&t[1], &t[4]) + t[3].Mul(&t[0], &t[4]) + t[0].Mul(&t[2], &t[4]) + t[0].Mul(&result, &t[0]) + t[2].Frobenius(&t[3]) + t[0].Mul(&t[2], &t[0]) + t[2].FrobeniusSquare(&t[4]) + t[0].Mul(&t[2], &t[0]) + t[2].Conjugate(&result) t[2].Mul(&t[2], &t[3]) - t[3].Conjugate(&result) - t[3].Mul(&t[3], &t[0]) - t[1].FrobeniusCube(&t[3]) - t[2].Mul(&t[2], &t[1]) - t[1].Frobenius(&t[0]) - t[1].Mul(&t[1], &t[2]) + t[2].FrobeniusCube(&t[2]) + t[0].Mul(&t[2], &t[0]) - result.Set(&t[1]) - - return result + return t[0] } // MillerLoop computes the multi-Miller loop -// ∏ᵢ MillerLoop(Pᵢ, Qᵢ) +// ∏ᵢ MillerLoop(Pᵢ, Qᵢ) = +// ∏ᵢ { fᵢ_{6x₀+2,Qᵢ}(Pᵢ) · ℓᵢ_{[6x₀+2]Qᵢ,π(Qᵢ)}(Pᵢ) · ℓᵢ_{[6x₀+2]Qᵢ+π(Qᵢ),-π²(Qᵢ)}(Pᵢ) } func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { n := len(P) if n == 0 || n != len(Q) { @@ -145,50 +139,125 @@ func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { qNeg[k].Neg(&q[k]) } - var l, l0 lineEvaluation - var tmp, result GT + var result GT result.SetOne() + var l2, l1 lineEvaluation + var prodLines [5]E2 + + // Compute ∏ᵢ { fᵢ_{6x₀+2,Q}(P) } + if n >= 1 { + // i = 64, separately to avoid an E12 Square + // (Square(res) = 1² = 1) + // loopCounter[64] = 0 + // k = 0, separately to avoid MulBy034 (res × ℓ) + // (assign line to res) + + // qProj[0] ← 2qProj[0] and l1 the tangent ℓ passing 2qProj[0] + qProj[0].doubleStep(&l1) + // line evaluation at P[0] (assign) + result.C0.B0.MulByElement(&l1.r0, &p[0].Y) + result.C1.B0.MulByElement(&l1.r1, &p[0].X) + result.C1.B1.Set(&l1.r2) + } + + if n >= 2 { + // k = 1, separately to avoid MulBy034 (res × ℓ) + // (res is also a line at this point, so we use Mul034By034 ℓ × ℓ) + + // qProj[1] ← 2qProj[1] and l1 the tangent ℓ passing 2qProj[1] + qProj[1].doubleStep(&l1) + // line evaluation at P[1] + l1.r0.MulByElement(&l1.r0, &p[1].Y) + l1.r1.MulByElement(&l1.r1, &p[1].X) + // ℓ × res + prodLines = fptower.Mul034By034(&l1.r0, &l1.r1, &l1.r2, &result.C0.B0, &result.C1.B0, &result.C1.B1) + result.C0.B0 = prodLines[0] + result.C0.B1 = prodLines[1] + result.C0.B2 = prodLines[2] + result.C1.B0 = prodLines[3] + result.C1.B1 = prodLines[4] + } - // i == len(loopCounter) - 2 + // k >= 2 + for k := 2; k < n; k++ { + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] + l1.r0.MulByElement(&l1.r0, &p[k].Y) + l1.r1.MulByElement(&l1.r1, &p[k].X) + // ℓ × res + result.MulBy034(&l1.r0, &l1.r1, &l1.r2) + } + + // i = 63, separately to avoid a doubleStep (loopCounter[63]=-1) + // (at this point qProj = 2Q, so 2qProj-Q=3Q is equivalent to qProj+Q=3Q + // this means doubleStep followed by an addMixedStep is equivalent to an + // addMixedStep here) + + result.Square(&result) for k := 0; k < n; k++ { - qProj[k].DoubleStep(&l) - // line evaluation - l.r0.MulByElement(&l.r0, &p[k].Y) - l.r1.MulByElement(&l.r1, &p[k].X) - result.MulBy034(&l.r0, &l.r1, &l.r2) + // l2 the line passing qProj[k] and -Q + // (avoids a point addition: qProj[k]-Q) + qProj[k].lineCompute(&l2, &qNeg[k]) + // line evaluation at P[k] + l2.r0.MulByElement(&l2.r0, &p[k].Y) + l2.r1.MulByElement(&l2.r1, &p[k].X) + // qProj[k] ← qProj[k]+Q[k] and + // l1 the line ℓ passing qProj[k] and Q[k] + qProj[k].addMixedStep(&l1, &q[k]) + // line evaluation at P[k] + l1.r0.MulByElement(&l1.r0, &p[k].Y) + l1.r1.MulByElement(&l1.r1, &p[k].X) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) } - for i := len(loopCounter) - 3; i >= 0; i-- { + // i <= 62 + for i := len(loopCounter) - 4; i >= 0; i-- { + // mutualize the square among n Miller loops // (∏ᵢfᵢ)² result.Square(&result) for k := 0; k < n; k++ { - qProj[k].DoubleStep(&l) - // line evaluation - l.r0.MulByElement(&l.r0, &p[k].Y) - l.r1.MulByElement(&l.r1, &p[k].X) + // qProj[k] ← 2qProj[k] and l1 the tangent ℓ passing 2qProj[k] + qProj[k].doubleStep(&l1) + // line evaluation at P[k] + l1.r0.MulByElement(&l1.r0, &p[k].Y) + l1.r1.MulByElement(&l1.r1, &p[k].X) if loopCounter[i] == 1 { - qProj[k].AddMixedStep(&l0, &q[k]) - // line evaluation - l0.r0.MulByElement(&l0.r0, &p[k].Y) - l0.r1.MulByElement(&l0.r1, &p[k].X) - tmp.Mul034by034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &tmp) + // qProj[k] ← qProj[k]+Q[k] and + // l2 the line ℓ passing qProj[k] and Q[k] + qProj[k].addMixedStep(&l2, &q[k]) + // line evaluation at P[k] + l2.r0.MulByElement(&l2.r0, &p[k].Y) + l2.r1.MulByElement(&l2.r1, &p[k].X) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) } else if loopCounter[i] == -1 { - qProj[k].AddMixedStep(&l0, &qNeg[k]) - // line evaluation - l0.r0.MulByElement(&l0.r0, &p[k].Y) - l0.r1.MulByElement(&l0.r1, &p[k].X) - tmp.Mul034by034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &tmp) + // qProj[k] ← qProj[k]-Q[k] and + // l2 the line ℓ passing qProj[k] and -Q[k] + qProj[k].addMixedStep(&l2, &qNeg[k]) + // line evaluation at P[k] + l2.r0.MulByElement(&l2.r0, &p[k].Y) + l2.r1.MulByElement(&l2.r1, &p[k].X) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) } else { - result.MulBy034(&l.r0, &l.r1, &l.r2) + // ℓ × res + result.MulBy034(&l1.r0, &l1.r1, &l1.r2) } } } + // Compute ∏ᵢ { ℓᵢ_{[6x₀+2]Q,π(Q)}(P) · ℓᵢ_{[6x₀+2]Q+π(Q),-π²(Q)}(P) } var Q1, Q2 G2Affine for k := 0; k < n; k++ { //Q1 = π(Q) @@ -199,23 +268,32 @@ func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { Q2.X.MulByNonResidue2Power2(&q[k].X) Q2.Y.MulByNonResidue2Power3(&q[k].Y).Neg(&Q2.Y) - qProj[k].AddMixedStep(&l0, &Q1) - l0.r0.MulByElement(&l0.r0, &p[k].Y) - l0.r1.MulByElement(&l0.r1, &p[k].X) - - qProj[k].AddMixedStep(&l, &Q2) - l.r0.MulByElement(&l.r0, &p[k].Y) - l.r1.MulByElement(&l.r1, &p[k].X) - tmp.Mul034by034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &tmp) + // qProj[k] ← qProj[k]+π(Q) and + // l1 the line passing qProj[k] and π(Q) + qProj[k].addMixedStep(&l2, &Q1) + // line evaluation at P[k] + l2.r0.MulByElement(&l2.r0, &p[k].Y) + l2.r1.MulByElement(&l2.r1, &p[k].X) + + // l2 the line passing qProj[k] and -π²(Q) + // (avoids a point addition: qProj[k]-π²(Q)) + qProj[k].lineCompute(&l1, &Q2) + // line evaluation at P[k] + l1.r0.MulByElement(&l1.r0, &p[k].Y) + l1.r1.MulByElement(&l1.r1, &p[k].X) + + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l1.r0, &l1.r1, &l1.r2, &l2.r0, &l2.r1, &l2.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) } return result, nil } -// DoubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop +// doubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g2Proj) DoubleStep(evaluations *lineEvaluation) { +func (p *g2Proj) doubleStep(evaluations *lineEvaluation) { // get some Element from our pool var t1, A, B, C, D, E, EE, F, G, H, I, J, K fptower.E2 @@ -254,9 +332,9 @@ func (p *g2Proj) DoubleStep(evaluations *lineEvaluation) { evaluations.r2.Set(&I) } -// AddMixedStep point addition in Mixed Homogenous projective and Affine coordinates +// addMixedStep point addition in Mixed Homogenous projective and Affine coordinates // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g2Proj) AddMixedStep(evaluations *lineEvaluation, a *G2Affine) { +func (p *g2Proj) addMixedStep(evaluations *lineEvaluation, a *G2Affine) { // get some Element from our pool var Y2Z1, X2Z1, O, L, C, D, E, F, G, H, t0, t1, t2, J fptower.E2 @@ -290,3 +368,23 @@ func (p *g2Proj) AddMixedStep(evaluations *lineEvaluation, a *G2Affine) { evaluations.r1.Neg(&O) evaluations.r2.Set(&J) } + +// lineCompute computes the line through p in Homogenous projective coordinates +// and a in affine coordinates. It does not compute the resulting point p+a. +func (p *g2Proj) lineCompute(evaluations *lineEvaluation, a *G2Affine) { + + // get some Element from our pool + var Y2Z1, X2Z1, O, L, t2, J fptower.E2 + Y2Z1.Mul(&a.Y, &p.z) + O.Sub(&p.y, &Y2Z1) + X2Z1.Mul(&a.X, &p.z) + L.Sub(&p.x, &X2Z1) + t2.Mul(&L, &a.Y) + J.Mul(&a.X, &O). + Sub(&J, &t2) + + // Line evaluation + evaluations.r0.Set(&L) + evaluations.r1.Neg(&O) + evaluations.r2.Set(&J) +} diff --git a/ecc/bw6-633/bw6-633.go b/ecc/bw6-633/bw6-633.go index 9fb439325e..b34f6c2125 100644 --- a/ecc/bw6-633/bw6-633.go +++ b/ecc/bw6-633/bw6-633.go @@ -38,7 +38,8 @@ import ( // ID BW6_633 ID const ID = ecc.BW6_633 -// bCurveCoeff b coeff of the curve Y²=X³+b +// aCurveCoeff is the a coefficients of the curve Y²=X³+ax+b +var aCurveCoeff fp.Element var bCurveCoeff fp.Element // bTwistCurveCoeff b coeff of the twist (defined over 𝔽p) curve @@ -76,7 +77,7 @@ var glvBasis ecc.Lattice var xGen big.Int func init() { - + aCurveCoeff.SetUint64(0) bCurveCoeff.SetUint64(4) bTwistCurveCoeff.SetUint64(8) // M-twist @@ -125,3 +126,8 @@ func Generators() (g1Jac G1Jac, g2Jac G2Jac, g1Aff G1Affine, g2Aff G2Affine) { g2Jac = g2Gen return } + +// CurveCoefficients returns the a, b coefficients of the curve equation. +func CurveCoefficients() (a, b fp.Element) { + return aCurveCoeff, bCurveCoeff +} diff --git a/ecc/bw6-633/ecdsa/ecdsa.go b/ecc/bw6-633/ecdsa/ecdsa.go index f264a1e479..c629b66fac 100644 --- a/ecc/bw6-633/ecdsa/ecdsa.go +++ b/ecc/bw6-633/ecdsa/ecdsa.go @@ -22,7 +22,6 @@ import ( "crypto/rand" "crypto/sha512" "crypto/subtle" - "errors" "hash" "io" "math/big" @@ -33,8 +32,6 @@ import ( "github.com/consensys/gnark-crypto/signature" ) -var errInvalidSig = errors.New("invalid signature") - const ( sizeFr = fr.Bytes sizeFp = fp.Bytes @@ -213,6 +210,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) kInv.ModInverse(k, order) P.X.BigInt(r) + r.Mod(r, order) if r.Sign() != 0 { break diff --git a/ecc/bw6-633/fp/element.go b/ecc/bw6-633/fp/element.go index 0fd0883ab8..ee9f329c94 100644 --- a/ecc/bw6-633/fp/element.go +++ b/ecc/bw6-633/fp/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -1220,12 +1221,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -1235,7 +1236,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bw6-633/fr/element.go b/ecc/bw6-633/fr/element.go index a2a8c3efb5..d1fd40b5c2 100644 --- a/ecc/bw6-633/fr/element.go +++ b/ecc/bw6-633/fr/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -765,12 +766,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -780,7 +781,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bw6-633/fr/fft/domain.go b/ecc/bw6-633/fr/fft/domain.go index 1af930fd75..ecb87f941a 100644 --- a/ecc/bw6-633/fr/fft/domain.go +++ b/ecc/bw6-633/fr/fft/domain.go @@ -63,30 +63,27 @@ type Domain struct { // NewDomain returns a subgroup with a power of 2 cardinality // cardinality >= m -func NewDomain(m uint64) *Domain { +// shift: when specified, it's the element by which the set of root of unity is shifted. +func NewDomain(m uint64, shift ...fr.Element) *Domain { domain := &Domain{} x := ecc.NextPowerOfTwo(m) domain.Cardinality = uint64(x) // generator of the largest 2-adic subgroup - var rootOfUnity fr.Element - rootOfUnity.SetString("4991787701895089137426454739366935169846548798279261157172811661565882460884369603588700158257") - const maxOrderRoot uint64 = 20 domain.FrMultiplicativeGen.SetUint64(13) + if len(shift) != 0 { + domain.FrMultiplicativeGen.Set(&shift[0]) + } domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen) - // find generator for Z/2^(log(m))Z - logx := uint64(bits.TrailingZeros64(x)) - if logx > maxOrderRoot { - panic(fmt.Sprintf("m (%d) is too big: the required root of unity does not exist", m)) + var err error + domain.Generator, err = Generator(m) + if err != nil { + panic(err) } - - // Generator = FinerGenerator^2 has order x - expo := uint64(1 << (maxOrderRoot - logx)) - domain.Generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x domain.GeneratorInv.Inverse(&domain.Generator) domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv) @@ -99,6 +96,28 @@ func NewDomain(m uint64) *Domain { return domain } +// Generator returns a generator for Z/2^(log(m))Z +// or an error if m is too big (required root of unity doesn't exist) +func Generator(m uint64) (fr.Element, error) { + x := ecc.NextPowerOfTwo(m) + + var rootOfUnity fr.Element + + rootOfUnity.SetString("4991787701895089137426454739366935169846548798279261157172811661565882460884369603588700158257") + const maxOrderRoot uint64 = 20 + + // find generator for Z/2^(log(m))Z + logx := uint64(bits.TrailingZeros64(x)) + if logx > maxOrderRoot { + return fr.Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m) + } + + expo := uint64(1 << (maxOrderRoot - logx)) + var generator fr.Element + generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x + return generator, nil +} + func (d *Domain) reverseCosetTables() { d.CosetTableReversed = make([]fr.Element, d.Cardinality) d.CosetTableInvReversed = make([]fr.Element, d.Cardinality) diff --git a/ecc/bw6-633/fr/fft/fft.go b/ecc/bw6-633/fr/fft/fft.go index 42e001930c..97a1a00d8c 100644 --- a/ecc/bw6-633/fr/fft/fft.go +++ b/ecc/bw6-633/fr/fft/fft.go @@ -18,7 +18,6 @@ package fft import ( "math/bits" - "runtime" "github.com/consensys/gnark-crypto/ecc" "github.com/consensys/gnark-crypto/internal/parallel" @@ -40,24 +39,18 @@ const butterflyThreshold = 16 // FFT computes (recursively) the discrete Fourier transform of a and stores the result in a // if decimation == DIT (decimation in time), the input must be in bit-reversed order // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order -// if coset if set, the FFT(a) returns the evaluation of a on a coset. -func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) { +func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option) { - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } + opt := options(opts...) // if coset != 0, scale by coset table - if _coset { + if opt.coset { scale := func(cosetTable []fr.Element) { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &cosetTable[i]) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableReversed) @@ -69,16 +62,16 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.Twiddles, 0, maxSplits, nil) + difFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.Twiddles, 0, maxSplits, nil) + ditFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } @@ -89,37 +82,31 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order // coset sets the shift of the fft (0 = no shift, standard fft) // len(a) must be a power of 2, and w must be a len(a)th root of unity in field F. -func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset ...bool) { - - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } +func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...Option) { + opt := options(opts...) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } // scale by CardinalityInv - if !_coset { + if !opt.coset { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) return } @@ -129,7 +116,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. a[i].Mul(&a[i], &cosetTable[i]). Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableInv) @@ -141,7 +128,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. } -func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -159,7 +146,7 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for i := start; i < end; i++ { fr.Butterfly(&a[i], &a[i+m]) @@ -182,17 +169,17 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon nextStage := stage + 1 if stage < maxSplits { chDone := make(chan struct{}, 1) - go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone) - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone, nbTasks) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - difFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + difFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } } -func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -210,12 +197,12 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon if stage < maxSplits { // that's the only time we fire go routines chDone := make(chan struct{}, 1) - go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone) - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone, nbTasks) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } @@ -223,7 +210,7 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for k := start; k < end; k++ { a[k+m].Mul(&a[k+m], &twiddles[stage][k]) diff --git a/ecc/bw6-633/fr/fft/fft_test.go b/ecc/bw6-633/fr/fft/fft_test.go index 19953549fe..b4f8ecd4a7 100644 --- a/ecc/bw6-633/fr/fft/fft_test.go +++ b/ecc/bw6-633/fr/fft/fft_test.go @@ -52,7 +52,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIF) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -79,7 +79,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIF, OnCoset()) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -108,7 +108,7 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFT(pol, DIT) sample := domainWithPrecompute.Generator sample.Exp(sample, big.NewInt(int64(ithpower))) @@ -134,8 +134,8 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) - domainWithPrecompute.FFTInverse(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIT) + domainWithPrecompute.FFTInverse(pol, DIF) BitReverse(pol) check := true @@ -163,8 +163,8 @@ func TestFFT(t *testing.T) { for i := 1; i <= nbCosets; i++ { BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, true) - domainWithPrecompute.FFTInverse(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) BitReverse(pol) for i := 0; i < len(pol); i++ { @@ -188,8 +188,8 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, false) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFTInverse(pol, DIF) + domainWithPrecompute.FFT(pol, DIT) check := true for i := 0; i < len(pol); i++ { @@ -211,14 +211,26 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, true) - domainWithPrecompute.FFT(pol, DIT, true) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) - check := true for i := 0; i < len(pol); i++ { - check = check && (pol[i] == backupPol[i]) + if !(pol[i].Equal(&backupPol[i])) { + return false + } } - return check + + // compute with nbTasks == 1 + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset(), WithNbTasks(1)) + domainWithPrecompute.FFT(pol, DIT, OnCoset(), WithNbTasks(1)) + + for i := 0; i < len(pol); i++ { + if !(pol[i].Equal(&backupPol[i])) { + return false + } + } + + return true }, )) @@ -265,14 +277,14 @@ func BenchmarkFFT(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, false) + domain.FFT(pol[:sizeDomain], DIT) } }) b.Run("fft 2**"+strconv.Itoa(i)+"bits (coset)", func(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, true) + domain.FFT(pol[:sizeDomain], DIT, OnCoset()) } }) } @@ -292,7 +304,7 @@ func BenchmarkFFTDITCosetReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIT, true) + domain.FFT(pol, DIT, OnCoset()) } } @@ -309,7 +321,7 @@ func BenchmarkFFTDIFReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIF, false) + domain.FFT(pol, DIF) } } diff --git a/ecc/bw6-633/fr/fft/options.go b/ecc/bw6-633/fr/fft/options.go new file mode 100644 index 0000000000..603b76f299 --- /dev/null +++ b/ecc/bw6-633/fr/fft/options.go @@ -0,0 +1,61 @@ +// Copyright 2020 ConsenSys Software Inc. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +// Code generated by consensys/gnark-crypto DO NOT EDIT + +package fft + +import "runtime" + +// Option defines option for altering the behavior of FFT methods. +// See the descriptions of functions returning instances of this type for +// particular options. +type Option func(*fftConfig) + +type fftConfig struct { + coset bool + nbTasks int +} + +// OnCoset if provided, FFT(a) returns the evaluation of a on a coset. +func OnCoset() Option { + return func(opt *fftConfig) { + opt.coset = true + } +} + +// WithNbTasks sets the max number of task (go routine) to spawn. Must be between 1 and 512. +func WithNbTasks(nbTasks int) Option { + if nbTasks < 1 { + nbTasks = 1 + } else if nbTasks > 512 { + nbTasks = 512 + } + return func(opt *fftConfig) { + opt.nbTasks = nbTasks + } +} + +// default options +func options(opts ...Option) fftConfig { + // apply options + opt := fftConfig{ + coset: false, + nbTasks: runtime.NumCPU(), + } + for _, option := range opts { + option(&opt) + } + return opt +} diff --git a/ecc/bw6-633/fr/iop/polynomial.go b/ecc/bw6-633/fr/iop/polynomial.go index 44f4710962..3c3a4d509c 100644 --- a/ecc/bw6-633/fr/iop/polynomial.go +++ b/ecc/bw6-633/fr/iop/polynomial.go @@ -146,11 +146,13 @@ func (p *Polynomial) Evaluate(x fr.Element) fr.Element { return p.polynomial.evaluate(x) } - // TODO find a way to retrieve the root properly instead of re generating the fft domain - d := fft.NewDomain(uint64(p.size)) var g fr.Element if p.shift <= 5 { - g = smallExp(d.Generator, p.shift) + gen, err := fft.Generator(uint64(p.size)) + if err != nil { + panic(err) + } + g = smallExp(gen, p.shift) x.Mul(&x, &g) return p.polynomial.evaluate(x) } @@ -288,11 +290,11 @@ func (p *Polynomial) ToLagrange(d *fft.Domain) *Polynomial { return p case lagrangeCosetRegular: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIT) case lagrangeCosetBitReverse: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIF) default: panic("unknown ID") @@ -317,10 +319,10 @@ func (p *Polynomial) ToCanonical(d *fft.Domain) *Polynomial { d.FFTInverse((*p.coefficients), fft.DIT) case lagrangeCosetRegular: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetBitReverse: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) default: panic("unknown ID") } @@ -342,18 +344,18 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial { switch id { case canonicalRegular: p.Layout = BitReverse - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case canonicalBitReverse: p.Layout = Regular - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeRegular: p.Layout = Regular d.FFTInverse((*p.coefficients), fft.DIF) - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeBitReverse: p.Layout = BitReverse d.FFTInverse((*p.coefficients), fft.DIT) - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetRegular, lagrangeCosetBitReverse: return p default: diff --git a/ecc/bw6-633/fr/iop/polynomial_test.go b/ecc/bw6-633/fr/iop/polynomial_test.go index bfc3ad47b1..08c15ac6bf 100644 --- a/ecc/bw6-633/fr/iop/polynomial_test.go +++ b/ecc/bw6-633/fr/iop/polynomial_test.go @@ -240,7 +240,7 @@ func fromLagrange4(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = Regular d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) return r } @@ -250,7 +250,7 @@ func fromLagrange5(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = BitReverse d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) fft.BitReverse(r.Coefficients()) return r } @@ -438,7 +438,7 @@ func fromCanonical4(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = Regular - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -448,7 +448,7 @@ func fromCanonical5(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = BitReverse - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -566,7 +566,7 @@ func fromLagrangeCoset0(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -576,7 +576,7 @@ func fromLagrangeCoset1(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -585,7 +585,7 @@ func fromLagrangeCoset2(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) return _p } @@ -595,7 +595,7 @@ func fromLagrangeCoset3(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) fft.BitReverse(_p.Coefficients()) return _p diff --git a/ecc/bw6-633/fr/iop/ratios.go b/ecc/bw6-633/fr/iop/ratios.go index 0a3417f9de..bd718f08b1 100644 --- a/ecc/bw6-633/fr/iop/ratios.go +++ b/ecc/bw6-633/fr/iop/ratios.go @@ -18,7 +18,10 @@ package iop import ( "errors" + "math/big" "math/bits" + "runtime" + "sync" "github.com/consensys/gnark-crypto/internal/parallel" @@ -213,16 +216,38 @@ func BuildRatioCopyConstraint( } }) - for i := 0; i < n-1; i++ { - coeffs[i+1].Mul(&coeffs[i+1], &coeffs[i]) - t[i+1].Mul(&t[i+1], &t[i]) + chCoeffs := make(chan struct{}, 1) + go func() { + for i := 2; i < n; i++ { + // ignoring coeffs[0] + coeffs[i].Mul(&coeffs[i], &coeffs[i-1]) + } + close(chCoeffs) + }() + + for i := 2; i < n; i++ { + // ignoring t[0] + t[i].Mul(&t[i], &t[i-1]) } + <-chCoeffs - t = fr.BatchInvert(t) - for i := 1; i < n; i++ { - coeffs[i].Mul(&coeffs[i], &t[i]) + // rough ratio inverse to mul; see if it makes sense to parallelize the batch inverse. + const ratioInvMul = 1000 / 17 + nbTasks := runtime.NumCPU() + if ratio := n / ratioInvMul; ratio < nbTasks { + nbTasks = ratio } + parallel.Execute(n-1, func(start, end int) { + // ignoring t[0] and coeff[0] + start++ + end++ + tInv := fr.BatchInvert(t[start:end]) + for i := start; i < end; i++ { + coeffs[i].Mul(&coeffs[i], &tInv[i-start]) + } + }, nbTasks) + res := NewPolynomial(&coeffs, expectedForm) // at this stage the result is in Lagrange form, Regular layout putInExpectedFormFromLagrangeRegular(res, domain, expectedForm) @@ -245,7 +270,7 @@ func putInExpectedFormFromLagrangeRegular(p *Polynomial, domain *fft.Domain, exp if expectedForm.Basis == LagrangeCoset { domain.FFTInverse(p.Coefficients(), fft.DIF) - domain.FFT(p.Coefficients(), fft.DIT, true) + domain.FFT(p.Coefficients(), fft.DIT, fft.OnCoset()) if expectedForm.Layout == BitReverse { fft.BitReverse(p.Coefficients()) } @@ -308,16 +333,42 @@ func getSupportIdentityPermutation(nbCopies int, domain *fft.Domain) []fr.Elemen res := make([]fr.Element, uint64(nbCopies)*domain.Cardinality) sizePoly := int(domain.Cardinality) - res[0].SetOne() - for i := 0; i < sizePoly-1; i++ { + // len(domain.Twiddle) == sizePoly / 2 + copy(res, domain.Twiddles[0]) + // remaining ones. + for i := (sizePoly / 2) - 1; i < sizePoly-1; i++ { res[i+1].Mul(&res[i], &domain.Generator) } + if nbCopies <= 1 { + return res + } + var wg sync.WaitGroup + wg.Add(nbCopies - 1) for i := 1; i < nbCopies; i++ { - copy(res[i*sizePoly:], res[(i-1)*sizePoly:i*int(domain.Cardinality)]) - for j := 0; j < sizePoly; j++ { - res[i*sizePoly+j].Mul(&res[i*sizePoly+j], &domain.FrMultiplicativeGen) + i := i + + var coset fr.Element + if i == 1 { + coset = domain.FrMultiplicativeGen + } else { + if len(domain.CosetTable) > i { + coset = domain.CosetTable[i] + } else { + coset.Exp(domain.FrMultiplicativeGen, big.NewInt(int64(i))) + } } + + go func() { + parallel.Execute(sizePoly, func(start, end int) { + for j := start; j < end; j++ { + res[i*sizePoly+j].Mul(&res[j], &coset) + } + }, (runtime.NumCPU()/(nbCopies-1))+1) + wg.Done() + }() } + wg.Wait() + return res } diff --git a/ecc/bw6-633/fr/kzg/kzg.go b/ecc/bw6-633/fr/kzg/kzg.go index e0dc1e66f9..dfb5565a13 100644 --- a/ecc/bw6-633/fr/kzg/kzg.go +++ b/ecc/bw6-633/fr/kzg/kzg.go @@ -26,6 +26,8 @@ import ( "github.com/consensys/gnark-crypto/ecc/bw6-633" "github.com/consensys/gnark-crypto/ecc/bw6-633/fr" "github.com/consensys/gnark-crypto/fiat-shamir" + + "github.com/consensys/gnark-crypto/internal/parallel" ) var ( @@ -275,14 +277,21 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr // gamma n in parallel, before reducing into foldedPolynomials foldedPolynomials := make([]fr.Element, largestPoly) copy(foldedPolynomials, polynomials[0]) - acc := gamma - var pj fr.Element + gammas := make([]fr.Element, len(polynomials)) + gammas[0] = gamma for i := 1; i < len(polynomials); i++ { - for j := 0; j < len(polynomials[i]); j++ { - pj.Mul(&polynomials[i][j], &acc) - foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) - } - acc.Mul(&acc, &gamma) + gammas[i].Mul(&gammas[i-1], &gamma) + } + + for i := 1; i < len(polynomials); i++ { + i := i + parallel.Execute(len(polynomials[i]), func(start, end int) { + var pj fr.Element + for j := start; j < end; j++ { + pj.Mul(&polynomials[i][j], &gammas[i-1]) + foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) + } + }) } // compute H diff --git a/ecc/bw6-633/fr/permutation/permutation.go b/ecc/bw6-633/fr/permutation/permutation.go index d773b5772f..98f772f083 100644 --- a/ecc/bw6-633/fr/permutation/permutation.go +++ b/ecc/bw6-633/fr/permutation/permutation.go @@ -191,15 +191,15 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } lz := make([]fr.Element, s) copy(lz, cz) - d.FFT(lz, fft.DIF, true) + d.FFT(lz, fft.DIF, fft.OnCoset()) // compute the first part of the numerator lt1 := make([]fr.Element, s) lt2 := make([]fr.Element, s) copy(lt1, ct1) copy(lt2, ct2) - d.FFT(lt1, fft.DIF, true) - d.FFT(lt2, fft.DIF, true) + d.FFT(lt1, fft.DIF, fft.OnCoset()) + d.FFT(lt2, fft.DIF, fft.OnCoset()) lsNumFirstPart := evaluateFirstPartNumReverse(lt1, lt2, lz, epsilon) // compute second part of the numerator @@ -222,7 +222,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } // get the quotient and commit it - d.FFTInverse(lsNum, fft.DIT, true) + d.FFTInverse(lsNum, fft.DIT, fft.OnCoset()) proof.q, err = kzg.Commit(lsNum, srs) if err != nil { return proof, err diff --git a/ecc/bw6-633/fr/plookup/vector.go b/ecc/bw6-633/fr/plookup/vector.go index f716ac2df7..1495b4e456 100644 --- a/ecc/bw6-633/fr/plookup/vector.go +++ b/ecc/bw6-633/fr/plookup/vector.go @@ -340,7 +340,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element Mul(&res[_i], &numLn[i%2]) } - domainBig.FFTInverse(res, fft.DIT, true) + domainBig.FFTInverse(res, fft.DIT, fft.OnCoset()) return res } @@ -476,11 +476,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) copy(_lh2, ch2) copy(_lt, ct) copy(_lf, cf) - domainBig.FFT(_lz, fft.DIF, true) - domainBig.FFT(_lh1, fft.DIF, true) - domainBig.FFT(_lh2, fft.DIF, true) - domainBig.FFT(_lt, fft.DIF, true) - domainBig.FFT(_lf, fft.DIF, true) + domainBig.FFT(_lz, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh1, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh2, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lt, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lf, fft.DIF, fft.OnCoset()) // compute h lh := evaluateNumBitReversed(_lz, _lh1, _lh2, _lt, _lf, beta, gamma, domainBig) diff --git a/ecc/bw6-633/internal/fptower/e6_pairing.go b/ecc/bw6-633/internal/fptower/e6_pairing.go index 691e862bc1..661a755191 100644 --- a/ecc/bw6-633/internal/fptower/e6_pairing.go +++ b/ecc/bw6-633/internal/fptower/e6_pairing.go @@ -57,8 +57,8 @@ func (z *E6) MulBy034(c0, c3, c4 *fp.Element) *E6 { } // Mul034By034 multiplication of sparse element (c0,0,0,c3,c4,0) by sparse element (d0,0,0,d3,d4,0) -func (z *E6) Mul034By034(d0, d3, d4, c0, c3, c4 *fp.Element) *E6 { - var tmp, x0, x3, x4, x04, x03, x34 fp.Element +func Mul034By034(d0, d3, d4, c0, c3, c4 *fp.Element) [5]fp.Element { + var z00, tmp, x0, x3, x4, x04, x03, x34 fp.Element x0.Mul(c0, d0) x3.Mul(c3, d3) x4.Mul(c4, d4) @@ -78,13 +78,30 @@ func (z *E6) Mul034By034(d0, d3, d4, c0, c3, c4 *fp.Element) *E6 { Sub(&x34, &x3). Sub(&x34, &x4) - z.B0.A0.MulByNonResidue(&x4). - Add(&z.B0.A0, &x0) - z.B0.A1.Set(&x3) - z.B0.A2.Set(&x34) - z.B1.A0.Set(&x03) - z.B1.A1.Set(&x04) - z.B1.A2.SetZero() + z00.MulByNonResidue(&x4). + Add(&z00, &x0) + + return [5]fp.Element{z00, x3, x34, x03, x04} +} + +// MulBy01234 multiplies z by an E12 sparse element of the form (x0, x1, x2, x3, x4, 0) +func (z *E6) MulBy01234(x *[5]fp.Element) *E6 { + var c1, a, b, c, z0, z1 E3 + c0 := &E3{A0: x[0], A1: x[1], A2: x[2]} + c1.A0 = x[3] + c1.A1 = x[4] + a.Add(&z.B0, &z.B1) + b.Add(c0, &c1) + a.Mul(&a, &b) + b.Mul(&z.B0, c0) + c.Set(&z.B1).MulBy01(&x[3], &x[4]) + z1.Sub(&a, &b) + z1.Sub(&z1, &c) + z0.MulByNonResidue(&c) + z0.Add(&z0, &b) + + z.B0 = z0 + z.B1 = z1 return z } diff --git a/ecc/bw6-633/marshal.go b/ecc/bw6-633/marshal.go index 78c1df948e..4325dbc38d 100644 --- a/ecc/bw6-633/marshal.go +++ b/ecc/bw6-633/marshal.go @@ -50,6 +50,8 @@ const ( // SizeOfGT represents the size in bytes that a GT element need in binary form const SizeOfGT = fptower.SizeOfGT +var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding") + // Encoder writes bw6-633 object values to an output stream type Encoder struct { w io.Writer @@ -365,6 +367,19 @@ func NoSubgroupChecks() func(*Decoder) { } } +// isZeroed checks that the provided bytes are at 0 +func isZeroed(firstByte byte, buf []byte) bool { + if firstByte != 0 { + return false + } + for _, b := range buf { + if b != 0 { + return false + } + } + return true +} + func (enc *Encoder) encode(v interface{}) (err error) { rv := reflect.ValueOf(v) if v == nil || (rv.Kind() == reflect.Ptr && rv.IsNil()) { @@ -674,13 +689,19 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineUncompressed, nil @@ -796,9 +817,12 @@ func (p *G1Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } @@ -921,13 +945,19 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineUncompressed, nil @@ -1043,9 +1073,12 @@ func (p *G2Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } diff --git a/ecc/bw6-633/pairing.go b/ecc/bw6-633/pairing.go index 337b104b51..27fb49be91 100644 --- a/ecc/bw6-633/pairing.go +++ b/ecc/bw6-633/pairing.go @@ -214,116 +214,221 @@ func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { // l_{p0,p1}(q) pProj01[k].Set(&pProj0[k]) - pProj01[k].AddMixedStep(&l01[k], &p1[k]) + pProj01[k].addMixedStep(&l01[k], &p1[k]) l01[k].r1.Mul(&l01[k].r1, &q[k].X) l01[k].r0.Mul(&l01[k].r0, &q[k].Y) // l_{-p0,p1}(q) pProj10[k].Neg(&pProj0[k]) - pProj10[k].AddMixedStep(&l10[k], &p1[k]) + pProj10[k].addMixedStep(&l10[k], &p1[k]) l10[k].r1.Mul(&l10[k].r1, &q[k].X) l10[k].r0.Mul(&l10[k].r0, &q[k].Y) } p01 := BatchProjectiveToAffineG1(pProj01) p10 := BatchProjectiveToAffineG1(pProj10) - // f_{a0+\lambda*a1,P}(Q) - var result, ss GT + // f_{a0+λ*a1,P}(Q) + var result GT result.SetOne() var l, l0 lineEvaluation + var prodLines [5]fp.Element var j int8 - // i = len(loopCounter)-2 - for k := 0; k < n; k++ { - pProj0[k].DoubleStep(&l0) + if n >= 1 { + // i = len(loopCounter0) - 2, separately to avoid an E12 Square + // (Square(res) = 1² = 1) + // j = 0 + // k = 0, separately to avoid MulBy034 (res × ℓ) + // (assign line to res) + + // pProj0[0] ← 2pProj0[0] and l0 the tangent ℓ passing 2pProj0[0] + pProj0[0].doubleStep(&l0) + // line evaluation at Q[0] (assign) + result.B1.A0.Mul(&l0.r1, &q[0].X) + result.B0.A0.Mul(&l0.r0, &q[0].Y) + result.B1.A1.Set(&l0.r2) + } + + // k = 1 + if n >= 2 { + // pProj0[1] ← 2pProj0[1] and l0 the tangent ℓ passing 2pProj0[1] + pProj0[1].doubleStep(&l0) + // line evaluation at Q[0] + l0.r1.Mul(&l0.r1, &q[1].X) + l0.r0.Mul(&l0.r0, &q[1].Y) + // ℓ × res + prodLines = fptower.Mul034By034(&l0.r0, &l0.r1, &l0.r2, &result.B0.A0, &result.B1.A0, &result.B1.A1) + result.B0.A0 = prodLines[0] + result.B0.A1 = prodLines[1] + result.B0.A2 = prodLines[2] + result.B1.A0 = prodLines[3] + result.B1.A1 = prodLines[4] + } + + // k >= 2 + for k := 2; k < n; k++ { + // pProj0[1] ← 2pProj0[1] and l0 the tangent ℓ passing 2pProj0[1] + pProj0[k].doubleStep(&l0) + // line evaluation at Q[k] l0.r1.Mul(&l0.r1, &q[k].X) l0.r0.Mul(&l0.r0, &q[k].Y) + // ℓ × res result.MulBy034(&l0.r0, &l0.r1, &l0.r2) } var tmp G1Affine - for i := len(loopCounter0) - 3; i >= 0; i-- { + for i := len(loopCounter0) - 3; i >= 1; i-- { + // (∏ᵢfᵢ)² + // mutualize the square among n Miller loops result.Square(&result) j = loopCounter0[i]*3 + loopCounter1[i] for k := 0; k < n; k++ { - pProj0[k].DoubleStep(&l0) + // pProj0[1] ← 2pProj0[1] and l0 the tangent ℓ passing 2pProj0[1] + pProj0[k].doubleStep(&l0) + // line evaluation at Q[k] l0.r1.Mul(&l0.r1, &q[k].X) l0.r0.Mul(&l0.r0, &q[k].Y) switch j { case -4: tmp.Neg(&p01[k]) - pProj0[k].AddMixedStep(&l, &tmp) + // pProj0[k] ← pProj0[k]-p01[k] and + // l the line ℓ passing pProj0[k] and -p01[k] + pProj0[k].addMixedStep(&l, &tmp) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) - result.MulBy034(&l0.r0, &l0.r1, &l0.r2). - Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) + // ℓ × res + result.MulBy034(&l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case -3: tmp.Neg(&p1[k]) - pProj0[k].AddMixedStep(&l, &tmp) + // pProj0[k] ← pProj0[k]-p1[k] and + // l the line ℓ passing pProj0[k] and -p1[k] + pProj0[k].addMixedStep(&l, &tmp) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case -2: - pProj0[k].AddMixedStep(&l, &p10[k]) + // pProj0[k] ← pProj0[k]+p10[k] and + // l the line ℓ passing pProj0[k] and p10[k] + pProj0[k].addMixedStep(&l, &p10[k]) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l10[k].r0, &l10[k].r1, &l10[k].r2) - result.MulBy034(&l0.r0, &l0.r1, &l0.r2). - Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) + // ℓ × res + result.MulBy034(&l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case -1: tmp.Neg(&p0[k]) - pProj0[k].AddMixedStep(&l, &tmp) + // pProj0[k] ← pProj0[k]-p0[k] and + // l the line ℓ passing pProj0[k] and -p0[k] + pProj0[k].addMixedStep(&l, &tmp) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case 0: + // ℓ × res result.MulBy034(&l0.r0, &l0.r1, &l0.r2) case 1: - pProj0[k].AddMixedStep(&l, &p0[k]) + // pProj0[k] ← pProj0[k]+p0[k] and + // l the line ℓ passing pProj0[k] and p0[k] + pProj0[k].addMixedStep(&l, &p0[k]) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case 2: tmp.Neg(&p10[k]) - pProj0[k].AddMixedStep(&l, &tmp) + // pProj0[k] ← pProj0[k]-p10[k] and + // l the line ℓ passing pProj0[k] and -p10[k] + pProj0[k].addMixedStep(&l, &tmp) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l10[k].r0, &l10[k].r1, &l10[k].r2) - result.MulBy034(&l0.r0, &l0.r1, &l0.r2). - Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) + // ℓ × res + result.MulBy034(&l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case 3: - pProj0[k].AddMixedStep(&l, &p1[k]) + // pProj0[k] ← pProj0[k]+p1[k] and + // l the line ℓ passing pProj0[k] and p1[k] + pProj0[k].addMixedStep(&l, &p1[k]) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &ss) + // (ℓ × ℓ) × res + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case 4: - pProj0[k].AddMixedStep(&l, &p01[k]) + // pProj0[k] ← pProj0[k]+p01[k] and + // l the line ℓ passing pProj0[k] and p01[k] + pProj0[k].addMixedStep(&l, &p01[k]) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) - result.MulBy034(&l0.r0, &l0.r1, &l0.r2). - Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) + // ℓ × res + result.MulBy034(&l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) default: return GT{}, errors.New("invalid loopCounter") } } } + // i = 0, separately to avoid a point addition + // j = 1 + result.Square(&result) + for k := 0; k < n; k++ { + // pProj0[k] ← 2pProj0[k] and l0 the tangent ℓ passing 2pProj0[k] + pProj0[k].doubleStep(&l0) + // line evaluation at Q[k] + l0.r1.Mul(&l0.r1, &q[k].X) + l0.r0.Mul(&l0.r0, &q[k].Y) + + // l the line passing pProj0[k] and p0 + pProj0[k].lineCompute(&l, &p0[k]) + // line evaluation at Q[k] + l.r1.Mul(&l.r1, &q[k].X) + l.r0.Mul(&l.r0, &q[k].Y) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) + } + return result, nil } -// DoubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop +// doubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g1Proj) DoubleStep(evaluations *lineEvaluation) { +func (p *g1Proj) doubleStep(evaluations *lineEvaluation) { // get some Element from our pool var t1, A, B, C, D, E, EE, F, G, H, I, J, K fp.Element @@ -366,9 +471,9 @@ func (p *g1Proj) DoubleStep(evaluations *lineEvaluation) { evaluations.r2.Set(&I) } -// AddMixedStep point addition in Mixed Homogenous projective and Affine coordinates +// addMixedStep point addition in Mixed Homogenous projective and Affine coordinates // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g1Proj) AddMixedStep(evaluations *lineEvaluation, a *G1Affine) { +func (p *g1Proj) addMixedStep(evaluations *lineEvaluation, a *G1Affine) { // get some Element from our pool var Y2Z1, X2Z1, O, L, C, D, E, F, G, H, t0, t1, t2, J fp.Element @@ -402,3 +507,23 @@ func (p *g1Proj) AddMixedStep(evaluations *lineEvaluation, a *G1Affine) { evaluations.r1.Neg(&O) evaluations.r2.Set(&J) } + +// lineCompute computes the line through p in Homogenous projective coordinates +// and a in affine coordinates. It does not compute the resulting point p+a. +func (p *g1Proj) lineCompute(evaluations *lineEvaluation, a *G1Affine) { + + // get some Element from our pool + var Y2Z1, X2Z1, O, L, t2, J fp.Element + Y2Z1.Mul(&a.Y, &p.z) + O.Sub(&p.y, &Y2Z1) + X2Z1.Mul(&a.X, &p.z) + L.Sub(&p.x, &X2Z1) + t2.Mul(&L, &a.Y) + J.Mul(&a.X, &O). + Sub(&J, &t2) + + // Line evaluation + evaluations.r0.Set(&L) + evaluations.r1.Neg(&O) + evaluations.r2.Set(&J) +} diff --git a/ecc/bw6-756/bw6-756.go b/ecc/bw6-756/bw6-756.go index 0204d7948a..6a1c71feda 100644 --- a/ecc/bw6-756/bw6-756.go +++ b/ecc/bw6-756/bw6-756.go @@ -38,7 +38,8 @@ import ( // ID BW6_756 ID const ID = ecc.BW6_756 -// bCurveCoeff b coeff of the curve Y²=X³+b +// aCurveCoeff is the a coefficients of the curve Y²=X³+ax+b +var aCurveCoeff fp.Element var bCurveCoeff fp.Element // bTwistCurveCoeff b coeff of the twist (defined over 𝔽p) curve @@ -76,7 +77,7 @@ var glvBasis ecc.Lattice var xGen big.Int func init() { - + aCurveCoeff.SetUint64(0) bCurveCoeff.SetOne() bTwistCurveCoeff.MulByNonResidue(&bCurveCoeff) @@ -124,3 +125,8 @@ func Generators() (g1Jac G1Jac, g2Jac G2Jac, g1Aff G1Affine, g2Aff G2Affine) { g2Jac = g2Gen return } + +// CurveCoefficients returns the a, b coefficients of the curve equation. +func CurveCoefficients() (a, b fp.Element) { + return aCurveCoeff, bCurveCoeff +} diff --git a/ecc/bw6-756/ecdsa/ecdsa.go b/ecc/bw6-756/ecdsa/ecdsa.go index 11c7725b5c..07b997a405 100644 --- a/ecc/bw6-756/ecdsa/ecdsa.go +++ b/ecc/bw6-756/ecdsa/ecdsa.go @@ -22,7 +22,6 @@ import ( "crypto/rand" "crypto/sha512" "crypto/subtle" - "errors" "hash" "io" "math/big" @@ -33,8 +32,6 @@ import ( "github.com/consensys/gnark-crypto/signature" ) -var errInvalidSig = errors.New("invalid signature") - const ( sizeFr = fr.Bytes sizeFp = fp.Bytes @@ -213,6 +210,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) kInv.ModInverse(k, order) P.X.BigInt(r) + r.Mod(r, order) if r.Sign() != 0 { break diff --git a/ecc/bw6-756/fp/element.go b/ecc/bw6-756/fp/element.go index ffe85b8d1b..ab7dcde2d7 100644 --- a/ecc/bw6-756/fp/element.go +++ b/ecc/bw6-756/fp/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -1444,12 +1445,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -1459,7 +1460,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bw6-756/fr/element.go b/ecc/bw6-756/fr/element.go index 6b23727b92..6f39091a26 100644 --- a/ecc/bw6-756/fr/element.go +++ b/ecc/bw6-756/fr/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -844,12 +845,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -859,7 +860,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bw6-756/fr/fft/domain.go b/ecc/bw6-756/fr/fft/domain.go index 2cf1957e97..015c1465e2 100644 --- a/ecc/bw6-756/fr/fft/domain.go +++ b/ecc/bw6-756/fr/fft/domain.go @@ -63,30 +63,27 @@ type Domain struct { // NewDomain returns a subgroup with a power of 2 cardinality // cardinality >= m -func NewDomain(m uint64) *Domain { +// shift: when specified, it's the element by which the set of root of unity is shifted. +func NewDomain(m uint64, shift ...fr.Element) *Domain { domain := &Domain{} x := ecc.NextPowerOfTwo(m) domain.Cardinality = uint64(x) // generator of the largest 2-adic subgroup - var rootOfUnity fr.Element - rootOfUnity.SetString("199251335866470442271346949249090720992237796757894062992204115206570647302191425225605716521843542790404563904580") - const maxOrderRoot uint64 = 41 domain.FrMultiplicativeGen.SetUint64(5) + if len(shift) != 0 { + domain.FrMultiplicativeGen.Set(&shift[0]) + } domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen) - // find generator for Z/2^(log(m))Z - logx := uint64(bits.TrailingZeros64(x)) - if logx > maxOrderRoot { - panic(fmt.Sprintf("m (%d) is too big: the required root of unity does not exist", m)) + var err error + domain.Generator, err = Generator(m) + if err != nil { + panic(err) } - - // Generator = FinerGenerator^2 has order x - expo := uint64(1 << (maxOrderRoot - logx)) - domain.Generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x domain.GeneratorInv.Inverse(&domain.Generator) domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv) @@ -99,6 +96,28 @@ func NewDomain(m uint64) *Domain { return domain } +// Generator returns a generator for Z/2^(log(m))Z +// or an error if m is too big (required root of unity doesn't exist) +func Generator(m uint64) (fr.Element, error) { + x := ecc.NextPowerOfTwo(m) + + var rootOfUnity fr.Element + + rootOfUnity.SetString("199251335866470442271346949249090720992237796757894062992204115206570647302191425225605716521843542790404563904580") + const maxOrderRoot uint64 = 41 + + // find generator for Z/2^(log(m))Z + logx := uint64(bits.TrailingZeros64(x)) + if logx > maxOrderRoot { + return fr.Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m) + } + + expo := uint64(1 << (maxOrderRoot - logx)) + var generator fr.Element + generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x + return generator, nil +} + func (d *Domain) reverseCosetTables() { d.CosetTableReversed = make([]fr.Element, d.Cardinality) d.CosetTableInvReversed = make([]fr.Element, d.Cardinality) diff --git a/ecc/bw6-756/fr/fft/fft.go b/ecc/bw6-756/fr/fft/fft.go index 499ab110b5..8ec51723a4 100644 --- a/ecc/bw6-756/fr/fft/fft.go +++ b/ecc/bw6-756/fr/fft/fft.go @@ -18,7 +18,6 @@ package fft import ( "math/bits" - "runtime" "github.com/consensys/gnark-crypto/ecc" "github.com/consensys/gnark-crypto/internal/parallel" @@ -40,24 +39,18 @@ const butterflyThreshold = 16 // FFT computes (recursively) the discrete Fourier transform of a and stores the result in a // if decimation == DIT (decimation in time), the input must be in bit-reversed order // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order -// if coset if set, the FFT(a) returns the evaluation of a on a coset. -func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) { +func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option) { - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } + opt := options(opts...) // if coset != 0, scale by coset table - if _coset { + if opt.coset { scale := func(cosetTable []fr.Element) { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &cosetTable[i]) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableReversed) @@ -69,16 +62,16 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.Twiddles, 0, maxSplits, nil) + difFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.Twiddles, 0, maxSplits, nil) + ditFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } @@ -89,37 +82,31 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order // coset sets the shift of the fft (0 = no shift, standard fft) // len(a) must be a power of 2, and w must be a len(a)th root of unity in field F. -func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset ...bool) { - - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } +func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...Option) { + opt := options(opts...) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } // scale by CardinalityInv - if !_coset { + if !opt.coset { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) return } @@ -129,7 +116,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. a[i].Mul(&a[i], &cosetTable[i]). Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableInv) @@ -141,7 +128,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. } -func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -159,7 +146,7 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for i := start; i < end; i++ { fr.Butterfly(&a[i], &a[i+m]) @@ -182,17 +169,17 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon nextStage := stage + 1 if stage < maxSplits { chDone := make(chan struct{}, 1) - go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone) - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone, nbTasks) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - difFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + difFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } } -func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -210,12 +197,12 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon if stage < maxSplits { // that's the only time we fire go routines chDone := make(chan struct{}, 1) - go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone) - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone, nbTasks) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } @@ -223,7 +210,7 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for k := start; k < end; k++ { a[k+m].Mul(&a[k+m], &twiddles[stage][k]) diff --git a/ecc/bw6-756/fr/fft/fft_test.go b/ecc/bw6-756/fr/fft/fft_test.go index 12b50ed60d..45eb27a9b2 100644 --- a/ecc/bw6-756/fr/fft/fft_test.go +++ b/ecc/bw6-756/fr/fft/fft_test.go @@ -52,7 +52,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIF) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -79,7 +79,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIF, OnCoset()) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -108,7 +108,7 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFT(pol, DIT) sample := domainWithPrecompute.Generator sample.Exp(sample, big.NewInt(int64(ithpower))) @@ -134,8 +134,8 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) - domainWithPrecompute.FFTInverse(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIT) + domainWithPrecompute.FFTInverse(pol, DIF) BitReverse(pol) check := true @@ -163,8 +163,8 @@ func TestFFT(t *testing.T) { for i := 1; i <= nbCosets; i++ { BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, true) - domainWithPrecompute.FFTInverse(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) BitReverse(pol) for i := 0; i < len(pol); i++ { @@ -188,8 +188,8 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, false) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFTInverse(pol, DIF) + domainWithPrecompute.FFT(pol, DIT) check := true for i := 0; i < len(pol); i++ { @@ -211,14 +211,26 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, true) - domainWithPrecompute.FFT(pol, DIT, true) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) - check := true for i := 0; i < len(pol); i++ { - check = check && (pol[i] == backupPol[i]) + if !(pol[i].Equal(&backupPol[i])) { + return false + } } - return check + + // compute with nbTasks == 1 + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset(), WithNbTasks(1)) + domainWithPrecompute.FFT(pol, DIT, OnCoset(), WithNbTasks(1)) + + for i := 0; i < len(pol); i++ { + if !(pol[i].Equal(&backupPol[i])) { + return false + } + } + + return true }, )) @@ -265,14 +277,14 @@ func BenchmarkFFT(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, false) + domain.FFT(pol[:sizeDomain], DIT) } }) b.Run("fft 2**"+strconv.Itoa(i)+"bits (coset)", func(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, true) + domain.FFT(pol[:sizeDomain], DIT, OnCoset()) } }) } @@ -292,7 +304,7 @@ func BenchmarkFFTDITCosetReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIT, true) + domain.FFT(pol, DIT, OnCoset()) } } @@ -309,7 +321,7 @@ func BenchmarkFFTDIFReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIF, false) + domain.FFT(pol, DIF) } } diff --git a/ecc/bw6-756/fr/fft/options.go b/ecc/bw6-756/fr/fft/options.go new file mode 100644 index 0000000000..603b76f299 --- /dev/null +++ b/ecc/bw6-756/fr/fft/options.go @@ -0,0 +1,61 @@ +// Copyright 2020 ConsenSys Software Inc. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +// Code generated by consensys/gnark-crypto DO NOT EDIT + +package fft + +import "runtime" + +// Option defines option for altering the behavior of FFT methods. +// See the descriptions of functions returning instances of this type for +// particular options. +type Option func(*fftConfig) + +type fftConfig struct { + coset bool + nbTasks int +} + +// OnCoset if provided, FFT(a) returns the evaluation of a on a coset. +func OnCoset() Option { + return func(opt *fftConfig) { + opt.coset = true + } +} + +// WithNbTasks sets the max number of task (go routine) to spawn. Must be between 1 and 512. +func WithNbTasks(nbTasks int) Option { + if nbTasks < 1 { + nbTasks = 1 + } else if nbTasks > 512 { + nbTasks = 512 + } + return func(opt *fftConfig) { + opt.nbTasks = nbTasks + } +} + +// default options +func options(opts ...Option) fftConfig { + // apply options + opt := fftConfig{ + coset: false, + nbTasks: runtime.NumCPU(), + } + for _, option := range opts { + option(&opt) + } + return opt +} diff --git a/ecc/bw6-756/fr/iop/polynomial.go b/ecc/bw6-756/fr/iop/polynomial.go index 9425359868..de4d0b86fa 100644 --- a/ecc/bw6-756/fr/iop/polynomial.go +++ b/ecc/bw6-756/fr/iop/polynomial.go @@ -146,11 +146,13 @@ func (p *Polynomial) Evaluate(x fr.Element) fr.Element { return p.polynomial.evaluate(x) } - // TODO find a way to retrieve the root properly instead of re generating the fft domain - d := fft.NewDomain(uint64(p.size)) var g fr.Element if p.shift <= 5 { - g = smallExp(d.Generator, p.shift) + gen, err := fft.Generator(uint64(p.size)) + if err != nil { + panic(err) + } + g = smallExp(gen, p.shift) x.Mul(&x, &g) return p.polynomial.evaluate(x) } @@ -288,11 +290,11 @@ func (p *Polynomial) ToLagrange(d *fft.Domain) *Polynomial { return p case lagrangeCosetRegular: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIT) case lagrangeCosetBitReverse: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIF) default: panic("unknown ID") @@ -317,10 +319,10 @@ func (p *Polynomial) ToCanonical(d *fft.Domain) *Polynomial { d.FFTInverse((*p.coefficients), fft.DIT) case lagrangeCosetRegular: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetBitReverse: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) default: panic("unknown ID") } @@ -342,18 +344,18 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial { switch id { case canonicalRegular: p.Layout = BitReverse - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case canonicalBitReverse: p.Layout = Regular - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeRegular: p.Layout = Regular d.FFTInverse((*p.coefficients), fft.DIF) - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeBitReverse: p.Layout = BitReverse d.FFTInverse((*p.coefficients), fft.DIT) - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetRegular, lagrangeCosetBitReverse: return p default: diff --git a/ecc/bw6-756/fr/iop/polynomial_test.go b/ecc/bw6-756/fr/iop/polynomial_test.go index 964db099cd..137bcc963f 100644 --- a/ecc/bw6-756/fr/iop/polynomial_test.go +++ b/ecc/bw6-756/fr/iop/polynomial_test.go @@ -240,7 +240,7 @@ func fromLagrange4(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = Regular d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) return r } @@ -250,7 +250,7 @@ func fromLagrange5(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = BitReverse d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) fft.BitReverse(r.Coefficients()) return r } @@ -438,7 +438,7 @@ func fromCanonical4(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = Regular - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -448,7 +448,7 @@ func fromCanonical5(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = BitReverse - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -566,7 +566,7 @@ func fromLagrangeCoset0(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -576,7 +576,7 @@ func fromLagrangeCoset1(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -585,7 +585,7 @@ func fromLagrangeCoset2(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) return _p } @@ -595,7 +595,7 @@ func fromLagrangeCoset3(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) fft.BitReverse(_p.Coefficients()) return _p diff --git a/ecc/bw6-756/fr/iop/ratios.go b/ecc/bw6-756/fr/iop/ratios.go index 6315ceff6f..98aa2bf91d 100644 --- a/ecc/bw6-756/fr/iop/ratios.go +++ b/ecc/bw6-756/fr/iop/ratios.go @@ -18,7 +18,10 @@ package iop import ( "errors" + "math/big" "math/bits" + "runtime" + "sync" "github.com/consensys/gnark-crypto/internal/parallel" @@ -213,16 +216,38 @@ func BuildRatioCopyConstraint( } }) - for i := 0; i < n-1; i++ { - coeffs[i+1].Mul(&coeffs[i+1], &coeffs[i]) - t[i+1].Mul(&t[i+1], &t[i]) + chCoeffs := make(chan struct{}, 1) + go func() { + for i := 2; i < n; i++ { + // ignoring coeffs[0] + coeffs[i].Mul(&coeffs[i], &coeffs[i-1]) + } + close(chCoeffs) + }() + + for i := 2; i < n; i++ { + // ignoring t[0] + t[i].Mul(&t[i], &t[i-1]) } + <-chCoeffs - t = fr.BatchInvert(t) - for i := 1; i < n; i++ { - coeffs[i].Mul(&coeffs[i], &t[i]) + // rough ratio inverse to mul; see if it makes sense to parallelize the batch inverse. + const ratioInvMul = 1000 / 17 + nbTasks := runtime.NumCPU() + if ratio := n / ratioInvMul; ratio < nbTasks { + nbTasks = ratio } + parallel.Execute(n-1, func(start, end int) { + // ignoring t[0] and coeff[0] + start++ + end++ + tInv := fr.BatchInvert(t[start:end]) + for i := start; i < end; i++ { + coeffs[i].Mul(&coeffs[i], &tInv[i-start]) + } + }, nbTasks) + res := NewPolynomial(&coeffs, expectedForm) // at this stage the result is in Lagrange form, Regular layout putInExpectedFormFromLagrangeRegular(res, domain, expectedForm) @@ -245,7 +270,7 @@ func putInExpectedFormFromLagrangeRegular(p *Polynomial, domain *fft.Domain, exp if expectedForm.Basis == LagrangeCoset { domain.FFTInverse(p.Coefficients(), fft.DIF) - domain.FFT(p.Coefficients(), fft.DIT, true) + domain.FFT(p.Coefficients(), fft.DIT, fft.OnCoset()) if expectedForm.Layout == BitReverse { fft.BitReverse(p.Coefficients()) } @@ -308,16 +333,42 @@ func getSupportIdentityPermutation(nbCopies int, domain *fft.Domain) []fr.Elemen res := make([]fr.Element, uint64(nbCopies)*domain.Cardinality) sizePoly := int(domain.Cardinality) - res[0].SetOne() - for i := 0; i < sizePoly-1; i++ { + // len(domain.Twiddle) == sizePoly / 2 + copy(res, domain.Twiddles[0]) + // remaining ones. + for i := (sizePoly / 2) - 1; i < sizePoly-1; i++ { res[i+1].Mul(&res[i], &domain.Generator) } + if nbCopies <= 1 { + return res + } + var wg sync.WaitGroup + wg.Add(nbCopies - 1) for i := 1; i < nbCopies; i++ { - copy(res[i*sizePoly:], res[(i-1)*sizePoly:i*int(domain.Cardinality)]) - for j := 0; j < sizePoly; j++ { - res[i*sizePoly+j].Mul(&res[i*sizePoly+j], &domain.FrMultiplicativeGen) + i := i + + var coset fr.Element + if i == 1 { + coset = domain.FrMultiplicativeGen + } else { + if len(domain.CosetTable) > i { + coset = domain.CosetTable[i] + } else { + coset.Exp(domain.FrMultiplicativeGen, big.NewInt(int64(i))) + } } + + go func() { + parallel.Execute(sizePoly, func(start, end int) { + for j := start; j < end; j++ { + res[i*sizePoly+j].Mul(&res[j], &coset) + } + }, (runtime.NumCPU()/(nbCopies-1))+1) + wg.Done() + }() } + wg.Wait() + return res } diff --git a/ecc/bw6-756/fr/kzg/kzg.go b/ecc/bw6-756/fr/kzg/kzg.go index aa75cea3b3..9a03e34dfd 100644 --- a/ecc/bw6-756/fr/kzg/kzg.go +++ b/ecc/bw6-756/fr/kzg/kzg.go @@ -26,6 +26,8 @@ import ( "github.com/consensys/gnark-crypto/ecc/bw6-756" "github.com/consensys/gnark-crypto/ecc/bw6-756/fr" "github.com/consensys/gnark-crypto/fiat-shamir" + + "github.com/consensys/gnark-crypto/internal/parallel" ) var ( @@ -275,14 +277,21 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr // gamma n in parallel, before reducing into foldedPolynomials foldedPolynomials := make([]fr.Element, largestPoly) copy(foldedPolynomials, polynomials[0]) - acc := gamma - var pj fr.Element + gammas := make([]fr.Element, len(polynomials)) + gammas[0] = gamma for i := 1; i < len(polynomials); i++ { - for j := 0; j < len(polynomials[i]); j++ { - pj.Mul(&polynomials[i][j], &acc) - foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) - } - acc.Mul(&acc, &gamma) + gammas[i].Mul(&gammas[i-1], &gamma) + } + + for i := 1; i < len(polynomials); i++ { + i := i + parallel.Execute(len(polynomials[i]), func(start, end int) { + var pj fr.Element + for j := start; j < end; j++ { + pj.Mul(&polynomials[i][j], &gammas[i-1]) + foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) + } + }) } // compute H diff --git a/ecc/bw6-756/fr/permutation/permutation.go b/ecc/bw6-756/fr/permutation/permutation.go index ae44190cbe..5cfe45c87d 100644 --- a/ecc/bw6-756/fr/permutation/permutation.go +++ b/ecc/bw6-756/fr/permutation/permutation.go @@ -191,15 +191,15 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } lz := make([]fr.Element, s) copy(lz, cz) - d.FFT(lz, fft.DIF, true) + d.FFT(lz, fft.DIF, fft.OnCoset()) // compute the first part of the numerator lt1 := make([]fr.Element, s) lt2 := make([]fr.Element, s) copy(lt1, ct1) copy(lt2, ct2) - d.FFT(lt1, fft.DIF, true) - d.FFT(lt2, fft.DIF, true) + d.FFT(lt1, fft.DIF, fft.OnCoset()) + d.FFT(lt2, fft.DIF, fft.OnCoset()) lsNumFirstPart := evaluateFirstPartNumReverse(lt1, lt2, lz, epsilon) // compute second part of the numerator @@ -222,7 +222,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } // get the quotient and commit it - d.FFTInverse(lsNum, fft.DIT, true) + d.FFTInverse(lsNum, fft.DIT, fft.OnCoset()) proof.q, err = kzg.Commit(lsNum, srs) if err != nil { return proof, err diff --git a/ecc/bw6-756/fr/plookup/vector.go b/ecc/bw6-756/fr/plookup/vector.go index 182be87cc0..3096ba9b15 100644 --- a/ecc/bw6-756/fr/plookup/vector.go +++ b/ecc/bw6-756/fr/plookup/vector.go @@ -340,7 +340,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element Mul(&res[_i], &numLn[i%2]) } - domainBig.FFTInverse(res, fft.DIT, true) + domainBig.FFTInverse(res, fft.DIT, fft.OnCoset()) return res } @@ -476,11 +476,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) copy(_lh2, ch2) copy(_lt, ct) copy(_lf, cf) - domainBig.FFT(_lz, fft.DIF, true) - domainBig.FFT(_lh1, fft.DIF, true) - domainBig.FFT(_lh2, fft.DIF, true) - domainBig.FFT(_lt, fft.DIF, true) - domainBig.FFT(_lf, fft.DIF, true) + domainBig.FFT(_lz, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh1, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh2, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lt, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lf, fft.DIF, fft.OnCoset()) // compute h lh := evaluateNumBitReversed(_lz, _lh1, _lh2, _lt, _lf, beta, gamma, domainBig) diff --git a/ecc/bw6-756/internal/fptower/e6.go b/ecc/bw6-756/internal/fptower/e6.go index e43bb26354..547b6ec23d 100644 --- a/ecc/bw6-756/internal/fptower/e6.go +++ b/ecc/bw6-756/internal/fptower/e6.go @@ -216,7 +216,7 @@ func (z *E6) CyclotomicSquareCompressed(x *E6) *E6 { // DecompressKarabina Karabina's cyclotomic square result // if g3 != 0 // -// g4 = (E * g5^2 + 3 * g1^2 - 2 * g2)/4g3 +// g4 = (E * g5² + 3 * g1² - 2 * g2)/4g3 // // if g3 == 0 // @@ -239,13 +239,13 @@ func (z *E6) DecompressKarabina(x *E6) *E6 { // g3 != 0 } else { - // t0 = g1^2 + // t0 = g1² t[0].Square(&x.B0.A1) - // t1 = 3 * g1^2 - 2 * g2 + // t1 = 3 * g1² - 2 * g2 t[1].Sub(&t[0], &x.B0.A2). Double(&t[1]). Add(&t[1], &t[0]) - // t0 = E * g5^2 + t1 + // t0 = E * g5² + t1 t[2].Square(&x.B1.A2) t[0].MulByNonResidue(&t[2]). Add(&t[0], &t[1]) @@ -614,12 +614,58 @@ func (z *E6) SetBytes(e []byte) error { } // IsInSubGroup ensures GT/E6 is in correct sugroup -// TODO: optimize func (z *E6) IsInSubGroup() bool { - var one, _z E6 - one.SetOne() - _z.Exp(*z, fr.Modulus()) - return _z.Equal(&one) + var tmp, a, _a, b E6 + var t [6]E6 + + // check z^(Phi_k(p)) == 1 + a.Frobenius(z) + b.Frobenius(&a).Mul(&b, z) + + if !a.Equal(&b) { + return false + } + + // check z^(p+1-t) == 1 + _a.Frobenius(z) + a.CyclotomicSquare(&_a).Mul(&a, &_a) // z^(3p) + + // t(x)-1 = (-x⁶ + 5x⁵ - 9x⁴ + 7x³ - 4x + 5)/3 + t[0].CyclotomicSquare(z). + CyclotomicSquare(&t[0]) // z^4 + t[1].Mul(&t[0], z) //z^5* + t[2].Expt(&t[0]). + Conjugate(&t[2]) // z^(-4u)* + tmp.CyclotomicSquare(&t[2]). + Expt(&tmp). + Expt(&tmp) // z^(-8u^3) + t[4].Expt(z). + Expt(&t[4]). + Expt(&t[4]) // z^(u^3) + t[3].Mul(&t[4], &tmp). + Conjugate(&t[3]) // z^(7u^3)* + t[4].Conjugate(&t[4]). + Mul(&t[4], &tmp). + Expt(&t[4]) // z^(-9u^4)* + t[5].Expt(&tmp). + Conjugate(&t[5]). + Mul(&t[5], &t[4]). + Expt(&t[5]) // z^(-u^5) + t[0].Expt(&t[5]) // z^(-u^6)* + tmp.Expt(&t[4]) // z^(-9u^5) + t[5].CyclotomicSquare(&t[5]). + CyclotomicSquare(&t[5]). + Conjugate(&t[5]). + Mul(&t[5], &tmp). + Conjugate(&t[5]) // z^(5u^5)* + + b.Mul(&t[1], &t[2]). + Mul(&b, &t[3]). + Mul(&b, &t[4]). + Mul(&b, &t[5]). + Mul(&b, &t[0]) // z^(3(t-1)) + + return a.Equal(&b) } // CompressTorus GT/E6 element to half its size diff --git a/ecc/bw6-756/internal/fptower/e6_pairing.go b/ecc/bw6-756/internal/fptower/e6_pairing.go index 60358a0190..6eb52c1904 100644 --- a/ecc/bw6-756/internal/fptower/e6_pairing.go +++ b/ecc/bw6-756/internal/fptower/e6_pairing.go @@ -94,8 +94,8 @@ func (z *E6) MulBy034(c0, c3, c4 *fp.Element) *E6 { } // Mul034By034 multiplication of sparse element (c0,0,0,c3,c4,0) by sparse element (d0,0,0,d3,d4,0) -func (z *E6) Mul034By034(d0, d3, d4, c0, c3, c4 *fp.Element) *E6 { - var tmp, x0, x3, x4, x04, x03, x34 fp.Element +func Mul034By034(d0, d3, d4, c0, c3, c4 *fp.Element) [5]fp.Element { + var z00, tmp, x0, x3, x4, x04, x03, x34 fp.Element x0.Mul(c0, d0) x3.Mul(c3, d3) x4.Mul(c4, d4) @@ -115,13 +115,30 @@ func (z *E6) Mul034By034(d0, d3, d4, c0, c3, c4 *fp.Element) *E6 { Sub(&x34, &x3). Sub(&x34, &x4) - z.B0.A0.MulByNonResidue(&x4). - Add(&z.B0.A0, &x0) - z.B0.A1.Set(&x3) - z.B0.A2.Set(&x34) - z.B1.A0.Set(&x03) - z.B1.A1.Set(&x04) - z.B1.A2.SetZero() + z00.MulByNonResidue(&x4). + Add(&z00, &x0) + + return [5]fp.Element{z00, x3, x34, x03, x04} +} + +// MulBy01234 multiplies z by an E12 sparse element of the form (x0, x1, x2, x3, x4, 0) +func (z *E6) MulBy01234(x *[5]fp.Element) *E6 { + var c1, a, b, c, z0, z1 E3 + c0 := &E3{A0: x[0], A1: x[1], A2: x[2]} + c1.A0 = x[3] + c1.A1 = x[4] + a.Add(&z.B0, &z.B1) + b.Add(c0, &c1) + a.Mul(&a, &b) + b.Mul(&z.B0, c0) + c.Set(&z.B1).MulBy01(&x[3], &x[4]) + z1.Sub(&a, &b) + z1.Sub(&z1, &c) + z0.MulByNonResidue(&c) + z0.Add(&z0, &b) + + z.B0 = z0 + z.B1 = z1 return z } diff --git a/ecc/bw6-756/marshal.go b/ecc/bw6-756/marshal.go index 8a3a01315a..868b345777 100644 --- a/ecc/bw6-756/marshal.go +++ b/ecc/bw6-756/marshal.go @@ -50,6 +50,8 @@ const ( // SizeOfGT represents the size in bytes that a GT element need in binary form const SizeOfGT = fptower.SizeOfGT +var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding") + // Encoder writes bw6-756 object values to an output stream type Encoder struct { w io.Writer @@ -365,6 +367,19 @@ func NoSubgroupChecks() func(*Decoder) { } } +// isZeroed checks that the provided bytes are at 0 +func isZeroed(firstByte byte, buf []byte) bool { + if firstByte != 0 { + return false + } + for _, b := range buf { + if b != 0 { + return false + } + } + return true +} + func (enc *Encoder) encode(v interface{}) (err error) { rv := reflect.ValueOf(v) if v == nil || (rv.Kind() == reflect.Ptr && rv.IsNil()) { @@ -674,13 +689,19 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineUncompressed, nil @@ -796,9 +817,12 @@ func (p *G1Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } @@ -921,13 +945,19 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineUncompressed, nil @@ -1043,9 +1073,12 @@ func (p *G2Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } diff --git a/ecc/bw6-756/pairing.go b/ecc/bw6-756/pairing.go index e4b1f3ad9b..9a3bc5b4cd 100644 --- a/ecc/bw6-756/pairing.go +++ b/ecc/bw6-756/pairing.go @@ -153,7 +153,10 @@ func FinalExponentiation(z *GT, _z ...*GT) GT { } // MillerLoop Optimal Tate alternative (or twisted ate or Eta revisited) -// computes the multi-Miller loop ∏ᵢ MillerLoop(Pᵢ, Qᵢ) +// computes the multi-Miller loop +// ∏ᵢ MillerLoop(Pᵢ, Qᵢ) = +// ∏ᵢ { fᵢ_{x₀+1+λ(x₀³-x₀²-x₀),Pᵢ}(Qᵢ) } +// // Alg.2 in https://eprint.iacr.org/2021/1359.pdf // Eq. (6) in https://hackmd.io/@gnark/BW6-761-changes func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { @@ -191,117 +194,222 @@ func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { // l_{p0,p1}(q) pProj01[k].Set(&pProj1[k]) - pProj01[k].AddMixedStep(&l01[k], &p0[k]) + pProj01[k].addMixedStep(&l01[k], &p0[k]) l01[k].r1.Mul(&l01[k].r1, &q[k].X) l01[k].r0.Mul(&l01[k].r0, &q[k].Y) // l_{p0,-p1}(q) pProj10[k].Neg(&pProj1[k]) - pProj10[k].AddMixedStep(&l10[k], &p0[k]) + pProj10[k].addMixedStep(&l10[k], &p0[k]) l10[k].r1.Mul(&l10[k].r1, &q[k].X) l10[k].r0.Mul(&l10[k].r0, &q[k].Y) } p01 := BatchProjectiveToAffineG1(pProj01) p10 := BatchProjectiveToAffineG1(pProj10) - // f_{a0+lambda*a1,P}(Q) - var result, ss GT + // f_{a0+λ*a1,P}(Q) + var result GT result.SetOne() var l, l0 lineEvaluation + var prodLines [5]fp.Element var j int8 - // i = len(loopCounter) - 2 - for k := 0; k < n; k++ { - pProj1[k].DoubleStep(&l0) + if n >= 1 { + // i = len(loopCounter0) - 2, separately to avoid an E12 Square + // (Square(res) = 1² = 1) + // j = 0 + // k = 0, separately to avoid MulBy034 (res × ℓ) + // (assign line to res) + + // pProj1[0] ← 2pProj1[0] and l0 the tangent ℓ passing 2pProj1[0] + pProj1[0].doubleStep(&l0) + // line evaluation at Q[0] (assign) + result.B1.A0.Mul(&l0.r1, &q[0].X) + result.B0.A0.Mul(&l0.r0, &q[0].Y) + result.B1.A1.Set(&l0.r2) + } + + // k = 1 + if n >= 2 { + // pProj1[1] ← 2pProj1[1] and l0 the tangent ℓ passing 2pProj1[1] + pProj1[1].doubleStep(&l0) + // line evaluation at Q[0] + l0.r1.Mul(&l0.r1, &q[1].X) + l0.r0.Mul(&l0.r0, &q[1].Y) + // ℓ × res + prodLines = fptower.Mul034By034(&l0.r0, &l0.r1, &l0.r2, &result.B0.A0, &result.B1.A0, &result.B1.A1) + result.B0.A0 = prodLines[0] + result.B0.A1 = prodLines[1] + result.B0.A2 = prodLines[2] + result.B1.A0 = prodLines[3] + result.B1.A1 = prodLines[4] + } + + // k >= 2 + for k := 2; k < n; k++ { + // pProj1[1] ← 2pProj1[1] and l0 the tangent ℓ passing 2pProj1[1] + pProj1[k].doubleStep(&l0) + // line evaluation at Q[k] l0.r1.Mul(&l0.r1, &q[k].X) l0.r0.Mul(&l0.r0, &q[k].Y) + // ℓ × res result.MulBy034(&l0.r0, &l0.r1, &l0.r2) } var tmp G1Affine - for i := len(loopCounter0) - 3; i >= 0; i-- { + for i := len(loopCounter0) - 3; i >= 1; i-- { // (∏ᵢfᵢ)² + // mutualize the square among n Miller loops result.Square(&result) j = loopCounter1[i]*3 + loopCounter0[i] for k := 0; k < n; k++ { - pProj1[k].DoubleStep(&l0) + // pProj1[1] ← 2pProj1[1] and l0 the tangent ℓ passing 2pProj1[1] + pProj1[k].doubleStep(&l0) + // line evaluation at Q[k] l0.r1.Mul(&l0.r1, &q[k].X) l0.r0.Mul(&l0.r0, &q[k].Y) switch j { case -4: tmp.Neg(&p01[k]) - pProj1[k].AddMixedStep(&l, &tmp) + // pProj1[k] ← pProj1[k]-p01[k] and + // l the line ℓ passing pProj1[k] and -p01[k] + pProj1[k].addMixedStep(&l, &tmp) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) - result.MulBy034(&l0.r0, &l0.r1, &l0.r2). - Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) + // ℓ × res + result.MulBy034(&l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case -3: tmp.Neg(&p1[k]) - pProj1[k].AddMixedStep(&l, &tmp) + // pProj1[k] ← pProj1[k]-p1[k] and + // l the line ℓ passing pProj1[k] and -p1[k] + pProj1[k].addMixedStep(&l, &tmp) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case -2: - pProj1[k].AddMixedStep(&l, &p10[k]) + // pProj1[k] ← pProj1[k]+p10[k] and + // l the line ℓ passing pProj1[k] and p10[k] + pProj1[k].addMixedStep(&l, &p10[k]) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) - result.MulBy034(&l0.r0, &l0.r1, &l0.r2). - Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) + // ℓ × res + result.MulBy034(&l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case -1: tmp.Neg(&p0[k]) - pProj1[k].AddMixedStep(&l, &tmp) + // pProj1[k] ← pProj1[k]-p0[k] and + // l the line ℓ passing pProj1[k] and -p0[k] + pProj1[k].addMixedStep(&l, &tmp) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case 0: + // ℓ × res result.MulBy034(&l0.r0, &l0.r1, &l0.r2) case 1: - pProj1[k].AddMixedStep(&l, &p0[k]) + // pProj1[k] ← pProj1[k]+p0[k] and + // l the line ℓ passing pProj1[k] and p0[k] + pProj1[k].addMixedStep(&l, &p0[k]) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case 2: tmp.Neg(&p10[k]) - pProj1[k].AddMixedStep(&l, &tmp) + // pProj1[k] ← pProj1[k]-p10[k] and + // l the line ℓ passing pProj1[k] and -p10[k] + pProj1[k].addMixedStep(&l, &tmp) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) - result.MulBy034(&l0.r0, &l0.r1, &l0.r2). - Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) + // ℓ × res + result.MulBy034(&l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case 3: - pProj1[k].AddMixedStep(&l, &p1[k]) + // pProj1[k] ← pProj1[k]+p1[k] and + // l the line ℓ passing pProj1[k] and p1[k] + pProj1[k].addMixedStep(&l, &p1[k]) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case 4: - pProj1[k].AddMixedStep(&l, &p01[k]) + // pProj1[k] ← pProj1[k]+p01[k] and + // l the line ℓ passing pProj1[k] and p01[k] + pProj1[k].addMixedStep(&l, &p01[k]) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) - result.MulBy034(&l0.r0, &l0.r1, &l0.r2). - Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) + // ℓ × res + result.MulBy034(&l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) default: return GT{}, errors.New("invalid loopCounter") } } } + // i = 0, separately to avoid a point addition + // j = -3 + result.Square(&result) + for k := 0; k < n; k++ { + // pProj1[k] ← 2pProj1[k] and l0 the tangent ℓ passing 2pProj1[k] + pProj1[k].doubleStep(&l0) + // line evaluation at Q[k] + l0.r1.Mul(&l0.r1, &q[k].X) + l0.r0.Mul(&l0.r0, &q[k].Y) + + tmp.Neg(&p1[k]) + // l the line passing pProj1[k] and -p1 + pProj1[k].lineCompute(&l, &tmp) + // line evaluation at Q[k] + l.r1.Mul(&l.r1, &q[k].X) + l.r0.Mul(&l.r0, &q[k].Y) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) + } + return result, nil } -// DoubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop +// doubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g1Proj) DoubleStep(evaluations *lineEvaluation) { +func (p *g1Proj) doubleStep(evaluations *lineEvaluation) { // get some Element from our pool var t1, A, B, C, D, E, EE, F, G, H, I, J, K fp.Element @@ -341,9 +449,9 @@ func (p *g1Proj) DoubleStep(evaluations *lineEvaluation) { evaluations.r2.Set(&I) } -// AddMixedStep point addition in Mixed Homogenous projective and Affine coordinates +// addMixedStep point addition in Mixed Homogenous projective and Affine coordinates // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g1Proj) AddMixedStep(evaluations *lineEvaluation, a *G1Affine) { +func (p *g1Proj) addMixedStep(evaluations *lineEvaluation, a *G1Affine) { // get some Element from our pool var Y2Z1, X2Z1, O, L, C, D, E, F, G, H, t0, t1, t2, J fp.Element @@ -377,3 +485,23 @@ func (p *g1Proj) AddMixedStep(evaluations *lineEvaluation, a *G1Affine) { evaluations.r1.Neg(&O) evaluations.r2.Set(&J) } + +// lineCompute computes the line through p in Homogenous projective coordinates +// and a in affine coordinates. It does not compute the resulting point p+a. +func (p *g1Proj) lineCompute(evaluations *lineEvaluation, a *G1Affine) { + + // get some Element from our pool + var Y2Z1, X2Z1, O, L, t2, J fp.Element + Y2Z1.Mul(&a.Y, &p.z) + O.Sub(&p.y, &Y2Z1) + X2Z1.Mul(&a.X, &p.z) + L.Sub(&p.x, &X2Z1) + t2.Mul(&L, &a.Y) + J.Mul(&a.X, &O). + Sub(&J, &t2) + + // Line evaluation + evaluations.r0.Set(&L) + evaluations.r1.Neg(&O) + evaluations.r2.Set(&J) +} diff --git a/ecc/bw6-761/bw6-761.go b/ecc/bw6-761/bw6-761.go index 6de70d9257..07668c69e0 100644 --- a/ecc/bw6-761/bw6-761.go +++ b/ecc/bw6-761/bw6-761.go @@ -30,6 +30,7 @@ package bw6761 import ( + "github.com/consensys/gnark-crypto/ecc/bw6-761/internal/fptower" "math/big" "github.com/consensys/gnark-crypto/ecc" @@ -40,7 +41,8 @@ import ( // ID BW6_761 ID const ID = ecc.BW6_761 -// bCurveCoeff b coeff of the curve Y²=X³+b +// aCurveCoeff is the a coefficients of the curve Y²=X³+ax+b +var aCurveCoeff fp.Element var bCurveCoeff fp.Element // bTwistCurveCoeff b coeff of the twist (defined over 𝔽p) curve @@ -77,8 +79,14 @@ var glvBasis ecc.Lattice // seed x₀ of the curve var xGen big.Int -func init() { +// 𝔽p3 +type E3 = fptower.E3 + +// 𝔽p6 +type E6 = fptower.E6 +func init() { + aCurveCoeff.SetUint64(0) bCurveCoeff.SetOne().Neg(&bCurveCoeff) // M-twist bTwistCurveCoeff.SetUint64(4) @@ -126,3 +134,8 @@ func Generators() (g1Jac G1Jac, g2Jac G2Jac, g1Aff G1Affine, g2Aff G2Affine) { g2Jac = g2Gen return } + +// CurveCoefficients returns the a, b coefficients of the curve equation. +func CurveCoefficients() (a, b fp.Element) { + return aCurveCoeff, bCurveCoeff +} diff --git a/ecc/bw6-761/ecdsa/ecdsa.go b/ecc/bw6-761/ecdsa/ecdsa.go index 7a6669fcab..033cd8f9d1 100644 --- a/ecc/bw6-761/ecdsa/ecdsa.go +++ b/ecc/bw6-761/ecdsa/ecdsa.go @@ -22,7 +22,6 @@ import ( "crypto/rand" "crypto/sha512" "crypto/subtle" - "errors" "hash" "io" "math/big" @@ -33,8 +32,6 @@ import ( "github.com/consensys/gnark-crypto/signature" ) -var errInvalidSig = errors.New("invalid signature") - const ( sizeFr = fr.Bytes sizeFp = fp.Bytes @@ -213,6 +210,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) kInv.ModInverse(k, order) P.X.BigInt(r) + r.Mod(r, order) if r.Sign() != 0 { break diff --git a/ecc/bw6-761/fp/element.go b/ecc/bw6-761/fp/element.go index a9a2391046..72ff7dda25 100644 --- a/ecc/bw6-761/fp/element.go +++ b/ecc/bw6-761/fp/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -1444,12 +1445,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -1459,7 +1460,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bw6-761/fr/element.go b/ecc/bw6-761/fr/element.go index d6f2c759b2..6bf7f0a568 100644 --- a/ecc/bw6-761/fr/element.go +++ b/ecc/bw6-761/fr/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -844,12 +845,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -859,7 +860,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/bw6-761/fr/fft/domain.go b/ecc/bw6-761/fr/fft/domain.go index 03dca56ebd..6b2b96e46a 100644 --- a/ecc/bw6-761/fr/fft/domain.go +++ b/ecc/bw6-761/fr/fft/domain.go @@ -63,30 +63,27 @@ type Domain struct { // NewDomain returns a subgroup with a power of 2 cardinality // cardinality >= m -func NewDomain(m uint64) *Domain { +// shift: when specified, it's the element by which the set of root of unity is shifted. +func NewDomain(m uint64, shift ...fr.Element) *Domain { domain := &Domain{} x := ecc.NextPowerOfTwo(m) domain.Cardinality = uint64(x) // generator of the largest 2-adic subgroup - var rootOfUnity fr.Element - rootOfUnity.SetString("32863578547254505029601261939868325669770508939375122462904745766352256812585773382134936404344547323199885654433") - const maxOrderRoot uint64 = 46 domain.FrMultiplicativeGen.SetUint64(15) + if len(shift) != 0 { + domain.FrMultiplicativeGen.Set(&shift[0]) + } domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen) - // find generator for Z/2^(log(m))Z - logx := uint64(bits.TrailingZeros64(x)) - if logx > maxOrderRoot { - panic(fmt.Sprintf("m (%d) is too big: the required root of unity does not exist", m)) + var err error + domain.Generator, err = Generator(m) + if err != nil { + panic(err) } - - // Generator = FinerGenerator^2 has order x - expo := uint64(1 << (maxOrderRoot - logx)) - domain.Generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x domain.GeneratorInv.Inverse(&domain.Generator) domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv) @@ -99,6 +96,28 @@ func NewDomain(m uint64) *Domain { return domain } +// Generator returns a generator for Z/2^(log(m))Z +// or an error if m is too big (required root of unity doesn't exist) +func Generator(m uint64) (fr.Element, error) { + x := ecc.NextPowerOfTwo(m) + + var rootOfUnity fr.Element + + rootOfUnity.SetString("32863578547254505029601261939868325669770508939375122462904745766352256812585773382134936404344547323199885654433") + const maxOrderRoot uint64 = 46 + + // find generator for Z/2^(log(m))Z + logx := uint64(bits.TrailingZeros64(x)) + if logx > maxOrderRoot { + return fr.Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m) + } + + expo := uint64(1 << (maxOrderRoot - logx)) + var generator fr.Element + generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x + return generator, nil +} + func (d *Domain) reverseCosetTables() { d.CosetTableReversed = make([]fr.Element, d.Cardinality) d.CosetTableInvReversed = make([]fr.Element, d.Cardinality) diff --git a/ecc/bw6-761/fr/fft/fft.go b/ecc/bw6-761/fr/fft/fft.go index 961e5a274c..404eb0fd13 100644 --- a/ecc/bw6-761/fr/fft/fft.go +++ b/ecc/bw6-761/fr/fft/fft.go @@ -18,7 +18,6 @@ package fft import ( "math/bits" - "runtime" "github.com/consensys/gnark-crypto/ecc" "github.com/consensys/gnark-crypto/internal/parallel" @@ -40,24 +39,18 @@ const butterflyThreshold = 16 // FFT computes (recursively) the discrete Fourier transform of a and stores the result in a // if decimation == DIT (decimation in time), the input must be in bit-reversed order // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order -// if coset if set, the FFT(a) returns the evaluation of a on a coset. -func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) { +func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option) { - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } + opt := options(opts...) // if coset != 0, scale by coset table - if _coset { + if opt.coset { scale := func(cosetTable []fr.Element) { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &cosetTable[i]) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableReversed) @@ -69,16 +62,16 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.Twiddles, 0, maxSplits, nil) + difFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.Twiddles, 0, maxSplits, nil) + ditFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } @@ -89,37 +82,31 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order // coset sets the shift of the fft (0 = no shift, standard fft) // len(a) must be a power of 2, and w must be a len(a)th root of unity in field F. -func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset ...bool) { - - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } +func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...Option) { + opt := options(opts...) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } // scale by CardinalityInv - if !_coset { + if !opt.coset { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) return } @@ -129,7 +116,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. a[i].Mul(&a[i], &cosetTable[i]). Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableInv) @@ -141,7 +128,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. } -func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -159,7 +146,7 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for i := start; i < end; i++ { fr.Butterfly(&a[i], &a[i+m]) @@ -182,17 +169,17 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon nextStage := stage + 1 if stage < maxSplits { chDone := make(chan struct{}, 1) - go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone) - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone, nbTasks) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - difFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + difFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } } -func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -210,12 +197,12 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon if stage < maxSplits { // that's the only time we fire go routines chDone := make(chan struct{}, 1) - go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone) - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone, nbTasks) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } @@ -223,7 +210,7 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for k := start; k < end; k++ { a[k+m].Mul(&a[k+m], &twiddles[stage][k]) diff --git a/ecc/bw6-761/fr/fft/fft_test.go b/ecc/bw6-761/fr/fft/fft_test.go index 57424feb01..a4166b63e9 100644 --- a/ecc/bw6-761/fr/fft/fft_test.go +++ b/ecc/bw6-761/fr/fft/fft_test.go @@ -52,7 +52,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIF) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -79,7 +79,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIF, OnCoset()) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -108,7 +108,7 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFT(pol, DIT) sample := domainWithPrecompute.Generator sample.Exp(sample, big.NewInt(int64(ithpower))) @@ -134,8 +134,8 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) - domainWithPrecompute.FFTInverse(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIT) + domainWithPrecompute.FFTInverse(pol, DIF) BitReverse(pol) check := true @@ -163,8 +163,8 @@ func TestFFT(t *testing.T) { for i := 1; i <= nbCosets; i++ { BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, true) - domainWithPrecompute.FFTInverse(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) BitReverse(pol) for i := 0; i < len(pol); i++ { @@ -188,8 +188,8 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, false) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFTInverse(pol, DIF) + domainWithPrecompute.FFT(pol, DIT) check := true for i := 0; i < len(pol); i++ { @@ -211,14 +211,26 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, true) - domainWithPrecompute.FFT(pol, DIT, true) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) - check := true for i := 0; i < len(pol); i++ { - check = check && (pol[i] == backupPol[i]) + if !(pol[i].Equal(&backupPol[i])) { + return false + } } - return check + + // compute with nbTasks == 1 + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset(), WithNbTasks(1)) + domainWithPrecompute.FFT(pol, DIT, OnCoset(), WithNbTasks(1)) + + for i := 0; i < len(pol); i++ { + if !(pol[i].Equal(&backupPol[i])) { + return false + } + } + + return true }, )) @@ -265,14 +277,14 @@ func BenchmarkFFT(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, false) + domain.FFT(pol[:sizeDomain], DIT) } }) b.Run("fft 2**"+strconv.Itoa(i)+"bits (coset)", func(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, true) + domain.FFT(pol[:sizeDomain], DIT, OnCoset()) } }) } @@ -292,7 +304,7 @@ func BenchmarkFFTDITCosetReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIT, true) + domain.FFT(pol, DIT, OnCoset()) } } @@ -309,7 +321,7 @@ func BenchmarkFFTDIFReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIF, false) + domain.FFT(pol, DIF) } } diff --git a/ecc/bw6-761/fr/fft/options.go b/ecc/bw6-761/fr/fft/options.go new file mode 100644 index 0000000000..603b76f299 --- /dev/null +++ b/ecc/bw6-761/fr/fft/options.go @@ -0,0 +1,61 @@ +// Copyright 2020 ConsenSys Software Inc. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +// Code generated by consensys/gnark-crypto DO NOT EDIT + +package fft + +import "runtime" + +// Option defines option for altering the behavior of FFT methods. +// See the descriptions of functions returning instances of this type for +// particular options. +type Option func(*fftConfig) + +type fftConfig struct { + coset bool + nbTasks int +} + +// OnCoset if provided, FFT(a) returns the evaluation of a on a coset. +func OnCoset() Option { + return func(opt *fftConfig) { + opt.coset = true + } +} + +// WithNbTasks sets the max number of task (go routine) to spawn. Must be between 1 and 512. +func WithNbTasks(nbTasks int) Option { + if nbTasks < 1 { + nbTasks = 1 + } else if nbTasks > 512 { + nbTasks = 512 + } + return func(opt *fftConfig) { + opt.nbTasks = nbTasks + } +} + +// default options +func options(opts ...Option) fftConfig { + // apply options + opt := fftConfig{ + coset: false, + nbTasks: runtime.NumCPU(), + } + for _, option := range opts { + option(&opt) + } + return opt +} diff --git a/ecc/bw6-761/fr/iop/polynomial.go b/ecc/bw6-761/fr/iop/polynomial.go index 92e2f49ac2..c5066b18b0 100644 --- a/ecc/bw6-761/fr/iop/polynomial.go +++ b/ecc/bw6-761/fr/iop/polynomial.go @@ -146,11 +146,13 @@ func (p *Polynomial) Evaluate(x fr.Element) fr.Element { return p.polynomial.evaluate(x) } - // TODO find a way to retrieve the root properly instead of re generating the fft domain - d := fft.NewDomain(uint64(p.size)) var g fr.Element if p.shift <= 5 { - g = smallExp(d.Generator, p.shift) + gen, err := fft.Generator(uint64(p.size)) + if err != nil { + panic(err) + } + g = smallExp(gen, p.shift) x.Mul(&x, &g) return p.polynomial.evaluate(x) } @@ -288,11 +290,11 @@ func (p *Polynomial) ToLagrange(d *fft.Domain) *Polynomial { return p case lagrangeCosetRegular: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIT) case lagrangeCosetBitReverse: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIF) default: panic("unknown ID") @@ -317,10 +319,10 @@ func (p *Polynomial) ToCanonical(d *fft.Domain) *Polynomial { d.FFTInverse((*p.coefficients), fft.DIT) case lagrangeCosetRegular: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetBitReverse: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) default: panic("unknown ID") } @@ -342,18 +344,18 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial { switch id { case canonicalRegular: p.Layout = BitReverse - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case canonicalBitReverse: p.Layout = Regular - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeRegular: p.Layout = Regular d.FFTInverse((*p.coefficients), fft.DIF) - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeBitReverse: p.Layout = BitReverse d.FFTInverse((*p.coefficients), fft.DIT) - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetRegular, lagrangeCosetBitReverse: return p default: diff --git a/ecc/bw6-761/fr/iop/polynomial_test.go b/ecc/bw6-761/fr/iop/polynomial_test.go index 52e696d974..6d253dd5de 100644 --- a/ecc/bw6-761/fr/iop/polynomial_test.go +++ b/ecc/bw6-761/fr/iop/polynomial_test.go @@ -240,7 +240,7 @@ func fromLagrange4(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = Regular d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) return r } @@ -250,7 +250,7 @@ func fromLagrange5(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = BitReverse d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) fft.BitReverse(r.Coefficients()) return r } @@ -438,7 +438,7 @@ func fromCanonical4(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = Regular - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -448,7 +448,7 @@ func fromCanonical5(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = BitReverse - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -566,7 +566,7 @@ func fromLagrangeCoset0(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -576,7 +576,7 @@ func fromLagrangeCoset1(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -585,7 +585,7 @@ func fromLagrangeCoset2(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) return _p } @@ -595,7 +595,7 @@ func fromLagrangeCoset3(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) fft.BitReverse(_p.Coefficients()) return _p diff --git a/ecc/bw6-761/fr/iop/ratios.go b/ecc/bw6-761/fr/iop/ratios.go index 9c883617c1..7d7bec6fd7 100644 --- a/ecc/bw6-761/fr/iop/ratios.go +++ b/ecc/bw6-761/fr/iop/ratios.go @@ -18,7 +18,10 @@ package iop import ( "errors" + "math/big" "math/bits" + "runtime" + "sync" "github.com/consensys/gnark-crypto/internal/parallel" @@ -213,16 +216,38 @@ func BuildRatioCopyConstraint( } }) - for i := 0; i < n-1; i++ { - coeffs[i+1].Mul(&coeffs[i+1], &coeffs[i]) - t[i+1].Mul(&t[i+1], &t[i]) + chCoeffs := make(chan struct{}, 1) + go func() { + for i := 2; i < n; i++ { + // ignoring coeffs[0] + coeffs[i].Mul(&coeffs[i], &coeffs[i-1]) + } + close(chCoeffs) + }() + + for i := 2; i < n; i++ { + // ignoring t[0] + t[i].Mul(&t[i], &t[i-1]) } + <-chCoeffs - t = fr.BatchInvert(t) - for i := 1; i < n; i++ { - coeffs[i].Mul(&coeffs[i], &t[i]) + // rough ratio inverse to mul; see if it makes sense to parallelize the batch inverse. + const ratioInvMul = 1000 / 17 + nbTasks := runtime.NumCPU() + if ratio := n / ratioInvMul; ratio < nbTasks { + nbTasks = ratio } + parallel.Execute(n-1, func(start, end int) { + // ignoring t[0] and coeff[0] + start++ + end++ + tInv := fr.BatchInvert(t[start:end]) + for i := start; i < end; i++ { + coeffs[i].Mul(&coeffs[i], &tInv[i-start]) + } + }, nbTasks) + res := NewPolynomial(&coeffs, expectedForm) // at this stage the result is in Lagrange form, Regular layout putInExpectedFormFromLagrangeRegular(res, domain, expectedForm) @@ -245,7 +270,7 @@ func putInExpectedFormFromLagrangeRegular(p *Polynomial, domain *fft.Domain, exp if expectedForm.Basis == LagrangeCoset { domain.FFTInverse(p.Coefficients(), fft.DIF) - domain.FFT(p.Coefficients(), fft.DIT, true) + domain.FFT(p.Coefficients(), fft.DIT, fft.OnCoset()) if expectedForm.Layout == BitReverse { fft.BitReverse(p.Coefficients()) } @@ -308,16 +333,42 @@ func getSupportIdentityPermutation(nbCopies int, domain *fft.Domain) []fr.Elemen res := make([]fr.Element, uint64(nbCopies)*domain.Cardinality) sizePoly := int(domain.Cardinality) - res[0].SetOne() - for i := 0; i < sizePoly-1; i++ { + // len(domain.Twiddle) == sizePoly / 2 + copy(res, domain.Twiddles[0]) + // remaining ones. + for i := (sizePoly / 2) - 1; i < sizePoly-1; i++ { res[i+1].Mul(&res[i], &domain.Generator) } + if nbCopies <= 1 { + return res + } + var wg sync.WaitGroup + wg.Add(nbCopies - 1) for i := 1; i < nbCopies; i++ { - copy(res[i*sizePoly:], res[(i-1)*sizePoly:i*int(domain.Cardinality)]) - for j := 0; j < sizePoly; j++ { - res[i*sizePoly+j].Mul(&res[i*sizePoly+j], &domain.FrMultiplicativeGen) + i := i + + var coset fr.Element + if i == 1 { + coset = domain.FrMultiplicativeGen + } else { + if len(domain.CosetTable) > i { + coset = domain.CosetTable[i] + } else { + coset.Exp(domain.FrMultiplicativeGen, big.NewInt(int64(i))) + } } + + go func() { + parallel.Execute(sizePoly, func(start, end int) { + for j := start; j < end; j++ { + res[i*sizePoly+j].Mul(&res[j], &coset) + } + }, (runtime.NumCPU()/(nbCopies-1))+1) + wg.Done() + }() } + wg.Wait() + return res } diff --git a/ecc/bw6-761/fr/kzg/kzg.go b/ecc/bw6-761/fr/kzg/kzg.go index 516589b9b6..f6636b9948 100644 --- a/ecc/bw6-761/fr/kzg/kzg.go +++ b/ecc/bw6-761/fr/kzg/kzg.go @@ -26,6 +26,8 @@ import ( "github.com/consensys/gnark-crypto/ecc/bw6-761" "github.com/consensys/gnark-crypto/ecc/bw6-761/fr" "github.com/consensys/gnark-crypto/fiat-shamir" + + "github.com/consensys/gnark-crypto/internal/parallel" ) var ( @@ -275,14 +277,21 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr // gamma n in parallel, before reducing into foldedPolynomials foldedPolynomials := make([]fr.Element, largestPoly) copy(foldedPolynomials, polynomials[0]) - acc := gamma - var pj fr.Element + gammas := make([]fr.Element, len(polynomials)) + gammas[0] = gamma for i := 1; i < len(polynomials); i++ { - for j := 0; j < len(polynomials[i]); j++ { - pj.Mul(&polynomials[i][j], &acc) - foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) - } - acc.Mul(&acc, &gamma) + gammas[i].Mul(&gammas[i-1], &gamma) + } + + for i := 1; i < len(polynomials); i++ { + i := i + parallel.Execute(len(polynomials[i]), func(start, end int) { + var pj fr.Element + for j := start; j < end; j++ { + pj.Mul(&polynomials[i][j], &gammas[i-1]) + foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) + } + }) } // compute H diff --git a/ecc/bw6-761/fr/permutation/permutation.go b/ecc/bw6-761/fr/permutation/permutation.go index 700b503d2d..d56d9a6d27 100644 --- a/ecc/bw6-761/fr/permutation/permutation.go +++ b/ecc/bw6-761/fr/permutation/permutation.go @@ -191,15 +191,15 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } lz := make([]fr.Element, s) copy(lz, cz) - d.FFT(lz, fft.DIF, true) + d.FFT(lz, fft.DIF, fft.OnCoset()) // compute the first part of the numerator lt1 := make([]fr.Element, s) lt2 := make([]fr.Element, s) copy(lt1, ct1) copy(lt2, ct2) - d.FFT(lt1, fft.DIF, true) - d.FFT(lt2, fft.DIF, true) + d.FFT(lt1, fft.DIF, fft.OnCoset()) + d.FFT(lt2, fft.DIF, fft.OnCoset()) lsNumFirstPart := evaluateFirstPartNumReverse(lt1, lt2, lz, epsilon) // compute second part of the numerator @@ -222,7 +222,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } // get the quotient and commit it - d.FFTInverse(lsNum, fft.DIT, true) + d.FFTInverse(lsNum, fft.DIT, fft.OnCoset()) proof.q, err = kzg.Commit(lsNum, srs) if err != nil { return proof, err diff --git a/ecc/bw6-761/fr/plookup/vector.go b/ecc/bw6-761/fr/plookup/vector.go index 15ac6c0c79..34da3f3733 100644 --- a/ecc/bw6-761/fr/plookup/vector.go +++ b/ecc/bw6-761/fr/plookup/vector.go @@ -340,7 +340,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element Mul(&res[_i], &numLn[i%2]) } - domainBig.FFTInverse(res, fft.DIT, true) + domainBig.FFTInverse(res, fft.DIT, fft.OnCoset()) return res } @@ -476,11 +476,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) copy(_lh2, ch2) copy(_lt, ct) copy(_lf, cf) - domainBig.FFT(_lz, fft.DIF, true) - domainBig.FFT(_lh1, fft.DIF, true) - domainBig.FFT(_lh2, fft.DIF, true) - domainBig.FFT(_lt, fft.DIF, true) - domainBig.FFT(_lf, fft.DIF, true) + domainBig.FFT(_lz, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh1, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh2, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lt, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lf, fft.DIF, fft.OnCoset()) // compute h lh := evaluateNumBitReversed(_lz, _lh1, _lh2, _lt, _lf, beta, gamma, domainBig) diff --git a/ecc/bw6-761/internal/fptower/e6_pairing.go b/ecc/bw6-761/internal/fptower/e6_pairing.go index b8d2ca40fe..2ec55cf6df 100644 --- a/ecc/bw6-761/internal/fptower/e6_pairing.go +++ b/ecc/bw6-761/internal/fptower/e6_pairing.go @@ -109,8 +109,8 @@ func (z *E6) MulBy034(c0, c3, c4 *fp.Element) *E6 { } // Mul034By034 multiplication of sparse element (c0,0,0,c3,c4,0) by sparse element (d0,0,0,d3,d4,0) -func (z *E6) Mul034By034(d0, d3, d4, c0, c3, c4 *fp.Element) *E6 { - var tmp, x0, x3, x4, x04, x03, x34 fp.Element +func Mul034By034(d0, d3, d4, c0, c3, c4 *fp.Element) [5]fp.Element { + var z00, tmp, x0, x3, x4, x04, x03, x34 fp.Element x0.Mul(c0, d0) x3.Mul(c3, d3) x4.Mul(c4, d4) @@ -130,13 +130,30 @@ func (z *E6) Mul034By034(d0, d3, d4, c0, c3, c4 *fp.Element) *E6 { Sub(&x34, &x3). Sub(&x34, &x4) - z.B0.A0.MulByNonResidue(&x4). - Add(&z.B0.A0, &x0) - z.B0.A1.Set(&x3) - z.B0.A2.Set(&x34) - z.B1.A0.Set(&x03) - z.B1.A1.Set(&x04) - z.B1.A2.SetZero() + z00.MulByNonResidue(&x4). + Add(&z00, &x0) + + return [5]fp.Element{z00, x3, x34, x03, x04} +} + +// MulBy01234 multiplies z by an E12 sparse element of the form (x0, x1, x2, x3, x4, 0) +func (z *E6) MulBy01234(x *[5]fp.Element) *E6 { + var c1, a, b, c, z0, z1 E3 + c0 := &E3{A0: x[0], A1: x[1], A2: x[2]} + c1.A0 = x[3] + c1.A1 = x[4] + a.Add(&z.B0, &z.B1) + b.Add(c0, &c1) + a.Mul(&a, &b) + b.Mul(&z.B0, c0) + c.Set(&z.B1).MulBy01(&x[3], &x[4]) + z1.Sub(&a, &b) + z1.Sub(&z1, &c) + z0.MulByNonResidue(&c) + z0.Add(&z0, &b) + + z.B0 = z0 + z.B1 = z1 return z } diff --git a/ecc/bw6-761/marshal.go b/ecc/bw6-761/marshal.go index ad6160197e..54bf3ed506 100644 --- a/ecc/bw6-761/marshal.go +++ b/ecc/bw6-761/marshal.go @@ -50,6 +50,8 @@ const ( // SizeOfGT represents the size in bytes that a GT element need in binary form const SizeOfGT = fptower.SizeOfGT +var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding") + // Encoder writes bw6-761 object values to an output stream type Encoder struct { w io.Writer @@ -365,6 +367,19 @@ func NoSubgroupChecks() func(*Decoder) { } } +// isZeroed checks that the provided bytes are at 0 +func isZeroed(firstByte byte, buf []byte) bool { + if firstByte != 0 { + return false + } + for _, b := range buf { + if b != 0 { + return false + } + } + return true +} + func (enc *Encoder) encode(v interface{}) (err error) { rv := reflect.ValueOf(v) if v == nil || (rv.Kind() == reflect.Ptr && rv.IsNil()) { @@ -674,13 +689,19 @@ func (p *G1Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG1AffineUncompressed, nil @@ -796,9 +817,12 @@ func (p *G1Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG1AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } @@ -921,13 +945,19 @@ func (p *G2Affine) setBytes(buf []byte, subGroupCheck bool) (int, error) { } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if mData == mCompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineCompressed, nil } if mData == mUncompressedInfinity { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineUncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOfG2AffineUncompressed, nil @@ -1043,9 +1073,12 @@ func (p *G2Affine) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, err er mData := buf[0] & mMask if mData == mCompressedInfinity { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOfG2AffineCompressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } diff --git a/ecc/bw6-761/pairing.go b/ecc/bw6-761/pairing.go index 4e5dcfa8d0..a5bad77332 100644 --- a/ecc/bw6-761/pairing.go +++ b/ecc/bw6-761/pairing.go @@ -1,4 +1,3 @@ -// Copyright 2020 ConsenSys AG // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. @@ -152,7 +151,10 @@ func FinalExponentiation(z *GT, _z ...*GT) GT { } // MillerLoop Optimal Tate alternative (or twisted ate or Eta revisited) -// computes the multi-Miller loop ∏ᵢ MillerLoop(Pᵢ, Qᵢ) +// computes the multi-Miller loop +// ∏ᵢ MillerLoop(Pᵢ, Qᵢ) = +// ∏ᵢ { fᵢ_{x₀+1+λ(x₀³-x₀²-x₀),Pᵢ}(Qᵢ) } +// // Alg.2 in https://eprint.iacr.org/2021/1359.pdf // Eq. (6) in https://hackmd.io/@gnark/BW6-761-changes func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { @@ -190,117 +192,222 @@ func MillerLoop(P []G1Affine, Q []G2Affine) (GT, error) { // l_{p0,p1}(q) pProj01[k].Set(&pProj1[k]) - pProj01[k].AddMixedStep(&l01[k], &p0[k]) + pProj01[k].addMixedStep(&l01[k], &p0[k]) l01[k].r1.Mul(&l01[k].r1, &q[k].X) l01[k].r0.Mul(&l01[k].r0, &q[k].Y) // l_{p0,-p1}(q) pProj10[k].Neg(&pProj1[k]) - pProj10[k].AddMixedStep(&l10[k], &p0[k]) + pProj10[k].addMixedStep(&l10[k], &p0[k]) l10[k].r1.Mul(&l10[k].r1, &q[k].X) l10[k].r0.Mul(&l10[k].r0, &q[k].Y) } p01 := BatchProjectiveToAffineG1(pProj01) p10 := BatchProjectiveToAffineG1(pProj10) - // f_{a0+\lambda*a1,P}(Q) - var result, ss GT + // f_{a0+λ*a1,P}(Q) + var result GT result.SetOne() var l, l0 lineEvaluation + var prodLines [5]fp.Element var j int8 - // i = len(loopCounter) - 2 - for k := 0; k < n; k++ { - pProj1[k].DoubleStep(&l0) + if n >= 1 { + // i = len(loopCounter0) - 2, separately to avoid an E12 Square + // (Square(res) = 1² = 1) + // j = 0 + // k = 0, separately to avoid MulBy034 (res × ℓ) + // (assign line to res) + + // pProj1[0] ← 2pProj1[0] and l0 the tangent ℓ passing 2pProj1[0] + pProj1[0].doubleStep(&l0) + // line evaluation at Q[0] (assign) + result.B1.A0.Mul(&l0.r1, &q[0].X) + result.B0.A0.Mul(&l0.r0, &q[0].Y) + result.B1.A1.Set(&l0.r2) + } + + // k = 1 + if n >= 2 { + // pProj1[1] ← 2pProj1[1] and l0 the tangent ℓ passing 2pProj1[1] + pProj1[1].doubleStep(&l0) + // line evaluation at Q[0] + l0.r1.Mul(&l0.r1, &q[1].X) + l0.r0.Mul(&l0.r0, &q[1].Y) + // ℓ × res + prodLines = fptower.Mul034By034(&l0.r0, &l0.r1, &l0.r2, &result.B0.A0, &result.B1.A0, &result.B1.A1) + result.B0.A0 = prodLines[0] + result.B0.A1 = prodLines[1] + result.B0.A2 = prodLines[2] + result.B1.A0 = prodLines[3] + result.B1.A1 = prodLines[4] + } + + // k >= 2 + for k := 2; k < n; k++ { + // pProj1[1] ← 2pProj1[1] and l0 the tangent ℓ passing 2pProj1[1] + pProj1[k].doubleStep(&l0) + // line evaluation at Q[k] l0.r1.Mul(&l0.r1, &q[k].X) l0.r0.Mul(&l0.r0, &q[k].Y) + // ℓ × res result.MulBy034(&l0.r0, &l0.r1, &l0.r2) } var tmp G1Affine - for i := len(loopCounter0) - 3; i >= 0; i-- { + for i := len(loopCounter0) - 3; i >= 1; i-- { // (∏ᵢfᵢ)² + // mutualize the square among n Miller loops result.Square(&result) j = loopCounter1[i]*3 + loopCounter0[i] for k := 0; k < n; k++ { - pProj1[k].DoubleStep(&l0) + // pProj1[1] ← 2pProj1[1] and l0 the tangent ℓ passing 2pProj1[1] + pProj1[k].doubleStep(&l0) + // line evaluation at Q[k] l0.r1.Mul(&l0.r1, &q[k].X) l0.r0.Mul(&l0.r0, &q[k].Y) switch j { case -4: tmp.Neg(&p01[k]) - pProj1[k].AddMixedStep(&l, &tmp) + // pProj1[k] ← pProj1[k]-p01[k] and + // l the line ℓ passing pProj1[k] and -p01[k] + pProj1[k].addMixedStep(&l, &tmp) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) - result.MulBy034(&l0.r0, &l0.r1, &l0.r2). - Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) + // ℓ × res + result.MulBy034(&l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case -3: tmp.Neg(&p1[k]) - pProj1[k].AddMixedStep(&l, &tmp) + // pProj1[k] ← pProj1[k]-p1[k] and + // l the line ℓ passing pProj1[k] and -p1[k] + pProj1[k].addMixedStep(&l, &tmp) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case -2: - pProj1[k].AddMixedStep(&l, &p10[k]) + // pProj1[k] ← pProj1[k]+p10[k] and + // l the line ℓ passing pProj1[k] and p10[k] + pProj1[k].addMixedStep(&l, &p10[k]) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) - result.MulBy034(&l0.r0, &l0.r1, &l0.r2). - Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) + // ℓ × res + result.MulBy034(&l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case -1: tmp.Neg(&p0[k]) - pProj1[k].AddMixedStep(&l, &tmp) + // pProj1[k] ← pProj1[k]-p0[k] and + // l the line ℓ passing pProj1[k] and -p0[k] + pProj1[k].addMixedStep(&l, &tmp) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case 0: + // ℓ × res result.MulBy034(&l0.r0, &l0.r1, &l0.r2) case 1: - pProj1[k].AddMixedStep(&l, &p0[k]) + // pProj1[k] ← pProj1[k]+p0[k] and + // l the line ℓ passing pProj1[k] and p0[k] + pProj1[k].addMixedStep(&l, &p0[k]) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case 2: tmp.Neg(&p10[k]) - pProj1[k].AddMixedStep(&l, &tmp) + // pProj1[k] ← pProj1[k]-p10[k] and + // l the line ℓ passing pProj1[k] and -p10[k] + pProj1[k].addMixedStep(&l, &tmp) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) - result.MulBy034(&l0.r0, &l0.r1, &l0.r2). - Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) + // ℓ × res + result.MulBy034(&l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case 3: - pProj1[k].AddMixedStep(&l, &p1[k]) + // pProj1[k] ← pProj1[k]+p1[k] and + // l the line ℓ passing pProj1[k] and p1[k] + pProj1[k].addMixedStep(&l, &p1[k]) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) - result.Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) case 4: - pProj1[k].AddMixedStep(&l, &p01[k]) + // pProj1[k] ← pProj1[k]+p01[k] and + // l the line ℓ passing pProj1[k] and p01[k] + pProj1[k].addMixedStep(&l, &p01[k]) + // line evaluation at Q[k] l.r1.Mul(&l.r1, &q[k].X) l.r0.Mul(&l.r0, &q[k].Y) - ss.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) - result.MulBy034(&l0.r0, &l0.r1, &l0.r2). - Mul(&result, &ss) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l01[k].r0, &l01[k].r1, &l01[k].r2) + // ℓ × res + result.MulBy034(&l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy01234(&prodLines) default: return GT{}, errors.New("invalid loopCounter") } } } + // i = 0, separately to avoid a point addition + // j = -3 + result.Square(&result) + for k := 0; k < n; k++ { + // pProj1[k] ← 2pProj1[k] and l0 the tangent ℓ passing 2pProj1[k] + pProj1[k].doubleStep(&l0) + // line evaluation at Q[k] + l0.r1.Mul(&l0.r1, &q[k].X) + l0.r0.Mul(&l0.r0, &q[k].Y) + + tmp.Neg(&p1[k]) + // l the line passing pProj1[k] and -p1 + pProj1[k].lineCompute(&l, &tmp) + // line evaluation at Q[k] + l.r1.Mul(&l.r1, &q[k].X) + l.r0.Mul(&l.r0, &q[k].Y) + // ℓ × ℓ + prodLines = fptower.Mul034By034(&l.r0, &l.r1, &l.r2, &l0.r0, &l0.r1, &l0.r2) + // (ℓ × ℓ) × res + result.MulBy034(&l0.r0, &l0.r1, &l0.r2) + } + return result, nil } -// DoubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop +// doubleStep doubles a point in Homogenous projective coordinates, and evaluates the line in Miller loop // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g1Proj) DoubleStep(evaluations *lineEvaluation) { +func (p *g1Proj) doubleStep(evaluations *lineEvaluation) { // get some Element from our pool var t1, A, B, C, D, E, EE, F, G, H, I, J, K fp.Element @@ -342,9 +449,9 @@ func (p *g1Proj) DoubleStep(evaluations *lineEvaluation) { evaluations.r2.Set(&I) } -// AddMixedStep point addition in Mixed Homogenous projective and Affine coordinates +// addMixedStep point addition in Mixed Homogenous projective and Affine coordinates // https://eprint.iacr.org/2013/722.pdf (Section 4.3) -func (p *g1Proj) AddMixedStep(evaluations *lineEvaluation, a *G1Affine) { +func (p *g1Proj) addMixedStep(evaluations *lineEvaluation, a *G1Affine) { // get some Element from our pool var Y2Z1, X2Z1, O, L, C, D, E, F, G, H, t0, t1, t2, J fp.Element @@ -378,3 +485,23 @@ func (p *g1Proj) AddMixedStep(evaluations *lineEvaluation, a *G1Affine) { evaluations.r1.Neg(&O) evaluations.r2.Set(&J) } + +// lineCompute computes the line through p in Homogenous projective coordinates +// and a in affine coordinates. It does not compute the resulting point p+a. +func (p *g1Proj) lineCompute(evaluations *lineEvaluation, a *G1Affine) { + + // get some Element from our pool + var Y2Z1, X2Z1, O, L, t2, J fp.Element + Y2Z1.Mul(&a.Y, &p.z) + O.Sub(&p.y, &Y2Z1) + X2Z1.Mul(&a.X, &p.z) + L.Sub(&p.x, &X2Z1) + t2.Mul(&L, &a.Y) + J.Mul(&a.X, &O). + Sub(&J, &t2) + + // Line evaluation + evaluations.r0.Set(&L) + evaluations.r1.Neg(&O) + evaluations.r2.Set(&J) +} diff --git a/ecc/secp256k1/ecdsa/ecdsa.go b/ecc/secp256k1/ecdsa/ecdsa.go index de7c735da8..e71985e3ec 100644 --- a/ecc/secp256k1/ecdsa/ecdsa.go +++ b/ecc/secp256k1/ecdsa/ecdsa.go @@ -33,8 +33,6 @@ import ( "github.com/consensys/gnark-crypto/signature" ) -var errInvalidSig = errors.New("invalid signature") - const ( sizeFr = fr.Bytes sizeFp = fp.Bytes @@ -110,6 +108,54 @@ func HashToInt(hash []byte) *big.Int { return ret } +// RecoverP recovers the value P (prover commitment) when creating a signature. +// It uses the recovery information v and part of the decomposed signature r. It +// is used internally for recovering the public key. +func RecoverP(v uint, r *big.Int) (*secp256k1.G1Affine, error) { + if r.Cmp(fr.Modulus()) >= 0 { + return nil, errors.New("r is larger than modulus") + } + if r.Cmp(big.NewInt(0)) <= 0 { + return nil, errors.New("r is negative") + } + x := new(big.Int).Set(r) + // if x is r or r+N + xChoice := (v & 2) >> 1 + // if y is y or -y + yChoice := v & 1 + // decompose limbs into big.Int value + // conditional +n based on xChoice + kn := big.NewInt(int64(xChoice)) + kn.Mul(kn, fr.Modulus()) + x.Add(x, kn) + // y^2 = x^3+ax+b + a, b := secp256k1.CurveCoefficients() + y := new(big.Int).Exp(x, big.NewInt(3), fp.Modulus()) + if !a.IsZero() { + y.Add(y, new(big.Int).Mul(a.BigInt(new(big.Int)), x)) + } + y.Add(y, b.BigInt(new(big.Int))) + y.Mod(y, fp.Modulus()) + // y = sqrt(y^2) + if y.ModSqrt(y, fp.Modulus()) == nil { + return nil, errors.New("no square root") + } + // y2 is -y + y2 := new(big.Int).Sub(fp.Modulus(), y) + // if yChoice == 0, return min(y, y2), else max(y, y2) + if (y.Cmp(y2) < 0) == (yChoice == 0) { + return &secp256k1.G1Affine{ + X: *new(fp.Element).SetBigInt(x), + Y: *new(fp.Element).SetBigInt(y), + }, nil + } else { + return &secp256k1.G1Affine{ + X: *new(fp.Element).SetBigInt(x), + Y: *new(fp.Element).SetBigInt(y2), + }, nil + } +} + type zr struct{} // Read replaces the contents of dst with zeros. It is safe for concurrent use. @@ -185,27 +231,31 @@ func (privKey *PrivateKey) Public() signature.PublicKey { return &pub } -// Sign performs the ECDSA signature +// SignForRecover performs the ECDSA signature and returns public key recovery information // // k ← 𝔽r (random) // P = k ⋅ g1Gen // r = x_P (mod order) // s = k⁻¹ . (m + sk ⋅ r) -// signature = {r, s} +// v = (div(x_P, order)<<1) || y_P[-1] // // SEC 1, Version 2.0, Section 4.1.3 -func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) { - scalar, r, s, kInv := new(big.Int), new(big.Int), new(big.Int), new(big.Int) +func (privKey *PrivateKey) SignForRecover(message []byte, hFunc hash.Hash) (v uint, r, s *big.Int, err error) { + halfp := new(big.Int).Sub(fp.Modulus(), big.NewInt(1)) + halfp.Div(halfp, big.NewInt(2)) + r, s = new(big.Int), new(big.Int) + + scalar, kInv := new(big.Int), new(big.Int) scalar.SetBytes(privKey.scalar[:sizeFr]) for { for { csprng, err := nonce(privKey, message) if err != nil { - return nil, err + return 0, nil, nil, err } k, err := randFieldElement(csprng) if err != nil { - return nil, err + return 0, nil, nil, err } var P secp256k1.G1Affine @@ -213,6 +263,13 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) kInv.ModInverse(k, order) P.X.BigInt(r) + // set how many times we overflow the scalar field + v |= (uint(new(big.Int).Div(r, order).Uint64())) << 1 + // set if y is small or big + if P.Y.BigInt(new(big.Int)).Cmp(halfp) >= 0 { + v |= 1 + } + r.Mod(r, order) if r.Sign() != 0 { break @@ -228,7 +285,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) hFunc.Reset() _, err := hFunc.Write(dataToHash[:]) if err != nil { - return nil, err + return 0, nil, nil, err } hramBin := hFunc.Sum(nil) m = HashToInt(hramBin) @@ -244,6 +301,23 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) } } + return v, r, s, nil +} + +// Sign performs the ECDSA signature +// +// k ← 𝔽r (random) +// P = k ⋅ g1Gen +// r = x_P (mod order) +// s = k⁻¹ . (m + sk ⋅ r) +// signature = {r, s} +// +// SEC 1, Version 2.0, Section 4.1.3 +func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) { + _, r, s, err := privKey.SignForRecover(message, hFunc) + if err != nil { + return nil, err + } var sig Signature r.FillBytes(sig.R[:sizeFr]) s.FillBytes(sig.S[:sizeFr]) diff --git a/ecc/secp256k1/ecdsa/ecdsa_test.go b/ecc/secp256k1/ecdsa/ecdsa_test.go index d69f035354..197b8e76da 100644 --- a/ecc/secp256k1/ecdsa/ecdsa_test.go +++ b/ecc/secp256k1/ecdsa/ecdsa_test.go @@ -62,6 +62,31 @@ func TestECDSA(t *testing.T) { properties.TestingRun(t, gopter.ConsoleReporter(false)) } +func TestRecoverPublicKey(t *testing.T) { + t.Parallel() + parameters := gopter.DefaultTestParameters() + properties := gopter.NewProperties(parameters) + properties.Property("[SECP256K1] test public key recover", prop.ForAll( + func() bool { + sk, err := GenerateKey(rand.Reader) + if err != nil { + return false + } + pk := sk.PublicKey + msg := []byte("test") + v, r, s, err := sk.SignForRecover(msg, nil) + if err != nil { + return false + } + var recovered PublicKey + if err = recovered.RecoverFrom(msg, v, r, s); err != nil { + return false + } + return pk.Equal(&recovered) + }, + )) + properties.TestingRun(t, gopter.ConsoleReporter(false)) +} // ------------------------------------------------------------ // benches @@ -88,3 +113,20 @@ func BenchmarkVerifyECDSA(b *testing.B) { privKey.PublicKey.Verify(sig, msg, nil) } } +func BenchmarkRecoverPublicKey(b *testing.B) { + sk, err := GenerateKey(rand.Reader) + if err != nil { + b.Fatal(err) + } + msg := []byte("bench") + v, r, s, err := sk.SignForRecover(msg, sha256.New()) + if err != nil { + b.Fatal(err) + } + for i := 0; i < b.N; i++ { + var recovered PublicKey + if err = recovered.RecoverFrom(msg, v, r, s); err != nil { + b.Fatal(err) + } + } +} diff --git a/ecc/secp256k1/ecdsa/marshal.go b/ecc/secp256k1/ecdsa/marshal.go index ff04c7d942..3372368abc 100644 --- a/ecc/secp256k1/ecdsa/marshal.go +++ b/ecc/secp256k1/ecdsa/marshal.go @@ -19,6 +19,10 @@ package ecdsa import ( "crypto/subtle" "io" + "math/big" + + "github.com/consensys/gnark-crypto/ecc/secp256k1" + "github.com/consensys/gnark-crypto/ecc/secp256k1/fr" ) // Bytes returns the binary representation of the public key @@ -52,6 +56,28 @@ func (pk *PublicKey) SetBytes(buf []byte) (int, error) { return n, nil } +// RecoverFrom recovers the public key from the message msg, recovery +// information v and decompose signature {r,s}. If recovery succeeded, the +// methods sets the current public key to the recovered value. Otherwise returns +// error and leaves current public key unchanged. +func (pk *PublicKey) RecoverFrom(msg []byte, v uint, r, s *big.Int) error { + P, err := RecoverP(v, r) + if err != nil { + return err + } + z := HashToInt(msg) + rinv := new(big.Int).ModInverse(r, fr.Modulus()) + u1 := new(big.Int).Mul(z, rinv) + u1.Neg(u1) + u1.Mod(u1, fr.Modulus()) + u2 := new(big.Int).Mul(s, rinv) + u2.Mod(u2, fr.Modulus()) + var Q secp256k1.G1Jac + Q.JointScalarMultiplicationBase(P, u1, u2) + pk.A.FromJacobian(&Q) + return nil +} + // Bytes returns the binary representation of pk, // as byte array publicKey||scalar // where publicKey is as publicKey.Bytes(), and diff --git a/ecc/secp256k1/fp/element.go b/ecc/secp256k1/fp/element.go index 03a50c1c68..9daa6873e7 100644 --- a/ecc/secp256k1/fp/element.go +++ b/ecc/secp256k1/fp/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -720,12 +721,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -735,7 +736,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/secp256k1/fr/element.go b/ecc/secp256k1/fr/element.go index 02445ebb60..99bc42fa4b 100644 --- a/ecc/secp256k1/fr/element.go +++ b/ecc/secp256k1/fr/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -720,12 +721,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -735,7 +736,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/secp256k1/secp256k1.go b/ecc/secp256k1/secp256k1.go index feed74366e..c315408371 100644 --- a/ecc/secp256k1/secp256k1.go +++ b/ecc/secp256k1/secp256k1.go @@ -39,7 +39,8 @@ import ( // ID secp256k1 ID const ID = ecc.SECP256K1 -// bCurveCoeff b coeff of the curve Y²=X³+b +// aCurveCoeff is the a coefficients of the curve Y²=X³+ax+b +var aCurveCoeff fp.Element var bCurveCoeff fp.Element // generator of the r-torsion group @@ -63,7 +64,7 @@ var lambdaGLV big.Int var glvBasis ecc.Lattice func init() { - + aCurveCoeff.SetUint64(0) bCurveCoeff.SetUint64(7) g1Gen.X.SetString("55066263022277343669578718895168534326250603453777594175500187360389116729240") @@ -89,3 +90,8 @@ func Generators() (g1Jac G1Jac, g1Aff G1Affine) { g1Jac = g1Gen return } + +// CurveCoefficients returns the a, b coefficients of the curve equation. +func CurveCoefficients() (a, b fp.Element) { + return aCurveCoeff, bCurveCoeff +} diff --git a/ecc/stark-curve/ecdsa/ecdsa.go b/ecc/stark-curve/ecdsa/ecdsa.go index 4707f32195..f9d9c5f0bd 100644 --- a/ecc/stark-curve/ecdsa/ecdsa.go +++ b/ecc/stark-curve/ecdsa/ecdsa.go @@ -33,8 +33,6 @@ import ( "github.com/consensys/gnark-crypto/signature" ) -var errInvalidSig = errors.New("invalid signature") - const ( sizeFr = fr.Bytes sizeFp = fp.Bytes @@ -110,6 +108,54 @@ func HashToInt(hash []byte) *big.Int { return ret } +// RecoverP recovers the value P (prover commitment) when creating a signature. +// It uses the recovery information v and part of the decomposed signature r. It +// is used internally for recovering the public key. +func RecoverP(v uint, r *big.Int) (*starkcurve.G1Affine, error) { + if r.Cmp(fr.Modulus()) >= 0 { + return nil, errors.New("r is larger than modulus") + } + if r.Cmp(big.NewInt(0)) <= 0 { + return nil, errors.New("r is negative") + } + x := new(big.Int).Set(r) + // if x is r or r+N + xChoice := (v & 2) >> 1 + // if y is y or -y + yChoice := v & 1 + // decompose limbs into big.Int value + // conditional +n based on xChoice + kn := big.NewInt(int64(xChoice)) + kn.Mul(kn, fr.Modulus()) + x.Add(x, kn) + // y^2 = x^3+ax+b + a, b := starkcurve.CurveCoefficients() + y := new(big.Int).Exp(x, big.NewInt(3), fp.Modulus()) + if !a.IsZero() { + y.Add(y, new(big.Int).Mul(a.BigInt(new(big.Int)), x)) + } + y.Add(y, b.BigInt(new(big.Int))) + y.Mod(y, fp.Modulus()) + // y = sqrt(y^2) + if y.ModSqrt(y, fp.Modulus()) == nil { + return nil, errors.New("no square root") + } + // y2 is -y + y2 := new(big.Int).Sub(fp.Modulus(), y) + // if yChoice == 0, return min(y, y2), else max(y, y2) + if (y.Cmp(y2) < 0) == (yChoice == 0) { + return &starkcurve.G1Affine{ + X: *new(fp.Element).SetBigInt(x), + Y: *new(fp.Element).SetBigInt(y), + }, nil + } else { + return &starkcurve.G1Affine{ + X: *new(fp.Element).SetBigInt(x), + Y: *new(fp.Element).SetBigInt(y2), + }, nil + } +} + type zr struct{} // Read replaces the contents of dst with zeros. It is safe for concurrent use. @@ -185,27 +231,31 @@ func (privKey *PrivateKey) Public() signature.PublicKey { return &pub } -// Sign performs the ECDSA signature +// SignForRecover performs the ECDSA signature and returns public key recovery information // // k ← 𝔽r (random) // P = k ⋅ g1Gen // r = x_P (mod order) // s = k⁻¹ . (m + sk ⋅ r) -// signature = {r, s} +// v = (div(x_P, order)<<1) || y_P[-1] // // SEC 1, Version 2.0, Section 4.1.3 -func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) { - scalar, r, s, kInv := new(big.Int), new(big.Int), new(big.Int), new(big.Int) +func (privKey *PrivateKey) SignForRecover(message []byte, hFunc hash.Hash) (v uint, r, s *big.Int, err error) { + halfp := new(big.Int).Sub(fp.Modulus(), big.NewInt(1)) + halfp.Div(halfp, big.NewInt(2)) + r, s = new(big.Int), new(big.Int) + + scalar, kInv := new(big.Int), new(big.Int) scalar.SetBytes(privKey.scalar[:sizeFr]) for { for { csprng, err := nonce(privKey, message) if err != nil { - return nil, err + return 0, nil, nil, err } k, err := randFieldElement(csprng) if err != nil { - return nil, err + return 0, nil, nil, err } var P starkcurve.G1Affine @@ -213,6 +263,13 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) kInv.ModInverse(k, order) P.X.BigInt(r) + // set how many times we overflow the scalar field + v |= (uint(new(big.Int).Div(r, order).Uint64())) << 1 + // set if y is small or big + if P.Y.BigInt(new(big.Int)).Cmp(halfp) >= 0 { + v |= 1 + } + r.Mod(r, order) if r.Sign() != 0 { break @@ -228,7 +285,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) hFunc.Reset() _, err := hFunc.Write(dataToHash[:]) if err != nil { - return nil, err + return 0, nil, nil, err } hramBin := hFunc.Sum(nil) m = HashToInt(hramBin) @@ -244,6 +301,23 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) } } + return v, r, s, nil +} + +// Sign performs the ECDSA signature +// +// k ← 𝔽r (random) +// P = k ⋅ g1Gen +// r = x_P (mod order) +// s = k⁻¹ . (m + sk ⋅ r) +// signature = {r, s} +// +// SEC 1, Version 2.0, Section 4.1.3 +func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) { + _, r, s, err := privKey.SignForRecover(message, hFunc) + if err != nil { + return nil, err + } var sig Signature r.FillBytes(sig.R[:sizeFr]) s.FillBytes(sig.S[:sizeFr]) diff --git a/ecc/stark-curve/ecdsa/ecdsa_test.go b/ecc/stark-curve/ecdsa/ecdsa_test.go index 5c7e69882c..5884ab5f4a 100644 --- a/ecc/stark-curve/ecdsa/ecdsa_test.go +++ b/ecc/stark-curve/ecdsa/ecdsa_test.go @@ -62,6 +62,31 @@ func TestECDSA(t *testing.T) { properties.TestingRun(t, gopter.ConsoleReporter(false)) } +func TestRecoverPublicKey(t *testing.T) { + t.Parallel() + parameters := gopter.DefaultTestParameters() + properties := gopter.NewProperties(parameters) + properties.Property("[STARK-CURVE] test public key recover", prop.ForAll( + func() bool { + sk, err := GenerateKey(rand.Reader) + if err != nil { + return false + } + pk := sk.PublicKey + msg := []byte("test") + v, r, s, err := sk.SignForRecover(msg, nil) + if err != nil { + return false + } + var recovered PublicKey + if err = recovered.RecoverFrom(msg, v, r, s); err != nil { + return false + } + return pk.Equal(&recovered) + }, + )) + properties.TestingRun(t, gopter.ConsoleReporter(false)) +} // ------------------------------------------------------------ // benches @@ -88,3 +113,20 @@ func BenchmarkVerifyECDSA(b *testing.B) { privKey.PublicKey.Verify(sig, msg, nil) } } +func BenchmarkRecoverPublicKey(b *testing.B) { + sk, err := GenerateKey(rand.Reader) + if err != nil { + b.Fatal(err) + } + msg := []byte("bench") + v, r, s, err := sk.SignForRecover(msg, sha256.New()) + if err != nil { + b.Fatal(err) + } + for i := 0; i < b.N; i++ { + var recovered PublicKey + if err = recovered.RecoverFrom(msg, v, r, s); err != nil { + b.Fatal(err) + } + } +} diff --git a/ecc/stark-curve/ecdsa/marshal.go b/ecc/stark-curve/ecdsa/marshal.go index 72d74c5cb1..258a5a74bd 100644 --- a/ecc/stark-curve/ecdsa/marshal.go +++ b/ecc/stark-curve/ecdsa/marshal.go @@ -19,6 +19,10 @@ package ecdsa import ( "crypto/subtle" "io" + "math/big" + + "github.com/consensys/gnark-crypto/ecc/stark-curve" + "github.com/consensys/gnark-crypto/ecc/stark-curve/fr" ) // Bytes returns the binary representation of the public key @@ -52,6 +56,28 @@ func (pk *PublicKey) SetBytes(buf []byte) (int, error) { return n, nil } +// RecoverFrom recovers the public key from the message msg, recovery +// information v and decompose signature {r,s}. If recovery succeeded, the +// methods sets the current public key to the recovered value. Otherwise returns +// error and leaves current public key unchanged. +func (pk *PublicKey) RecoverFrom(msg []byte, v uint, r, s *big.Int) error { + P, err := RecoverP(v, r) + if err != nil { + return err + } + z := HashToInt(msg) + rinv := new(big.Int).ModInverse(r, fr.Modulus()) + u1 := new(big.Int).Mul(z, rinv) + u1.Neg(u1) + u1.Mod(u1, fr.Modulus()) + u2 := new(big.Int).Mul(s, rinv) + u2.Mod(u2, fr.Modulus()) + var Q starkcurve.G1Jac + Q.JointScalarMultiplicationBase(P, u1, u2) + pk.A.FromJacobian(&Q) + return nil +} + // Bytes returns the binary representation of pk, // as byte array publicKey||scalar // where publicKey is as publicKey.Bytes(), and diff --git a/ecc/stark-curve/fp/element.go b/ecc/stark-curve/fp/element.go index 9e4886de99..9d729df35a 100644 --- a/ecc/stark-curve/fp/element.go +++ b/ecc/stark-curve/fp/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -692,12 +693,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -707,7 +708,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/stark-curve/fr/element.go b/ecc/stark-curve/fr/element.go index d24623beb5..37e6c9c4ec 100644 --- a/ecc/stark-curve/fr/element.go +++ b/ecc/stark-curve/fr/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -692,12 +693,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -707,7 +708,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/ecc/stark-curve/g1.go b/ecc/stark-curve/g1.go index dd806bd9dc..848c036ef9 100644 --- a/ecc/stark-curve/g1.go +++ b/ecc/stark-curve/g1.go @@ -393,10 +393,7 @@ func (p *G1Jac) IsOnCurve() bool { // IsInSubGroup returns true if p is on the r-torsion, false otherwise. func (p *G1Jac) IsInSubGroup() bool { - var res G1Jac - res.ScalarMultiplication(&res, fr.Modulus()) - - return res.IsOnCurve() && res.Z.IsZero() + return p.IsOnCurve() } diff --git a/ecc/stark-curve/stark_curve.go b/ecc/stark-curve/stark_curve.go index 443839dec7..c7ec96f8db 100644 --- a/ecc/stark-curve/stark_curve.go +++ b/ecc/stark-curve/stark_curve.go @@ -36,7 +36,8 @@ import ( // ID stark_curve ID const ID = ecc.STARK_CURVE -// bCurveCoeff b coeff of the curve Y²=X³+x+b +// aCurveCoeff is the a coefficients of the curve Y²=X³+ax+b +var aCurveCoeff fp.Element var bCurveCoeff fp.Element // generator of the r-torsion group @@ -48,7 +49,7 @@ var g1GenAff G1Affine var g1Infinity G1Jac func init() { - + aCurveCoeff.SetUint64(1) bCurveCoeff.SetString("3141592653589793238462643383279502884197169399375105820974944592307816406665") g1Gen.X.SetString("874739451078007766457464989774322083649278607533249481151382481072868806602") @@ -69,3 +70,8 @@ func Generators() (g1Jac G1Jac, g1Aff G1Affine) { g1Jac = g1Gen return } + +// CurveCoefficients returns the a, b coefficients of the curve equation. +func CurveCoefficients() (a, b fp.Element) { + return aCurveCoeff, bCurveCoeff +} diff --git a/field/generator/config/field_test.go b/field/generator/config/field_test.go index f57cc5574d..70fd77bc22 100644 --- a/field/generator/config/field_test.go +++ b/field/generator/config/field_test.go @@ -201,7 +201,11 @@ func genField(t *testing.T) gopter.Gen { genField := func() *FieldConfig { nbWords := minNbWords + mrand.Intn(maxNbWords-minNbWords) //#nosec G404 -- This is a false positive - bitLen := nbWords*64 - 1 - mrand.Intn(64) //#nosec G404 -- This is a false positive + bitLen := nbWords*64 - mrand.Intn(64) //#nosec G404 -- This is a false positive + + if bitLen < 2 { + bitLen = 2 + } modulus, err := rand.Prime(rand.Reader, bitLen) if err != nil { diff --git a/field/generator/internal/templates/element/base.go b/field/generator/internal/templates/element/base.go index 39e8a351bc..4812a20805 100644 --- a/field/generator/internal/templates/element/base.go +++ b/field/generator/internal/templates/element/base.go @@ -15,6 +15,7 @@ import ( "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" + "github.com/bits-and-blooms/bitset" ) // {{.ElementName}} represents a field element stored on {{.NbWords}} words (uint64) @@ -564,12 +565,12 @@ func BatchInvert(a []{{.ElementName}}) []{{.ElementName}} { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i:=0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -579,7 +580,7 @@ func BatchInvert(a []{{.ElementName}}) []{{.ElementName}} { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/field/goldilocks/element.go b/field/goldilocks/element.go index d6d28dc0c8..27e34a8fa6 100644 --- a/field/goldilocks/element.go +++ b/field/goldilocks/element.go @@ -27,6 +27,7 @@ import ( "strconv" "strings" + "github.com/bits-and-blooms/bitset" "github.com/consensys/gnark-crypto/field/hash" "github.com/consensys/gnark-crypto/field/pool" ) @@ -506,12 +507,12 @@ func BatchInvert(a []Element) []Element { return res } - zeroes := make([]bool, len(a)) + zeroes := bitset.New(uint(len(a))) accumulator := One() for i := 0; i < len(a); i++ { if a[i].IsZero() { - zeroes[i] = true + zeroes.Set(uint(i)) continue } res[i] = accumulator @@ -521,7 +522,7 @@ func BatchInvert(a []Element) []Element { accumulator.Inverse(&accumulator) for i := len(a) - 1; i >= 0; i-- { - if zeroes[i] { + if zeroes.Test(uint(i)) { continue } res[i].Mul(&res[i], &accumulator) diff --git a/go.mod b/go.mod index 4c6426bcf0..843b7bcadd 100644 --- a/go.mod +++ b/go.mod @@ -3,6 +3,7 @@ module github.com/consensys/gnark-crypto go 1.18 require ( + github.com/bits-and-blooms/bitset v1.5.0 github.com/consensys/bavard v0.1.13 github.com/leanovate/gopter v0.2.9 github.com/mmcloughlin/addchain v0.4.0 @@ -19,4 +20,4 @@ require ( github.com/spf13/pflag v1.0.5 // indirect gopkg.in/yaml.v3 v3.0.1 // indirect rsc.io/tmplfunc v0.0.3 // indirect -) \ No newline at end of file +) diff --git a/go.sum b/go.sum index b3ae5f84f9..0b3798313f 100644 --- a/go.sum +++ b/go.sum @@ -1,3 +1,5 @@ +github.com/bits-and-blooms/bitset v1.5.0 h1:NpE8frKRLGHIcEzkR+gZhiioW1+WbYV6fKwD6ZIpQT8= +github.com/bits-and-blooms/bitset v1.5.0/go.mod h1:gIdJ4wp64HaoK2YrL1Q5/N7Y16edYb8uY+O0FJTyyDA= github.com/consensys/bavard v0.1.13 h1:oLhMLOFGTLdlda/kma4VOJazblc7IM5y5QPd2A/YjhQ= github.com/consensys/bavard v0.1.13/go.mod h1:9ItSMtA/dXMAiL7BG6bqW2m3NdSEObYWoH223nGHukI= github.com/cpuguy83/go-md2man/v2 v2.0.2/go.mod h1:tgQtvFlXSQOSOSIRvRPT7W67SCa46tRHOmNcaadrF8o= diff --git a/internal/generator/ecc/template/marshal.go.tmpl b/internal/generator/ecc/template/marshal.go.tmpl index 4f31c9c3e9..fb1a9aa610 100644 --- a/internal/generator/ecc/template/marshal.go.tmpl +++ b/internal/generator/ecc/template/marshal.go.tmpl @@ -54,6 +54,7 @@ const ( // SizeOfGT represents the size in bytes that a GT element need in binary form const SizeOfGT = fptower.SizeOfGT +var ErrInvalidInfinityEncoding = errors.New("invalid infinity point encoding") // Encoder writes {{.Name}} object values to an output stream type Encoder struct { @@ -377,6 +378,19 @@ func NoSubgroupChecks() func(*Decoder) { } } +// isZeroed checks that the provided bytes are at 0 +func isZeroed(firstByte byte, buf []byte) bool { + if firstByte != 0 { + return false + } + for _, b := range buf { + if b != 0 { + return false + } + } + return true +} + {{template "encode" dict "Raw" ""}} {{template "encode" dict "Raw" "Raw"}} @@ -564,7 +578,7 @@ func (p *{{ $.TAffine }}) Bytes() (res [SizeOf{{ $.TAffine }}Compressed]byte) { // we store X and mask the most significant word with our metadata mask {{- if eq $.CoordType "fptower.E2"}} - // p.X.A1 | p.X.A0 + // p.X.A1 | p.X.A0 {{- $offset := $.sizeOfFp}} {{- template "putFp" dict "all" .all "OffSet" $offset "From" "p.X.A0"}} {{- template "putFp" dict "all" .all "OffSet" 0 "From" "p.X.A1"}} @@ -681,8 +695,11 @@ func (p *{{ $.TAffine }}) setBytes(buf []byte, subGroupCheck bool) (int, error) } } - // if infinity is encoded in the metadata, we don't need to read the buffer + // infinity encoded, we still check that the buffer is full of zeroes. if (mData == mCompressedInfinity) { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOf{{ $.TAffine }}Compressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOf{{ $.TAffine }}Compressed, nil @@ -690,6 +707,9 @@ func (p *{{ $.TAffine }}) setBytes(buf []byte, subGroupCheck bool) (int, error) {{- if ge .all.FpUnusedBits 3}} if (mData == mUncompressedInfinity) { + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOf{{ $.TAffine }}Uncompressed]) { + return 0, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() return SizeOf{{ $.TAffine }}Uncompressed, nil @@ -901,9 +921,12 @@ func (p *{{ $.TAffine }}) unsafeSetCompressedBytes(buf []byte) (isInfinity bool, mData := buf[0] & mMask if (mData == mCompressedInfinity) { + isInfinity = true + if !isZeroed(buf[0] & ^mMask, buf[1:SizeOf{{ $.TAffine }}Compressed]) { + return isInfinity, ErrInvalidInfinityEncoding + } p.X.SetZero() p.Y.SetZero() - isInfinity = true return isInfinity, nil } diff --git a/internal/generator/ecdsa/template/ecdsa.go.tmpl b/internal/generator/ecdsa/template/ecdsa.go.tmpl index fd953cdf42..3d5264c98d 100644 --- a/internal/generator/ecdsa/template/ecdsa.go.tmpl +++ b/internal/generator/ecdsa/template/ecdsa.go.tmpl @@ -4,7 +4,9 @@ import ( "crypto/rand" "crypto/sha512" "crypto/subtle" + {{- if or (eq .Name "secp256k1") (eq .Name "bn254") (eq .Name "stark-curve") }} "errors" + {{- end }} "hash" "io" "math/big" @@ -15,8 +17,6 @@ import ( "github.com/consensys/gnark-crypto/signature" ) -var errInvalidSig = errors.New("invalid signature") - const ( sizeFr = fr.Bytes sizeFp = fp.Bytes @@ -101,6 +101,58 @@ func HashToInt(hash []byte) *big.Int { return ret } +{{- if or (eq .Name "secp256k1") (eq .Name "bn254") (eq .Name "stark-curve") }} +// RecoverP recovers the value P (prover commitment) when creating a signature. +// It uses the recovery information v and part of the decomposed signature r. It +// is used internally for recovering the public key. +func RecoverP(v uint, r *big.Int) (*{{ .CurvePackage }}.G1Affine, error) { + if r.Cmp(fr.Modulus()) >= 0 { + return nil, errors.New("r is larger than modulus") + } + if r.Cmp(big.NewInt(0)) <= 0 { + return nil, errors.New("r is negative") + } + x := new(big.Int).Set(r) + {{- /* actually we want use a mask which corresponds to maximum cofactor of the curve. But this is when + we generalize the implementation over arbitrary curve.*/}} + // if x is r or r+N + xChoice := (v & 2) >> 1 + // if y is y or -y + yChoice := v & 1 + // decompose limbs into big.Int value + // conditional +n based on xChoice + kn := big.NewInt(int64(xChoice)) + kn.Mul(kn, fr.Modulus()) + x.Add(x, kn) + // y^2 = x^3+ax+b + a, b := {{ .CurvePackage }}.CurveCoefficients() + y := new(big.Int).Exp(x, big.NewInt(3), fp.Modulus()) + if !a.IsZero() { + y.Add(y, new(big.Int).Mul(a.BigInt(new(big.Int)), x)) + } + y.Add(y, b.BigInt(new(big.Int))) + y.Mod(y, fp.Modulus()) + // y = sqrt(y^2) + if y.ModSqrt(y, fp.Modulus()) == nil { + return nil, errors.New("no square root") + } + // y2 is -y + y2 := new(big.Int).Sub(fp.Modulus(), y) + // if yChoice == 0, return min(y, y2), else max(y, y2) + if (y.Cmp(y2) < 0) == (yChoice == 0) { + return &{{ .CurvePackage }}.G1Affine{ + X: *new(fp.Element).SetBigInt(x), + Y: *new(fp.Element).SetBigInt(y), + }, nil + } else { + return &{{ .CurvePackage }}.G1Affine{ + X: *new(fp.Element).SetBigInt(x), + Y: *new(fp.Element).SetBigInt(y2), + }, nil + } +} +{{- end}} + type zr struct{} // Read replaces the contents of dst with zeros. It is safe for concurrent use. @@ -176,6 +228,101 @@ func (privKey *PrivateKey) Public() signature.PublicKey { return &pub } +{{- if or (eq .Name "secp256k1") (eq .Name "bn254") (eq .Name "stark-curve") }} +// SignForRecover performs the ECDSA signature and returns public key recovery information +// +// k ← 𝔽r (random) +// P = k ⋅ g1Gen +// r = x_P (mod order) +// s = k⁻¹ . (m + sk ⋅ r) +// v = (div(x_P, order)<<1) || y_P[-1] +// +// SEC 1, Version 2.0, Section 4.1.3 +func (privKey *PrivateKey) SignForRecover(message []byte, hFunc hash.Hash) (v uint, r, s *big.Int, err error) { + halfp := new(big.Int).Sub(fp.Modulus(), big.NewInt(1)) + halfp.Div(halfp, big.NewInt(2)) + r, s = new(big.Int), new(big.Int) + + scalar, kInv := new(big.Int), new(big.Int) + scalar.SetBytes(privKey.scalar[:sizeFr]) + for { + for { + csprng, err := nonce(privKey, message) + if err != nil { + return 0, nil, nil, err + } + k, err := randFieldElement(csprng) + if err != nil { + return 0, nil, nil, err + } + + var P {{ .CurvePackage }}.G1Affine + P.ScalarMultiplicationBase(k) + kInv.ModInverse(k, order) + + P.X.BigInt(r) + // set how many times we overflow the scalar field + v |= (uint(new(big.Int).Div(r, order).Uint64())) << 1 + // set if y is small or big + if P.Y.BigInt(new(big.Int)).Cmp(halfp) >= 0 { + v |= 1 + } + + r.Mod(r, order) + if r.Sign() != 0 { + break + } + } + s.Mul(r, scalar) + + var m *big.Int + if hFunc != nil { + // compute the hash of the message as an integer + dataToHash := make([]byte, len(message)) + copy(dataToHash[:], message[:]) + hFunc.Reset() + _, err := hFunc.Write(dataToHash[:]) + if err != nil { + return 0, nil, nil, err + } + hramBin := hFunc.Sum(nil) + m = HashToInt(hramBin) + } else { + m = HashToInt(message) + } + + s.Add(m, s). + Mul(kInv, s). + Mod(s, order) // order != 0 + if s.Sign() != 0 { + break + } + } + + return v, r, s, nil +} + +// Sign performs the ECDSA signature +// +// k ← 𝔽r (random) +// P = k ⋅ g1Gen +// r = x_P (mod order) +// s = k⁻¹ . (m + sk ⋅ r) +// signature = {r, s} +// +// SEC 1, Version 2.0, Section 4.1.3 +func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) { + _, r, s, err := privKey.SignForRecover(message, hFunc) + if err != nil { + return nil, err + } + var sig Signature + r.FillBytes(sig.R[:sizeFr]) + s.FillBytes(sig.S[:sizeFr]) + + return sig.Bytes(), nil +} +{{- else }} // Sign performs the ECDSA signature // // k ← 𝔽r (random) @@ -204,6 +351,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) kInv.ModInverse(k, order) P.X.BigInt(r) + r.Mod(r, order) if r.Sign() != 0 { break @@ -211,7 +359,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) } s.Mul(r, scalar) - var m *big.Int + var m *big.Int if hFunc != nil { // compute the hash of the message as an integer dataToHash := make([]byte, len(message)) @@ -225,13 +373,13 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) m = HashToInt(hramBin) } else { m = HashToInt(message) - } + } s.Add(m, s). Mul(kInv, s). Mod(s, order) // order != 0 if s.Sign() != 0 { - break + break } } @@ -241,6 +389,7 @@ func (privKey *PrivateKey) Sign(message []byte, hFunc hash.Hash) ([]byte, error) return sig.Bytes(), nil } +{{- end }} // Verify validates the ECDSA signature // diff --git a/internal/generator/ecdsa/template/ecdsa.test.go.tmpl b/internal/generator/ecdsa/template/ecdsa.test.go.tmpl index a068f2e1be..f098204d20 100644 --- a/internal/generator/ecdsa/template/ecdsa.test.go.tmpl +++ b/internal/generator/ecdsa/template/ecdsa.test.go.tmpl @@ -45,6 +45,34 @@ func TestECDSA(t *testing.T) { properties.TestingRun(t, gopter.ConsoleReporter(false)) } +{{- if or (eq .Name "secp256k1") (eq .Name "bn254") (eq .Name "stark-curve") }} +func TestRecoverPublicKey(t *testing.T) { + t.Parallel() + parameters := gopter.DefaultTestParameters() + properties := gopter.NewProperties(parameters) + properties.Property("[{{ toUpper .Name }}] test public key recover", prop.ForAll( + func() bool { + sk, err := GenerateKey(rand.Reader) + if err != nil { + return false + } + pk := sk.PublicKey + msg := []byte("test") + v, r, s, err := sk.SignForRecover(msg, nil) + if err != nil { + return false + } + var recovered PublicKey + if err = recovered.RecoverFrom(msg, v, r, s); err != nil { + return false + } + return pk.Equal(&recovered) + }, + )) + properties.TestingRun(t, gopter.ConsoleReporter(false)) +} +{{- end }} + // ------------------------------------------------------------ // benches @@ -70,3 +98,23 @@ func BenchmarkVerifyECDSA(b *testing.B) { privKey.PublicKey.Verify(sig, msg, nil) } } + +{{- if or (eq .Name "secp256k1") (eq .Name "bn254") (eq .Name "stark-curve") }} +func BenchmarkRecoverPublicKey(b *testing.B) { + sk, err := GenerateKey(rand.Reader) + if err != nil { + b.Fatal(err) + } + msg := []byte("bench") + v, r, s, err := sk.SignForRecover(msg, sha256.New()) + if err != nil { + b.Fatal(err) + } + for i := 0; i < b.N; i++ { + var recovered PublicKey + if err = recovered.RecoverFrom(msg, v, r, s); err != nil { + b.Fatal(err) + } + } +} +{{- end }} \ No newline at end of file diff --git a/internal/generator/ecdsa/template/marshal.go.tmpl b/internal/generator/ecdsa/template/marshal.go.tmpl index 2e76fe21e0..81e2a2a8cb 100644 --- a/internal/generator/ecdsa/template/marshal.go.tmpl +++ b/internal/generator/ecdsa/template/marshal.go.tmpl @@ -1,6 +1,12 @@ import ( "crypto/subtle" "io" + {{- if or (eq .Name "secp256k1") (eq .Name "bn254") (eq .Name "stark-curve") }} + "math/big" + + "github.com/consensys/gnark-crypto/ecc/{{ .Name }}" + "github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr" + {{- end }} ) // Bytes returns the binary representation of the public key @@ -38,6 +44,30 @@ func (pk *PublicKey) SetBytes(buf []byte) (int, error) { return n, nil } +{{- if or (eq .Name "secp256k1") (eq .Name "bn254") (eq .Name "stark-curve") }} +// RecoverFrom recovers the public key from the message msg, recovery +// information v and decompose signature {r,s}. If recovery succeeded, the +// methods sets the current public key to the recovered value. Otherwise returns +// error and leaves current public key unchanged. +func (pk *PublicKey) RecoverFrom(msg []byte, v uint, r, s *big.Int) error { + P, err := RecoverP(v, r) + if err != nil { + return err + } + z := HashToInt(msg) + rinv := new(big.Int).ModInverse(r, fr.Modulus()) + u1 := new(big.Int).Mul(z, rinv) + u1.Neg(u1) + u1.Mod(u1, fr.Modulus()) + u2 := new(big.Int).Mul(s, rinv) + u2.Mod(u2, fr.Modulus()) + var Q {{ .CurvePackage }}.G1Jac + Q.JointScalarMultiplicationBase(P, u1, u2) + pk.A.FromJacobian(&Q) + return nil +} +{{- end }} + // Bytes returns the binary representation of pk, // as byte array publicKey||scalar // where publicKey is as publicKey.Bytes(), and diff --git a/internal/generator/fft/generate.go b/internal/generator/fft/generate.go index 031a247d24..0df0335140 100644 --- a/internal/generator/fft/generate.go +++ b/internal/generator/fft/generate.go @@ -16,6 +16,7 @@ func Generate(conf config.Curve, baseDir string, bgen *bavard.BatchGenerator) er {File: filepath.Join(baseDir, "domain.go"), Templates: []string{"domain.go.tmpl", "imports.go.tmpl"}}, {File: filepath.Join(baseDir, "fft_test.go"), Templates: []string{"tests/fft.go.tmpl", "imports.go.tmpl"}}, {File: filepath.Join(baseDir, "fft.go"), Templates: []string{"fft.go.tmpl", "imports.go.tmpl"}}, + {File: filepath.Join(baseDir, "options.go"), Templates: []string{"options.go.tmpl", "imports.go.tmpl"}}, } return bgen.Generate(conf, conf.Package, "./fft/template/", entries...) } diff --git a/internal/generator/fft/template/domain.go.tmpl b/internal/generator/fft/template/domain.go.tmpl index bdabf4a3e5..722332cf87 100644 --- a/internal/generator/fft/template/domain.go.tmpl +++ b/internal/generator/fft/template/domain.go.tmpl @@ -45,73 +45,101 @@ type Domain struct { // NewDomain returns a subgroup with a power of 2 cardinality // cardinality >= m -func NewDomain(m uint64) *Domain { +// shift: when specified, it's the element by which the set of root of unity is shifted. +func NewDomain(m uint64, shift ...fr.Element) *Domain { domain := &Domain{} x := ecc.NextPowerOfTwo(m) domain.Cardinality = uint64(x) // generator of the largest 2-adic subgroup + {{if eq .Name "bls12-378"}} + domain.FrMultiplicativeGen.SetUint64(22) + {{else if eq .Name "bls12-377"}} + domain.FrMultiplicativeGen.SetUint64(22) + {{else if eq .Name "bls12-381"}} + domain.FrMultiplicativeGen.SetUint64(7) + {{else if eq .Name "bn254"}} + domain.FrMultiplicativeGen.SetUint64(5) + {{else if eq .Name "bw6-761"}} + domain.FrMultiplicativeGen.SetUint64(15) + {{else if eq .Name "bw6-756"}} + domain.FrMultiplicativeGen.SetUint64(5) + {{else if eq .Name "bw6-633"}} + domain.FrMultiplicativeGen.SetUint64(13) + {{else if eq .Name "bls24-315"}} + domain.FrMultiplicativeGen.SetUint64(7) + {{else if eq .Name "bls24-317"}} + domain.FrMultiplicativeGen.SetUint64(7) + {{end}} + + if len(shift) != 0 { + domain.FrMultiplicativeGen.Set(&shift[0]) + } + domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen) + + var err error + domain.Generator, err = Generator(m) + if err != nil { + panic(err) + } + domain.GeneratorInv.Inverse(&domain.Generator) + domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv) + + // twiddle factors + domain.preComputeTwiddles() + + // store the bit reversed coset tables + domain.reverseCosetTables() + + return domain +} + +// Generator returns a generator for Z/2^(log(m))Z +// or an error if m is too big (required root of unity doesn't exist) +func Generator(m uint64) (fr.Element, error) { + x := ecc.NextPowerOfTwo(m) + var rootOfUnity fr.Element {{if eq .Name "bls12-378"}} rootOfUnity.SetString("4045585818372166415418670827807793147093034396422209590578257013290761627990") const maxOrderRoot uint64 = 42 - domain.FrMultiplicativeGen.SetUint64(22) {{else if eq .Name "bls12-377"}} rootOfUnity.SetString("8065159656716812877374967518403273466521432693661810619979959746626482506078") const maxOrderRoot uint64 = 47 - domain.FrMultiplicativeGen.SetUint64(22) {{else if eq .Name "bls12-381"}} rootOfUnity.SetString("10238227357739495823651030575849232062558860180284477541189508159991286009131") const maxOrderRoot uint64 = 32 - domain.FrMultiplicativeGen.SetUint64(7) {{else if eq .Name "bn254"}} rootOfUnity.SetString("19103219067921713944291392827692070036145651957329286315305642004821462161904") const maxOrderRoot uint64 = 28 - domain.FrMultiplicativeGen.SetUint64(5) {{else if eq .Name "bw6-761"}} rootOfUnity.SetString("32863578547254505029601261939868325669770508939375122462904745766352256812585773382134936404344547323199885654433") const maxOrderRoot uint64 = 46 - domain.FrMultiplicativeGen.SetUint64(15) {{else if eq .Name "bw6-756"}} rootOfUnity.SetString("199251335866470442271346949249090720992237796757894062992204115206570647302191425225605716521843542790404563904580") const maxOrderRoot uint64 = 41 - domain.FrMultiplicativeGen.SetUint64(5) {{else if eq .Name "bw6-633"}} rootOfUnity.SetString("4991787701895089137426454739366935169846548798279261157172811661565882460884369603588700158257") const maxOrderRoot uint64 = 20 - domain.FrMultiplicativeGen.SetUint64(13) {{else if eq .Name "bls24-315"}} rootOfUnity.SetString("1792993287828780812362846131493071959406149719416102105453370749552622525216") const maxOrderRoot uint64 = 22 - domain.FrMultiplicativeGen.SetUint64(7) {{else if eq .Name "bls24-317"}} rootOfUnity.SetString("16532287748948254263922689505213135976137839535221842169193829039521719560631") const maxOrderRoot uint64 = 60 - domain.FrMultiplicativeGen.SetUint64(7) {{end}} - domain.FrMultiplicativeGenInv.Inverse(&domain.FrMultiplicativeGen) - // find generator for Z/2^(log(m))Z logx := uint64(bits.TrailingZeros64(x)) if logx > maxOrderRoot { - panic(fmt.Sprintf("m (%d) is too big: the required root of unity does not exist", m)) + return fr.Element{}, fmt.Errorf("m (%d) is too big: the required root of unity does not exist", m) } - // Generator = FinerGenerator^2 has order x expo := uint64(1 << (maxOrderRoot - logx)) - domain.Generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x - domain.GeneratorInv.Inverse(&domain.Generator) - domain.CardinalityInv.SetUint64(uint64(x)).Inverse(&domain.CardinalityInv) - - // twiddle factors - domain.preComputeTwiddles() - - // store the bit reversed coset tables - domain.reverseCosetTables() - - return domain + var generator fr.Element + generator.Exp(rootOfUnity, big.NewInt(int64(expo))) // order x + return generator, nil } func (d *Domain) reverseCosetTables() { diff --git a/internal/generator/fft/template/fft.go.tmpl b/internal/generator/fft/template/fft.go.tmpl index 2a3f47a55d..405207a190 100644 --- a/internal/generator/fft/template/fft.go.tmpl +++ b/internal/generator/fft/template/fft.go.tmpl @@ -1,6 +1,5 @@ import ( "math/bits" - "runtime" "github.com/consensys/gnark-crypto/ecc" "github.com/consensys/gnark-crypto/internal/parallel" @@ -22,24 +21,18 @@ const butterflyThreshold = 16 // FFT computes (recursively) the discrete Fourier transform of a and stores the result in a // if decimation == DIT (decimation in time), the input must be in bit-reversed order // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order -// if coset if set, the FFT(a) returns the evaluation of a on a coset. -func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) { +func (domain *Domain) FFT(a []fr.Element, decimation Decimation, opts ...Option) { - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } + opt := options(opts...) // if coset != 0, scale by coset table - if _coset { + if opt.coset { scale := func(cosetTable []fr.Element) { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &cosetTable[i]) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableReversed) @@ -51,16 +44,16 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.Twiddles, 0, maxSplits, nil) + difFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.Twiddles, 0, maxSplits, nil) + ditFFT(a, domain.Twiddles, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } @@ -71,37 +64,31 @@ func (domain *Domain) FFT(a []fr.Element, decimation Decimation, coset ...bool) // if decimation == DIF (decimation in frequency), the output will be in bit-reversed order // coset sets the shift of the fft (0 = no shift, standard fft) // len(a) must be a power of 2, and w must be a len(a)th root of unity in field F. -func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset ...bool) { - - numCPU := uint64(runtime.NumCPU()) - - _coset := false - if len(coset) > 0 { - _coset = coset[0] - } +func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, opts ...Option) { + opt := options(opts...) // find the stage where we should stop spawning go routines in our recursive calls // (ie when we have as many go routines running as we have available CPUs) - maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(numCPU)) - if numCPU <= 1 { + maxSplits := bits.TrailingZeros64(ecc.NextPowerOfTwo(uint64(opt.nbTasks))) + if opt.nbTasks == 1 { maxSplits = -1 } switch decimation { case DIF: - difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + difFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) case DIT: - ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil) + ditFFT(a, domain.TwiddlesInv, 0, maxSplits, nil, opt.nbTasks) default: panic("not implemented") } // scale by CardinalityInv - if !_coset { + if !opt.coset { parallel.Execute(len(a), func(start, end int) { for i := start; i < end; i++ { a[i].Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) return } @@ -111,7 +98,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. a[i].Mul(&a[i], &cosetTable[i]). Mul(&a[i], &domain.CardinalityInv) } - }) + }, opt.nbTasks) } if decimation == DIT { scale(domain.CosetTableInv) @@ -123,7 +110,7 @@ func (domain *Domain) FFTInverse(a []fr.Element, decimation Decimation, coset .. } -func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -141,7 +128,7 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for i := start; i < end; i++ { fr.Butterfly(&a[i], &a[i+m]) @@ -164,17 +151,17 @@ func difFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon nextStage := stage + 1 if stage < maxSplits { chDone := make(chan struct{}, 1) - go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone) - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go difFFT(a[m:n], twiddles, nextStage, maxSplits, chDone, nbTasks) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - difFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - difFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + difFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + difFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } } -func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}) { +func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDone chan struct{}, nbTasks int) { if chDone != nil { defer close(chDone) } @@ -192,12 +179,12 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon if stage < maxSplits { // that's the only time we fire go routines chDone := make(chan struct{}, 1) - go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone) - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) + go ditFFT(a[m:], twiddles, nextStage, maxSplits, chDone, nbTasks) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) <-chDone } else { - ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil) - ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil) + ditFFT(a[0:m], twiddles, nextStage, maxSplits, nil, nbTasks) + ditFFT(a[m:n], twiddles, nextStage, maxSplits, nil, nbTasks) } @@ -205,7 +192,7 @@ func ditFFT(a []fr.Element, twiddles [][]fr.Element, stage, maxSplits int, chDon // but we have only numCPU / stage cpus available if (m > butterflyThreshold) && (stage < maxSplits) { // 1 << stage == estimated used CPUs - numCPU := runtime.NumCPU() / (1 << (stage)) + numCPU := nbTasks / (1 << (stage)) parallel.Execute(m, func(start, end int) { for k := start; k < end; k++ { a[k+m].Mul(&a[k+m], &twiddles[stage][k]) diff --git a/internal/generator/fft/template/options.go.tmpl b/internal/generator/fft/template/options.go.tmpl new file mode 100644 index 0000000000..450da97bf8 --- /dev/null +++ b/internal/generator/fft/template/options.go.tmpl @@ -0,0 +1,43 @@ +import "runtime" + +// Option defines option for altering the behavior of FFT methods. +// See the descriptions of functions returning instances of this type for +// particular options. +type Option func(*fftConfig) + +type fftConfig struct { + coset bool + nbTasks int +} + +// OnCoset if provided, FFT(a) returns the evaluation of a on a coset. +func OnCoset() Option { + return func(opt *fftConfig) { + opt.coset = true + } +} + +// WithNbTasks sets the max number of task (go routine) to spawn. Must be between 1 and 512. +func WithNbTasks(nbTasks int) Option { + if nbTasks < 1 { + nbTasks = 1 + } else if nbTasks > 512 { + nbTasks = 512 + } + return func(opt *fftConfig) { + opt.nbTasks = nbTasks + } +} + +// default options +func options(opts ...Option) fftConfig { + // apply options + opt := fftConfig{ + coset: false, + nbTasks: runtime.NumCPU(), + } + for _, option := range opts { + option(&opt) + } + return opt +} \ No newline at end of file diff --git a/internal/generator/fft/template/tests/fft.go.tmpl b/internal/generator/fft/template/tests/fft.go.tmpl index e49f0a18ac..d440aa77e5 100644 --- a/internal/generator/fft/template/tests/fft.go.tmpl +++ b/internal/generator/fft/template/tests/fft.go.tmpl @@ -35,7 +35,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIF) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -62,7 +62,7 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFT(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIF, OnCoset()) BitReverse(pol) sample := domainWithPrecompute.Generator @@ -91,7 +91,7 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFT(pol, DIT) sample := domainWithPrecompute.Generator sample.Exp(sample, big.NewInt(int64(ithpower))) @@ -117,8 +117,8 @@ func TestFFT(t *testing.T) { copy(backupPol, pol) BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, false) - domainWithPrecompute.FFTInverse(pol, DIF, false) + domainWithPrecompute.FFT(pol, DIT) + domainWithPrecompute.FFTInverse(pol, DIF) BitReverse(pol) check := true @@ -146,8 +146,8 @@ func TestFFT(t *testing.T) { for i := 1; i <= nbCosets; i++ { BitReverse(pol) - domainWithPrecompute.FFT(pol, DIT, true) - domainWithPrecompute.FFTInverse(pol, DIF, true) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) BitReverse(pol) for i := 0; i < len(pol); i++ { @@ -171,8 +171,8 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, false) - domainWithPrecompute.FFT(pol, DIT, false) + domainWithPrecompute.FFTInverse(pol, DIF) + domainWithPrecompute.FFT(pol, DIT) check := true for i := 0; i < len(pol); i++ { @@ -194,14 +194,26 @@ func TestFFT(t *testing.T) { } copy(backupPol, pol) - domainWithPrecompute.FFTInverse(pol, DIF, true) - domainWithPrecompute.FFT(pol, DIT, true) + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset()) + domainWithPrecompute.FFT(pol, DIT, OnCoset()) - check := true for i := 0; i < len(pol); i++ { - check = check && (pol[i] == backupPol[i]) + if !(pol[i].Equal(&backupPol[i])) { + return false + } } - return check + + // compute with nbTasks == 1 + domainWithPrecompute.FFTInverse(pol, DIF, OnCoset(), WithNbTasks(1)) + domainWithPrecompute.FFT(pol, DIT, OnCoset(), WithNbTasks(1)) + + for i := 0; i < len(pol); i++ { + if !(pol[i].Equal(&backupPol[i])) { + return false + } + } + + return true }, )) @@ -248,14 +260,14 @@ func BenchmarkFFT(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, false) + domain.FFT(pol[:sizeDomain], DIT) } }) b.Run("fft 2**"+strconv.Itoa(i)+"bits (coset)", func(b *testing.B) { domain := NewDomain(uint64(sizeDomain)) b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol[:sizeDomain], DIT, true) + domain.FFT(pol[:sizeDomain], DIT, OnCoset()) } }) } @@ -275,7 +287,7 @@ func BenchmarkFFTDITCosetReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIT, true) + domain.FFT(pol, DIT, OnCoset()) } } @@ -292,7 +304,7 @@ func BenchmarkFFTDIFReference(b *testing.B) { b.ResetTimer() for j := 0; j < b.N; j++ { - domain.FFT(pol, DIF, false) + domain.FFT(pol, DIF) } } diff --git a/internal/generator/iop/template/polynomial.go.tmpl b/internal/generator/iop/template/polynomial.go.tmpl index be34d88919..46bfb7cd94 100644 --- a/internal/generator/iop/template/polynomial.go.tmpl +++ b/internal/generator/iop/template/polynomial.go.tmpl @@ -133,11 +133,13 @@ func (p *Polynomial) Evaluate(x fr.Element) fr.Element { return p.polynomial.evaluate(x) } - // TODO find a way to retrieve the root properly instead of re generating the fft domain - d := fft.NewDomain(uint64(p.size)) var g fr.Element if p.shift <= 5 { - g = smallExp(d.Generator, p.shift) + gen, err := fft.Generator(uint64(p.size)) + if err != nil { + panic(err) + } + g = smallExp(gen, p.shift) x.Mul(&x, &g) return p.polynomial.evaluate(x) } @@ -279,11 +281,11 @@ func (p *Polynomial) ToLagrange(d *fft.Domain) *Polynomial { return p case lagrangeCosetRegular: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIT) case lagrangeCosetBitReverse: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) d.FFT((*p.coefficients), fft.DIF) default: panic("unknown ID") @@ -308,10 +310,10 @@ func (p *Polynomial) ToCanonical(d *fft.Domain) *Polynomial { d.FFTInverse((*p.coefficients), fft.DIT) case lagrangeCosetRegular: p.Layout = BitReverse - d.FFTInverse((*p.coefficients), fft.DIF, true) + d.FFTInverse((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetBitReverse: p.Layout = Regular - d.FFTInverse((*p.coefficients), fft.DIT, true) + d.FFTInverse((*p.coefficients), fft.DIT, fft.OnCoset()) default: panic("unknown ID") } @@ -333,18 +335,18 @@ func (p *Polynomial) ToLagrangeCoset(d *fft.Domain) *Polynomial { switch id { case canonicalRegular: p.Layout = BitReverse - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case canonicalBitReverse: p.Layout = Regular - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeRegular: p.Layout = Regular d.FFTInverse((*p.coefficients), fft.DIF) - d.FFT((*p.coefficients), fft.DIT, true) + d.FFT((*p.coefficients), fft.DIT, fft.OnCoset()) case lagrangeBitReverse: p.Layout = BitReverse d.FFTInverse((*p.coefficients), fft.DIT) - d.FFT((*p.coefficients), fft.DIF, true) + d.FFT((*p.coefficients), fft.DIF, fft.OnCoset()) case lagrangeCosetRegular, lagrangeCosetBitReverse: return p default: diff --git a/internal/generator/iop/template/polynomial.test.go.tmpl b/internal/generator/iop/template/polynomial.test.go.tmpl index 9388cce53e..0bf76239be 100644 --- a/internal/generator/iop/template/polynomial.test.go.tmpl +++ b/internal/generator/iop/template/polynomial.test.go.tmpl @@ -223,7 +223,7 @@ func fromLagrange4(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = Regular d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) return r } @@ -233,7 +233,7 @@ func fromLagrange5(p *Polynomial, d *fft.Domain) *Polynomial { r.Basis = LagrangeCoset r.Layout = BitReverse d.FFTInverse(r.Coefficients(), fft.DIF) - d.FFT(r.Coefficients(), fft.DIT, true) + d.FFT(r.Coefficients(), fft.DIT, fft.OnCoset()) fft.BitReverse(r.Coefficients()) return r } @@ -421,7 +421,7 @@ func fromCanonical4(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = Regular - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -431,7 +431,7 @@ func fromCanonical5(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = LagrangeCoset _p.Layout = BitReverse - d.FFT(_p.Coefficients(), fft.DIF, true) + d.FFT(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -549,7 +549,7 @@ func fromLagrangeCoset0(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) fft.BitReverse(_p.Coefficients()) return _p } @@ -559,7 +559,7 @@ func fromLagrangeCoset1(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Canonical _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) return _p } @@ -568,7 +568,7 @@ func fromLagrangeCoset2(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = Regular - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) return _p } @@ -578,7 +578,7 @@ func fromLagrangeCoset3(p *Polynomial, d *fft.Domain) *Polynomial { _p := p.Clone() _p.Basis = Lagrange _p.Layout = BitReverse - d.FFTInverse(_p.Coefficients(), fft.DIF, true) + d.FFTInverse(_p.Coefficients(), fft.DIF, fft.OnCoset()) d.FFT(_p.Coefficients(), fft.DIT) fft.BitReverse(_p.Coefficients()) return _p diff --git a/internal/generator/iop/template/ratios.go.tmpl b/internal/generator/iop/template/ratios.go.tmpl index 92b64e91ca..a0abcffe8b 100644 --- a/internal/generator/iop/template/ratios.go.tmpl +++ b/internal/generator/iop/template/ratios.go.tmpl @@ -1,6 +1,9 @@ import ( "errors" "math/bits" + "math/big" + "runtime" + "sync" "github.com/consensys/gnark-crypto/internal/parallel" @@ -196,18 +199,40 @@ func BuildRatioCopyConstraint( t[i+1].Set(&d) } }) - - for i := 0; i < n-1; i++ { - coeffs[i+1].Mul(&coeffs[i+1], &coeffs[i]) - t[i+1].Mul(&t[i+1], &t[i]) + chCoeffs := make(chan struct{},1) + go func() { + for i := 2; i < n; i++ { + // ignoring coeffs[0] + coeffs[i].Mul(&coeffs[i], &coeffs[i-1]) + } + close(chCoeffs) + }() + + for i := 2; i < n; i++ { + // ignoring t[0] + t[i].Mul(&t[i], &t[i-1]) } + <-chCoeffs - t = fr.BatchInvert(t) - for i := 1; i < n; i++ { - coeffs[i].Mul(&coeffs[i], &t[i]) + // rough ratio inverse to mul; see if it makes sense to parallelize the batch inverse. + const ratioInvMul = 1000 / 17 + nbTasks := runtime.NumCPU() + if ratio := n / ratioInvMul; ratio < nbTasks { + nbTasks = ratio } + + parallel.Execute(n-1, func(start, end int) { + // ignoring t[0] and coeff[0] + start++ + end++ + tInv := fr.BatchInvert(t[start:end]) + for i := start; i < end; i++ { + coeffs[i].Mul(&coeffs[i], &tInv[i-start]) + } + }, nbTasks) + res := NewPolynomial(&coeffs, expectedForm) // at this stage the result is in Lagrange form, Regular layout putInExpectedFormFromLagrangeRegular(res, domain, expectedForm) @@ -230,7 +255,7 @@ func putInExpectedFormFromLagrangeRegular(p *Polynomial, domain *fft.Domain, exp if expectedForm.Basis == LagrangeCoset { domain.FFTInverse(p.Coefficients(), fft.DIF) - domain.FFT(p.Coefficients(), fft.DIT, true) + domain.FFT(p.Coefficients(), fft.DIT, fft.OnCoset()) if expectedForm.Layout == BitReverse { fft.BitReverse(p.Coefficients()) } @@ -289,20 +314,46 @@ func buildDomain(n int, domain *fft.Domain) (*fft.Domain, error) { // nbCopies is the number of cosets of the roots of unity that are needed, including the set of // roots of unity itself. func getSupportIdentityPermutation(nbCopies int, domain *fft.Domain) []fr.Element { - + res := make([]fr.Element, uint64(nbCopies)*domain.Cardinality) sizePoly := int(domain.Cardinality) - res[0].SetOne() - for i := 0; i < sizePoly-1; i++ { + // len(domain.Twiddle) == sizePoly / 2 + copy(res, domain.Twiddles[0]) + // remaining ones. + for i := (sizePoly/2) - 1; i < sizePoly-1; i++ { res[i+1].Mul(&res[i], &domain.Generator) } + if nbCopies <= 1 { + return res + } + var wg sync.WaitGroup + wg.Add(nbCopies - 1) for i := 1; i < nbCopies; i++ { - copy(res[i*sizePoly:], res[(i-1)*sizePoly:i*int(domain.Cardinality)]) - for j := 0; j < sizePoly; j++ { - res[i*sizePoly+j].Mul(&res[i*sizePoly+j], &domain.FrMultiplicativeGen) + i := i + + var coset fr.Element + if i == 1 { + coset = domain.FrMultiplicativeGen + } else { + if len(domain.CosetTable) > i { + coset = domain.CosetTable[i] + } else { + coset.Exp(domain.FrMultiplicativeGen, big.NewInt(int64(i))) + } } + + go func() { + parallel.Execute(sizePoly, func(start, end int) { + for j := start; j < end; j++ { + res[i*sizePoly+j].Mul(&res[j], &coset) + } + }, (runtime.NumCPU() / (nbCopies - 1)) + 1) + wg.Done() + }() } + wg.Wait() + return res } diff --git a/internal/generator/kzg/template/kzg.go.tmpl b/internal/generator/kzg/template/kzg.go.tmpl index 91b1db22ac..0f42fb5a27 100644 --- a/internal/generator/kzg/template/kzg.go.tmpl +++ b/internal/generator/kzg/template/kzg.go.tmpl @@ -8,6 +8,8 @@ import ( "github.com/consensys/gnark-crypto/ecc/{{ .Name }}" "github.com/consensys/gnark-crypto/ecc/{{ .Name }}/fr" "github.com/consensys/gnark-crypto/fiat-shamir" + + "github.com/consensys/gnark-crypto/internal/parallel" ) var ( @@ -257,14 +259,21 @@ func BatchOpenSinglePoint(polynomials [][]fr.Element, digests []Digest, point fr // gamma n in parallel, before reducing into foldedPolynomials foldedPolynomials := make([]fr.Element, largestPoly) copy(foldedPolynomials, polynomials[0]) - acc := gamma - var pj fr.Element + gammas := make([]fr.Element, len(polynomials)) + gammas[0] = gamma + for i := 1 ; i < len(polynomials); i++ { + gammas[i].Mul(&gammas[i-1], &gamma) + } + for i := 1; i < len(polynomials); i++ { - for j := 0; j < len(polynomials[i]); j++ { - pj.Mul(&polynomials[i][j], &acc) - foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) - } - acc.Mul(&acc, &gamma) + i := i + parallel.Execute(len(polynomials[i]), func(start, end int) { + var pj fr.Element + for j:= start; j < end; j ++ { + pj.Mul(&polynomials[i][j], &gammas[i-1]) + foldedPolynomials[j].Add(&foldedPolynomials[j], &pj) + } + }) } // compute H diff --git a/internal/generator/permutation/template/permutation.go.tmpl b/internal/generator/permutation/template/permutation.go.tmpl index 109e097dc4..3bc6815b25 100644 --- a/internal/generator/permutation/template/permutation.go.tmpl +++ b/internal/generator/permutation/template/permutation.go.tmpl @@ -173,15 +173,15 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } lz := make([]fr.Element, s) copy(lz, cz) - d.FFT(lz, fft.DIF, true) + d.FFT(lz, fft.DIF, fft.OnCoset()) // compute the first part of the numerator lt1 := make([]fr.Element, s) lt2 := make([]fr.Element, s) copy(lt1, ct1) copy(lt2, ct2) - d.FFT(lt1, fft.DIF, true) - d.FFT(lt2, fft.DIF, true) + d.FFT(lt1, fft.DIF, fft.OnCoset()) + d.FFT(lt2, fft.DIF, fft.OnCoset()) lsNumFirstPart := evaluateFirstPartNumReverse(lt1, lt2, lz, epsilon) // compute second part of the numerator @@ -204,7 +204,7 @@ func Prove(srs *kzg.SRS, t1, t2 []fr.Element) (Proof, error) { } // get the quotient and commit it - d.FFTInverse(lsNum, fft.DIT, true) + d.FFTInverse(lsNum, fft.DIT, fft.OnCoset()) proof.q, err = kzg.Commit(lsNum, srs) if err != nil { return proof, err diff --git a/internal/generator/plookup/template/vector.go.tmpl b/internal/generator/plookup/template/vector.go.tmpl index 64aceb98cc..55478d7e01 100644 --- a/internal/generator/plookup/template/vector.go.tmpl +++ b/internal/generator/plookup/template/vector.go.tmpl @@ -322,7 +322,7 @@ func computeQuotientCanonical(alpha fr.Element, lh, lh0, lhn, lh1h2 []fr.Element Mul(&res[_i], &numLn[i%2]) } - domainBig.FFTInverse(res, fft.DIT, true) + domainBig.FFTInverse(res, fft.DIT, fft.OnCoset()) return res } @@ -459,11 +459,11 @@ func ProveLookupVector(srs *kzg.SRS, f, t fr.Vector) (ProofLookupVector, error) copy(_lh2, ch2) copy(_lt, ct) copy(_lf, cf) - domainBig.FFT(_lz, fft.DIF, true) - domainBig.FFT(_lh1, fft.DIF, true) - domainBig.FFT(_lh2, fft.DIF, true) - domainBig.FFT(_lt, fft.DIF, true) - domainBig.FFT(_lf, fft.DIF, true) + domainBig.FFT(_lz, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh1, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lh2, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lt, fft.DIF, fft.OnCoset()) + domainBig.FFT(_lf, fft.DIF, fft.OnCoset()) // compute h lh := evaluateNumBitReversed(_lz, _lh1, _lh2, _lt, _lf, beta, gamma, domainBig) diff --git a/internal/generator/tower/template/fq12over6over2/fq6.go.tmpl b/internal/generator/tower/template/fq12over6over2/fq6.go.tmpl index c48ffe575c..347f00f378 100644 --- a/internal/generator/tower/template/fq12over6over2/fq6.go.tmpl +++ b/internal/generator/tower/template/fq12over6over2/fq6.go.tmpl @@ -108,6 +108,34 @@ func (z *E6) MulByE2(x *E6, y *E2) *E6 { return z } +// MulBy12 multiplication by sparse element (0,b1,b2) +func (x *E6) MulBy12(b1, b2 *E2) *E6 { + var t1, t2, c0, tmp, c1, c2 E2 + t1.Mul(&x.B1, b1) + t2.Mul(&x.B2, b2) + c0.Add(&x.B1, &x.B2) + tmp.Add(b1, b2) + c0.Mul(&c0, &tmp) + c0.Sub(&c0, &t1) + c0.Sub(&c0, &t2) + c0.MulByNonResidue(&c0) + c1.Add(&x.B0, &x.B1) + c1.Mul(&c1, b1) + c1.Sub(&c1, &t1) + tmp.MulByNonResidue(&t2) + c1.Add(&c1, &tmp) + tmp.Add(&x.B0, &x.B2) + c2.Mul(b2, &tmp) + c2.Sub(&c2, &t2) + c2.Add(&c2, &t1) + + x.B0 = c0 + x.B1 = c1 + x.B2 = c2 + + return x +} + // MulBy01 multiplication by sparse element (c0,c1,0) func (z *E6) MulBy01(c0, c1 *E2) *E6 { diff --git a/internal/parallel/execute.go b/internal/parallel/execute.go index 803de3c1b1..05f9a8f666 100644 --- a/internal/parallel/execute.go +++ b/internal/parallel/execute.go @@ -11,7 +11,19 @@ func Execute(nbIterations int, work func(int, int), maxCpus ...int) { nbTasks := runtime.NumCPU() if len(maxCpus) == 1 { nbTasks = maxCpus[0] + if nbTasks < 1 { + nbTasks = 1 + } else if nbTasks > 512 { + nbTasks = 512 + } + } + + if nbTasks == 1 { + // no go routines + work(0, nbIterations) + return } + nbIterationsPerCpus := nbIterations / nbTasks // more CPUs than tasks: a CPU will work on exactly one iteration