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donna_64.cpp
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// donna_64.cpp - written and placed in public domain by Jeffrey Walton
// Crypto++ specific implementation wrapped around Andrew
// Moon's public domain curve25519-donna and ed25519-donna,
// https://github.com/floodyberry/curve25519-donna and
// https://github.com/floodyberry/ed25519-donna.
// The curve25519 and ed25519 source files multiplex different repos and
// architectures using namespaces. The repos are Andrew Moon's
// curve25519-donna and ed25519-donna. The architectures are 32-bit, 64-bit
// and SSE. For example, 32-bit x25519 uses symbols from Donna::X25519 and
// Donna::Arch32.
// A fair amount of duplication happens below, but we could not directly
// use curve25519 for both x25519 and ed25519. A close examination reveals
// slight differences in the implementation. For example, look at the
// two curve25519_sub functions.
// If needed, see Moon's commit "Go back to ignoring 256th bit [sic]",
// https://github.com/floodyberry/curve25519-donna/commit/57a683d18721a658
#include "pch.h"
#include "config.h"
#include "donna.h"
#include "secblock.h"
#include "sha.h"
#include "misc.h"
#include "cpu.h"
#include <istream>
#include <sstream>
#if CRYPTOPP_GCC_DIAGNOSTIC_AVAILABLE
# pragma GCC diagnostic ignored "-Wunused-function"
#endif
#if CRYPTOPP_MSC_VERSION
# pragma warning(disable: 4244)
#endif
// Squash MS LNK4221 and libtool warnings
extern const char DONNA64_FNAME[] = __FILE__;
ANONYMOUS_NAMESPACE_BEGIN
// Can't use GetAlignmentOf<word64>() because of C++11 and constexpr
// Can use 'const unsigned int' because of MSVC 2013
#if (CRYPTOPP_BOOL_X86 || CRYPTOPP_BOOL_X32 || CRYPTOPP_BOOL_X64)
# define ALIGN_SPEC 16
#else
# define ALIGN_SPEC 8
#endif
ANONYMOUS_NAMESPACE_END
#if defined(CRYPTOPP_CURVE25519_64BIT)
#include "donna_64.h"
ANONYMOUS_NAMESPACE_BEGIN
using CryptoPP::byte;
using CryptoPP::word64;
using CryptoPP::GetWord;
using CryptoPP::PutWord;
using CryptoPP::LITTLE_ENDIAN_ORDER;
inline word64 U8TO64_LE(const byte* p)
{
return GetWord<word64>(false, LITTLE_ENDIAN_ORDER, p);
}
inline void U64TO8_LE(byte* p, word64 w)
{
PutWord(false, LITTLE_ENDIAN_ORDER, p, w);
}
ANONYMOUS_NAMESPACE_END
NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)
NAMESPACE_BEGIN(X25519)
ANONYMOUS_NAMESPACE_BEGIN
using CryptoPP::byte;
using CryptoPP::word32;
using CryptoPP::sword32;
using CryptoPP::word64;
using CryptoPP::sword64;
using CryptoPP::GetBlock;
using CryptoPP::LittleEndian;
// Bring in all the symbols from the 64-bit header
using namespace CryptoPP::Donna::Arch64;
/* out = in */
inline void
curve25519_copy(bignum25519 out, const bignum25519 in) {
out[0] = in[0]; out[1] = in[1];
out[2] = in[2]; out[3] = in[3];
out[4] = in[4];
}
/* out = a + b */
inline void
curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
out[0] = a[0] + b[0];
out[1] = a[1] + b[1];
out[2] = a[2] + b[2];
out[3] = a[3] + b[3];
out[4] = a[4] + b[4];
}
/* out = a - b */
inline void
curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
out[0] = a[0] + two54m152 - b[0];
out[1] = a[1] + two54m8 - b[1];
out[2] = a[2] + two54m8 - b[2];
out[3] = a[3] + two54m8 - b[3];
out[4] = a[4] + two54m8 - b[4];
}
/* out = (in * scalar) */
inline void
curve25519_scalar_product(bignum25519 out, const bignum25519 in, const word64 scalar) {
word128 a;
word64 c;
#if defined(CRYPTOPP_WORD128_AVAILABLE)
a = ((word128) in[0]) * scalar; out[0] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
a = ((word128) in[1]) * scalar + c; out[1] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
a = ((word128) in[2]) * scalar + c; out[2] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
a = ((word128) in[3]) * scalar + c; out[3] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
a = ((word128) in[4]) * scalar + c; out[4] = (word64)a & reduce_mask_51; c = (word64)(a >> 51);
out[0] += c * 19;
#else
mul64x64_128(a, in[0], scalar) out[0] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
mul64x64_128(a, in[1], scalar) add128_64(a, c) out[1] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
mul64x64_128(a, in[2], scalar) add128_64(a, c) out[2] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
mul64x64_128(a, in[3], scalar) add128_64(a, c) out[3] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
mul64x64_128(a, in[4], scalar) add128_64(a, c) out[4] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
out[0] += c * 19;
#endif
}
/* out = a * b */
inline void
curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
word128 mul;
#endif
word128 t[5];
word64 r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
r0 = b[0]; r1 = b[1]; r2 = b[2]; r3 = b[3]; r4 = b[4];
s0 = a[0]; s1 = a[1]; s2 = a[2]; s3 = a[3]; s4 = a[4];
#if defined(CRYPTOPP_WORD128_AVAILABLE)
t[0] = ((word128) r0) * s0;
t[1] = ((word128) r0) * s1 + ((word128) r1) * s0;
t[2] = ((word128) r0) * s2 + ((word128) r2) * s0 + ((word128) r1) * s1;
t[3] = ((word128) r0) * s3 + ((word128) r3) * s0 + ((word128) r1) * s2 + ((word128) r2) * s1;
t[4] = ((word128) r0) * s4 + ((word128) r4) * s0 + ((word128) r3) * s1 + ((word128) r1) * s3 + ((word128) r2) * s2;
#else
mul64x64_128(t[0], r0, s0)
mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul)
mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul)
mul64x64_128(t[3], r0, s3) mul64x64_128(mul, r3, s0) add128(t[3], mul) mul64x64_128(mul, r1, s2) add128(t[3], mul) mul64x64_128(mul, r2, s1) add128(t[3], mul)
mul64x64_128(t[4], r0, s4) mul64x64_128(mul, r4, s0) add128(t[4], mul) mul64x64_128(mul, r3, s1) add128(t[4], mul) mul64x64_128(mul, r1, s3) add128(t[4], mul) mul64x64_128(mul, r2, s2) add128(t[4], mul)
#endif
r1 *= 19; r2 *= 19; r3 *= 19; r4 *= 19;
#if defined(CRYPTOPP_WORD128_AVAILABLE)
t[0] += ((word128) r4) * s1 + ((word128) r1) * s4 + ((word128) r2) * s3 + ((word128) r3) * s2;
t[1] += ((word128) r4) * s2 + ((word128) r2) * s4 + ((word128) r3) * s3;
t[2] += ((word128) r4) * s3 + ((word128) r3) * s4;
t[3] += ((word128) r4) * s4;
#else
mul64x64_128(mul, r4, s1) add128(t[0], mul) mul64x64_128(mul, r1, s4) add128(t[0], mul) mul64x64_128(mul, r2, s3) add128(t[0], mul) mul64x64_128(mul, r3, s2) add128(t[0], mul)
mul64x64_128(mul, r4, s2) add128(t[1], mul) mul64x64_128(mul, r2, s4) add128(t[1], mul) mul64x64_128(mul, r3, s3) add128(t[1], mul)
mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul)
mul64x64_128(mul, r4, s4) add128(t[3], mul)
#endif
r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
r1 += c;
out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
}
/* out = in^(2 * count) */
inline void
curve25519_square_times(bignum25519 out, const bignum25519 in, word64 count) {
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
word128 mul;
#endif
word128 t[5];
word64 r0,r1,r2,r3,r4,c;
word64 d0,d1,d2,d4,d419;
r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
do {
d0 = r0 * 2; d1 = r1 * 2;
d2 = r2 * 2 * 19;
d419 = r4 * 19; d4 = d419 * 2;
#if defined(CRYPTOPP_WORD128_AVAILABLE)
t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
#else
mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
#endif
r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
r1 += c;
} while(--count);
out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
}
inline void
curve25519_square(bignum25519 out, const bignum25519 in) {
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
word128 mul;
#endif
word128 t[5];
word64 r0,r1,r2,r3,r4,c;
word64 d0,d1,d2,d4,d419;
r0 = in[0]; r1 = in[1]; r2 = in[2]; r3 = in[3]; r4 = in[4];
d0 = r0 * 2; d1 = r1 * 2;
d2 = r2 * 2 * 19;
d419 = r4 * 19; d4 = d419 * 2;
#if defined(CRYPTOPP_WORD128_AVAILABLE)
t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
#else
mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
#endif
r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
r1 += c;
out[0] = r0; out[1] = r1; out[2] = r2; out[3] = r3; out[4] = r4;
}
/* Take a little-endian, 32-byte number and expand it into polynomial form */
inline void
curve25519_expand(bignum25519 out, const byte *in) {
word64 x0,x1,x2,x3;
GetBlock<word64, LittleEndian> block(in);
block(x0)(x1)(x2)(x3);
out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13);
out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26);
out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39);
out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12);
out[4] = x3 & reduce_mask_51; /* ignore the top bit */
}
/* Take a fully reduced polynomial form number and contract it into a
* little-endian, 32-byte array
*/
inline void
curve25519_contract(byte *out, const bignum25519 input) {
word64 t[5];
word64 f, i;
t[0] = input[0];
t[1] = input[1];
t[2] = input[2];
t[3] = input[3];
t[4] = input[4];
#define curve25519_contract_carry() \
t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \
t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \
t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \
t[4] += t[3] >> 51; t[3] &= reduce_mask_51;
#define curve25519_contract_carry_full() curve25519_contract_carry() \
t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51;
#define curve25519_contract_carry_final() curve25519_contract_carry() \
t[4] &= reduce_mask_51;
curve25519_contract_carry_full()
curve25519_contract_carry_full()
/* now t is between 0 and 2^255-1, properly carried. */
/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
t[0] += 19;
curve25519_contract_carry_full()
/* now between 19 and 2^255-1 in both cases, and offset by 19. */
t[0] += 0x8000000000000 - 19;
t[1] += 0x8000000000000 - 1;
t[2] += 0x8000000000000 - 1;
t[3] += 0x8000000000000 - 1;
t[4] += 0x8000000000000 - 1;
/* now between 2^255 and 2^256-20, and offset by 2^255. */
curve25519_contract_carry_final()
#define write51full(n,shift) \
f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \
for (i = 0; i < 8; i++, f >>= 8) *out++ = (byte)f;
#define write51(n) write51full(n,13*n)
write51(0)
write51(1)
write51(2)
write51(3)
#undef curve25519_contract_carry
#undef curve25519_contract_carry_full
#undef curve25519_contract_carry_final
#undef write51full
#undef write51
}
/*
* Swap the contents of [qx] and [qpx] iff @swap is non-zero
*/
inline void
curve25519_swap_conditional(bignum25519 x, bignum25519 qpx, word64 iswap) {
const word64 swap = (word64)(-(sword64)iswap);
word64 x0,x1,x2,x3,x4;
x0 = swap & (x[0] ^ qpx[0]); x[0] ^= x0; qpx[0] ^= x0;
x1 = swap & (x[1] ^ qpx[1]); x[1] ^= x1; qpx[1] ^= x1;
x2 = swap & (x[2] ^ qpx[2]); x[2] ^= x2; qpx[2] ^= x2;
x3 = swap & (x[3] ^ qpx[3]); x[3] ^= x3; qpx[3] ^= x3;
x4 = swap & (x[4] ^ qpx[4]); x[4] ^= x4; qpx[4] ^= x4;
}
/*
* In: b = 2^5 - 2^0
* Out: b = 2^250 - 2^0
*/
void
curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
ALIGN(ALIGN_SPEC) bignum25519 t0,c;
/* 2^5 - 2^0 */ /* b */
/* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5);
/* 2^10 - 2^0 */ curve25519_mul(b, t0, b);
/* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10);
/* 2^20 - 2^0 */ curve25519_mul(c, t0, b);
/* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20);
/* 2^40 - 2^0 */ curve25519_mul(t0, t0, c);
/* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10);
/* 2^50 - 2^0 */ curve25519_mul(b, t0, b);
/* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50);
/* 2^100 - 2^0 */ curve25519_mul(c, t0, b);
/* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100);
/* 2^200 - 2^0 */ curve25519_mul(t0, t0, c);
/* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50);
/* 2^250 - 2^0 */ curve25519_mul(b, t0, b);
}
/*
* z^(p - 2) = z(2^255 - 21)
*/
void
curve25519_recip(bignum25519 out, const bignum25519 z) {
ALIGN(ALIGN_SPEC) bignum25519 a, t0, b;
/* 2 */ curve25519_square(a, z); /* a = 2 */
/* 8 */ curve25519_square_times(t0, a, 2);
/* 9 */ curve25519_mul(b, t0, z); /* b = 9 */
/* 11 */ curve25519_mul(a, b, a); /* a = 11 */
/* 22 */ curve25519_square(t0, a);
/* 2^5 - 2^0 = 31 */ curve25519_mul(b, t0, b);
/* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
/* 2^255 - 2^5 */ curve25519_square_times(b, b, 5);
/* 2^255 - 21 */ curve25519_mul(out, b, a);
}
ANONYMOUS_NAMESPACE_END
NAMESPACE_END // X25519
NAMESPACE_END // Donna
NAMESPACE_END // CryptoPP
//******************************* ed25519 *******************************//
NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)
NAMESPACE_BEGIN(Ed25519)
ANONYMOUS_NAMESPACE_BEGIN
using CryptoPP::byte;
using CryptoPP::word32;
using CryptoPP::sword32;
using CryptoPP::word64;
using CryptoPP::sword64;
using CryptoPP::GetBlock;
using CryptoPP::LittleEndian;
using CryptoPP::SHA512;
// Bring in all the symbols from the 64-bit header
using namespace CryptoPP::Donna::Arch64;
/* out = in */
inline void
curve25519_copy(bignum25519 out, const bignum25519 in) {
out[0] = in[0]; out[1] = in[1];
out[2] = in[2]; out[3] = in[3];
out[4] = in[4];
}
/* out = a + b */
inline void
curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
out[4] = a[4] + b[4];
}
/* out = a + b, where a and/or b are the result of a basic op (add,sub) */
inline void
curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
out[0] = a[0] + b[0]; out[1] = a[1] + b[1];
out[2] = a[2] + b[2]; out[3] = a[3] + b[3];
out[4] = a[4] + b[4];
}
inline void
curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
word64 c;
out[0] = a[0] + b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
out[1] = a[1] + b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
out[2] = a[2] + b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
out[3] = a[3] + b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
out[4] = a[4] + b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
out[0] += c * 19;
}
/* out = a - b */
inline void
curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
out[0] = a[0] + twoP0 - b[0];
out[1] = a[1] + twoP1234 - b[1];
out[2] = a[2] + twoP1234 - b[2];
out[3] = a[3] + twoP1234 - b[3];
out[4] = a[4] + twoP1234 - b[4];
}
/* out = a - b, where a and/or b are the result of a basic op (add,sub) */
inline void
curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
out[0] = a[0] + fourP0 - b[0];
out[1] = a[1] + fourP1234 - b[1];
out[2] = a[2] + fourP1234 - b[2];
out[3] = a[3] + fourP1234 - b[3];
out[4] = a[4] + fourP1234 - b[4];
}
inline void
curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
word64 c;
out[0] = a[0] + fourP0 - b[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
out[1] = a[1] + fourP1234 - b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
out[2] = a[2] + fourP1234 - b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
out[3] = a[3] + fourP1234 - b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
out[4] = a[4] + fourP1234 - b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
out[0] += c * 19;
}
/* out = -a */
inline void
curve25519_neg(bignum25519 out, const bignum25519 a) {
word64 c;
out[0] = twoP0 - a[0] ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
out[1] = twoP1234 - a[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
out[2] = twoP1234 - a[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
out[3] = twoP1234 - a[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
out[4] = twoP1234 - a[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
out[0] += c * 19;
}
/* out = a * b */
inline void
curve25519_mul(bignum25519 out, const bignum25519 in2, const bignum25519 in) {
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
word128 mul;
#endif
word128 t[5];
word64 r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
r0 = in[0]; r1 = in[1];
r2 = in[2]; r3 = in[3];
r4 = in[4];
s0 = in2[0]; s1 = in2[1];
s2 = in2[2]; s3 = in2[3];
s4 = in2[4];
#if defined(CRYPTOPP_WORD128_AVAILABLE)
t[0] = ((word128) r0) * s0;
t[1] = ((word128) r0) * s1 + ((word128) r1) * s0;
t[2] = ((word128) r0) * s2 + ((word128) r2) * s0 + ((word128) r1) * s1;
t[3] = ((word128) r0) * s3 + ((word128) r3) * s0 + ((word128) r1) * s2 + ((word128) r2) * s1;
t[4] = ((word128) r0) * s4 + ((word128) r4) * s0 + ((word128) r3) * s1 + ((word128) r1) * s3 + ((word128) r2) * s2;
#else
mul64x64_128(t[0], r0, s0)
mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul)
mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul)
mul64x64_128(t[3], r0, s3) mul64x64_128(mul, r3, s0) add128(t[3], mul) mul64x64_128(mul, r1, s2) add128(t[3], mul) mul64x64_128(mul, r2, s1) add128(t[3], mul)
mul64x64_128(t[4], r0, s4) mul64x64_128(mul, r4, s0) add128(t[4], mul) mul64x64_128(mul, r3, s1) add128(t[4], mul) mul64x64_128(mul, r1, s3) add128(t[4], mul) mul64x64_128(mul, r2, s2) add128(t[4], mul)
#endif
r1 *= 19; r2 *= 19;
r3 *= 19; r4 *= 19;
#if defined(CRYPTOPP_WORD128_AVAILABLE)
t[0] += ((word128) r4) * s1 + ((word128) r1) * s4 + ((word128) r2) * s3 + ((word128) r3) * s2;
t[1] += ((word128) r4) * s2 + ((word128) r2) * s4 + ((word128) r3) * s3;
t[2] += ((word128) r4) * s3 + ((word128) r3) * s4;
t[3] += ((word128) r4) * s4;
#else
mul64x64_128(mul, r4, s1) add128(t[0], mul) mul64x64_128(mul, r1, s4) add128(t[0], mul) mul64x64_128(mul, r2, s3) add128(t[0], mul) mul64x64_128(mul, r3, s2) add128(t[0], mul)
mul64x64_128(mul, r4, s2) add128(t[1], mul) mul64x64_128(mul, r2, s4) add128(t[1], mul) mul64x64_128(mul, r3, s3) add128(t[1], mul)
mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul)
mul64x64_128(mul, r4, s4) add128(t[3], mul)
#endif
r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
r1 += c;
out[0] = r0; out[1] = r1;
out[2] = r2; out[3] = r3;
out[4] = r4;
}
void
curve25519_mul_noinline(bignum25519 out, const bignum25519 in2, const bignum25519 in) {
curve25519_mul(out, in2, in);
}
/* out = in^(2 * count) */
void
curve25519_square_times(bignum25519 out, const bignum25519 in, word64 count) {
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
word128 mul;
#endif
word128 t[5];
word64 r0,r1,r2,r3,r4,c;
word64 d0,d1,d2,d4,d419;
r0 = in[0]; r1 = in[1];
r2 = in[2]; r3 = in[3];
r4 = in[4];
do {
d0 = r0 * 2;
d1 = r1 * 2;
d2 = r2 * 2 * 19;
d419 = r4 * 19;
d4 = d419 * 2;
#if defined(CRYPTOPP_WORD128_AVAILABLE)
t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
#else
mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
#endif
r0 = lo128(t[0]) & reduce_mask_51;
r1 = lo128(t[1]) & reduce_mask_51; shl128(c, t[0], 13); r1 += c;
r2 = lo128(t[2]) & reduce_mask_51; shl128(c, t[1], 13); r2 += c;
r3 = lo128(t[3]) & reduce_mask_51; shl128(c, t[2], 13); r3 += c;
r4 = lo128(t[4]) & reduce_mask_51; shl128(c, t[3], 13); r4 += c;
shl128(c, t[4], 13); r0 += c * 19;
c = r0 >> 51; r0 &= reduce_mask_51;
r1 += c ; c = r1 >> 51; r1 &= reduce_mask_51;
r2 += c ; c = r2 >> 51; r2 &= reduce_mask_51;
r3 += c ; c = r3 >> 51; r3 &= reduce_mask_51;
r4 += c ; c = r4 >> 51; r4 &= reduce_mask_51;
r0 += c * 19;
} while(--count);
out[0] = r0; out[1] = r1;
out[2] = r2; out[3] = r3;
out[4] = r4;
}
inline void
curve25519_square(bignum25519 out, const bignum25519 in) {
#if !defined(CRYPTOPP_WORD128_AVAILABLE)
word128 mul;
#endif
word128 t[5];
word64 r0,r1,r2,r3,r4,c;
word64 d0,d1,d2,d4,d419;
r0 = in[0]; r1 = in[1];
r2 = in[2]; r3 = in[3];
r4 = in[4];
d0 = r0 * 2; d1 = r1 * 2;
d2 = r2 * 2 * 19;
d419 = r4 * 19;
d4 = d419 * 2;
#if defined(CRYPTOPP_WORD128_AVAILABLE)
t[0] = ((word128) r0) * r0 + ((word128) d4) * r1 + (((word128) d2) * (r3 ));
t[1] = ((word128) d0) * r1 + ((word128) d4) * r2 + (((word128) r3) * (r3 * 19));
t[2] = ((word128) d0) * r2 + ((word128) r1) * r1 + (((word128) d4) * (r3 ));
t[3] = ((word128) d0) * r3 + ((word128) d1) * r2 + (((word128) r4) * (d419 ));
t[4] = ((word128) d0) * r4 + ((word128) d1) * r3 + (((word128) r2) * (r2 ));
#else
mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
#endif
r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
r1 += c;
out[0] = r0; out[1] = r1;
out[2] = r2; out[3] = r3;
out[4] = r4;
}
/* Take a little-endian, 32-byte number and expand it into polynomial form */
inline void
curve25519_expand(bignum25519 out, const byte *in) {
word64 x0,x1,x2,x3;
GetBlock<word64, LittleEndian> block(in);
block(x0)(x1)(x2)(x3);
out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13);
out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26);
out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39);
out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12);
out[4] = x3 & reduce_mask_51;
}
/* Take a fully reduced polynomial form number and contract it into a
* little-endian, 32-byte array
*/
inline void
curve25519_contract(byte *out, const bignum25519 input) {
word64 t[5];
word64 f, i;
t[0] = input[0];
t[1] = input[1];
t[2] = input[2];
t[3] = input[3];
t[4] = input[4];
#define curve25519_contract_carry() \
t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \
t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \
t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \
t[4] += t[3] >> 51; t[3] &= reduce_mask_51;
#define curve25519_contract_carry_full() curve25519_contract_carry() \
t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51;
#define curve25519_contract_carry_final() curve25519_contract_carry() \
t[4] &= reduce_mask_51;
curve25519_contract_carry_full()
curve25519_contract_carry_full()
/* now t is between 0 and 2^255-1, properly carried. */
/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
t[0] += 19;
curve25519_contract_carry_full()
/* now between 19 and 2^255-1 in both cases, and offset by 19. */
t[0] += (reduce_mask_51 + 1) - 19;
t[1] += (reduce_mask_51 + 1) - 1;
t[2] += (reduce_mask_51 + 1) - 1;
t[3] += (reduce_mask_51 + 1) - 1;
t[4] += (reduce_mask_51 + 1) - 1;
/* now between 2^255 and 2^256-20, and offset by 2^255. */
curve25519_contract_carry_final()
#define write51full(n,shift) \
f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \
for (i = 0; i < 8; i++, f >>= 8) *out++ = (byte)f;
#define write51(n) write51full(n,13*n)
write51(0)
write51(1)
write51(2)
write51(3)
}
#if !defined(ED25519_GCC_64BIT_CHOOSE)
/* out = (flag) ? in : out */
inline void
curve25519_move_conditional_bytes(byte out[96], const byte in[96], word64 flag)
{
// TODO: enable this code path once we can test and benchmark it.
// It is about 24 insns shorter, it avoids punning which may be UB,
// and it is guaranteed constant time.
#if defined(__GNUC__) && defined(__x86_64__) && 0
const word32 iter = 96/sizeof(word64);
word64* outq = reinterpret_cast<word64*>(out);
const word64* inq = reinterpret_cast<const word64*>(in);
word64 idx=0, val;
__asm__ __volatile__ (
".att_syntax ;\n"
"cmpq $0, %[flag] ;\n" // compare, set ZERO flag
"movq %[iter], %%rcx ;\n" // load iteration count
"1: ;\n"
" movq (%[idx],%[out]), %[val] ;\n" // val = out[idx]
" cmovnzq (%[idx],%[in]), %[val] ;\n" // copy in[idx] to val if NZ
" movq %[val], (%[idx],%[out]) ;\n" // out[idx] = val
" leaq 8(%[idx]), %[idx] ;\n" // increment index
" loopnz 1b ;\n" // does not affect flags
: [out] "+S" (outq), [in] "+D" (inq),
[idx] "+b" (idx), [val] "=r" (val)
: [flag] "g" (flag), [iter] "I" (iter)
: "rcx", "memory", "cc"
);
#else
const word64 nb = flag - 1, b = ~nb;
const word64 *inq = (const word64 *)(const void*)in;
word64 *outq = (word64 *)(void *)out;
outq[0] = (outq[0] & nb) | (inq[0] & b);
outq[1] = (outq[1] & nb) | (inq[1] & b);
outq[2] = (outq[2] & nb) | (inq[2] & b);
outq[3] = (outq[3] & nb) | (inq[3] & b);
outq[4] = (outq[4] & nb) | (inq[4] & b);
outq[5] = (outq[5] & nb) | (inq[5] & b);
outq[6] = (outq[6] & nb) | (inq[6] & b);
outq[7] = (outq[7] & nb) | (inq[7] & b);
outq[8] = (outq[8] & nb) | (inq[8] & b);
outq[9] = (outq[9] & nb) | (inq[9] & b);
outq[10] = (outq[10] & nb) | (inq[10] & b);
outq[11] = (outq[11] & nb) | (inq[11] & b);
#endif
}
/* if (iswap) swap(a, b) */
inline void
curve25519_swap_conditional(bignum25519 a, bignum25519 b, word64 iswap) {
const word64 swap = (word64)(-(sword64)iswap);
word64 x0,x1,x2,x3,x4;
x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0;
x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1;
x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2;
x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3;
x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4;
}
#endif /* ED25519_GCC_64BIT_CHOOSE */
// ************************************************************************************
inline void
ed25519_hash(byte *hash, const byte *in, size_t inlen) {
SHA512().CalculateDigest(hash, in, inlen);
}
inline void
ed25519_extsk(hash_512bits extsk, const byte sk[32]) {
ed25519_hash(extsk, sk, 32);
extsk[0] &= 248;
extsk[31] &= 127;
extsk[31] |= 64;
}
void
UpdateFromStream(HashTransformation& hash, std::istream& stream)
{
SecByteBlock block(4096);
while (stream.read((char*)block.begin(), block.size()))
hash.Update(block, block.size());
std::streamsize rem = stream.gcount();
if (rem)
hash.Update(block, rem);
block.SetMark(0);
}
void
ed25519_hram(hash_512bits hram, const byte RS[64], const byte pk[32], const byte *m, size_t mlen) {
SHA512 hash;
hash.Update(RS, 32);
hash.Update(pk, 32);
hash.Update(m, mlen);
hash.Final(hram);
}
void
ed25519_hram(hash_512bits hram, const byte RS[64], const byte pk[32], std::istream& stream) {
SHA512 hash;
hash.Update(RS, 32);
hash.Update(pk, 32);
UpdateFromStream(hash, stream);
hash.Final(hram);
}
bignum256modm_element_t
lt_modm(bignum256modm_element_t a, bignum256modm_element_t b) {
return (a - b) >> 63;
}
void
reduce256_modm(bignum256modm r) {
bignum256modm t;
bignum256modm_element_t b = 0, pb, mask;
/* t = r - m */
pb = 0;
pb += modm_m[0]; b = lt_modm(r[0], pb); t[0] = (r[0] - pb + (b << 56)); pb = b;
pb += modm_m[1]; b = lt_modm(r[1], pb); t[1] = (r[1] - pb + (b << 56)); pb = b;
pb += modm_m[2]; b = lt_modm(r[2], pb); t[2] = (r[2] - pb + (b << 56)); pb = b;
pb += modm_m[3]; b = lt_modm(r[3], pb); t[3] = (r[3] - pb + (b << 56)); pb = b;
pb += modm_m[4]; b = lt_modm(r[4], pb); t[4] = (r[4] - pb + (b << 32));
/* keep r if r was smaller than m */
mask = b - 1;
r[0] ^= mask & (r[0] ^ t[0]);
r[1] ^= mask & (r[1] ^ t[1]);
r[2] ^= mask & (r[2] ^ t[2]);
r[3] ^= mask & (r[3] ^ t[3]);
r[4] ^= mask & (r[4] ^ t[4]);
}
void
barrett_reduce256_modm(bignum256modm r, const bignum256modm q1, const bignum256modm r1) {
bignum256modm q3, r2;
word128 c, mul;
bignum256modm_element_t f, b, pb;
/* q1 = x >> 248 = 264 bits = 5 56 bit elements
q2 = mu * q1
q3 = (q2 / 256(32+1)) = q2 / (2^8)^(32+1) = q2 >> 264 */
mul64x64_128(c, modm_mu[0], q1[3]) mul64x64_128(mul, modm_mu[3], q1[0]) add128(c, mul) mul64x64_128(mul, modm_mu[1], q1[2]) add128(c, mul) mul64x64_128(mul, modm_mu[2], q1[1]) add128(c, mul) shr128(f, c, 56);
mul64x64_128(c, modm_mu[0], q1[4]) add128_64(c, f) mul64x64_128(mul, modm_mu[4], q1[0]) add128(c, mul) mul64x64_128(mul, modm_mu[3], q1[1]) add128(c, mul) mul64x64_128(mul, modm_mu[1], q1[3]) add128(c, mul) mul64x64_128(mul, modm_mu[2], q1[2]) add128(c, mul)
f = lo128(c); q3[0] = (f >> 40) & 0xffff; shr128(f, c, 56);
mul64x64_128(c, modm_mu[4], q1[1]) add128_64(c, f) mul64x64_128(mul, modm_mu[1], q1[4]) add128(c, mul) mul64x64_128(mul, modm_mu[2], q1[3]) add128(c, mul) mul64x64_128(mul, modm_mu[3], q1[2]) add128(c, mul)
f = lo128(c); q3[0] |= (f << 16) & 0xffffffffffffff; q3[1] = (f >> 40) & 0xffff; shr128(f, c, 56);
mul64x64_128(c, modm_mu[4], q1[2]) add128_64(c, f) mul64x64_128(mul, modm_mu[2], q1[4]) add128(c, mul) mul64x64_128(mul, modm_mu[3], q1[3]) add128(c, mul)
f = lo128(c); q3[1] |= (f << 16) & 0xffffffffffffff; q3[2] = (f >> 40) & 0xffff; shr128(f, c, 56);
mul64x64_128(c, modm_mu[4], q1[3]) add128_64(c, f) mul64x64_128(mul, modm_mu[3], q1[4]) add128(c, mul)
f = lo128(c); q3[2] |= (f << 16) & 0xffffffffffffff; q3[3] = (f >> 40) & 0xffff; shr128(f, c, 56);
mul64x64_128(c, modm_mu[4], q1[4]) add128_64(c, f)
f = lo128(c); q3[3] |= (f << 16) & 0xffffffffffffff; q3[4] = (f >> 40) & 0xffff; shr128(f, c, 56);
q3[4] |= (f << 16);
mul64x64_128(c, modm_m[0], q3[0])
r2[0] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
mul64x64_128(c, modm_m[0], q3[1]) add128_64(c, f) mul64x64_128(mul, modm_m[1], q3[0]) add128(c, mul)
r2[1] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
mul64x64_128(c, modm_m[0], q3[2]) add128_64(c, f) mul64x64_128(mul, modm_m[2], q3[0]) add128(c, mul) mul64x64_128(mul, modm_m[1], q3[1]) add128(c, mul)
r2[2] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
mul64x64_128(c, modm_m[0], q3[3]) add128_64(c, f) mul64x64_128(mul, modm_m[3], q3[0]) add128(c, mul) mul64x64_128(mul, modm_m[1], q3[2]) add128(c, mul) mul64x64_128(mul, modm_m[2], q3[1]) add128(c, mul)
r2[3] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
mul64x64_128(c, modm_m[0], q3[4]) add128_64(c, f) mul64x64_128(mul, modm_m[4], q3[0]) add128(c, mul) mul64x64_128(mul, modm_m[3], q3[1]) add128(c, mul) mul64x64_128(mul, modm_m[1], q3[3]) add128(c, mul) mul64x64_128(mul, modm_m[2], q3[2]) add128(c, mul)
r2[4] = lo128(c) & 0x0000ffffffffff;
pb = 0;
pb += r2[0]; b = lt_modm(r1[0], pb); r[0] = (r1[0] - pb + (b << 56)); pb = b;
pb += r2[1]; b = lt_modm(r1[1], pb); r[1] = (r1[1] - pb + (b << 56)); pb = b;
pb += r2[2]; b = lt_modm(r1[2], pb); r[2] = (r1[2] - pb + (b << 56)); pb = b;
pb += r2[3]; b = lt_modm(r1[3], pb); r[3] = (r1[3] - pb + (b << 56)); pb = b;
pb += r2[4]; b = lt_modm(r1[4], pb); r[4] = (r1[4] - pb + (b << 40));
reduce256_modm(r);
reduce256_modm(r);
}
void
add256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
bignum256modm_element_t c;
c = x[0] + y[0]; r[0] = c & 0xffffffffffffff; c >>= 56;
c += x[1] + y[1]; r[1] = c & 0xffffffffffffff; c >>= 56;
c += x[2] + y[2]; r[2] = c & 0xffffffffffffff; c >>= 56;
c += x[3] + y[3]; r[3] = c & 0xffffffffffffff; c >>= 56;
c += x[4] + y[4]; r[4] = c;
reduce256_modm(r);
}
void
mul256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
bignum256modm q1, r1;
word128 c, mul;
bignum256modm_element_t f;
mul64x64_128(c, x[0], y[0])
f = lo128(c); r1[0] = f & 0xffffffffffffff; shr128(f, c, 56);
mul64x64_128(c, x[0], y[1]) add128_64(c, f) mul64x64_128(mul, x[1], y[0]) add128(c, mul)
f = lo128(c); r1[1] = f & 0xffffffffffffff; shr128(f, c, 56);
mul64x64_128(c, x[0], y[2]) add128_64(c, f) mul64x64_128(mul, x[2], y[0]) add128(c, mul) mul64x64_128(mul, x[1], y[1]) add128(c, mul)
f = lo128(c); r1[2] = f & 0xffffffffffffff; shr128(f, c, 56);
mul64x64_128(c, x[0], y[3]) add128_64(c, f) mul64x64_128(mul, x[3], y[0]) add128(c, mul) mul64x64_128(mul, x[1], y[2]) add128(c, mul) mul64x64_128(mul, x[2], y[1]) add128(c, mul)
f = lo128(c); r1[3] = f & 0xffffffffffffff; shr128(f, c, 56);
mul64x64_128(c, x[0], y[4]) add128_64(c, f) mul64x64_128(mul, x[4], y[0]) add128(c, mul) mul64x64_128(mul, x[3], y[1]) add128(c, mul) mul64x64_128(mul, x[1], y[3]) add128(c, mul) mul64x64_128(mul, x[2], y[2]) add128(c, mul)
f = lo128(c); r1[4] = f & 0x0000ffffffffff; q1[0] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
mul64x64_128(c, x[4], y[1]) add128_64(c, f) mul64x64_128(mul, x[1], y[4]) add128(c, mul) mul64x64_128(mul, x[2], y[3]) add128(c, mul) mul64x64_128(mul, x[3], y[2]) add128(c, mul)
f = lo128(c); q1[0] |= (f << 32) & 0xffffffffffffff; q1[1] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
mul64x64_128(c, x[4], y[2]) add128_64(c, f) mul64x64_128(mul, x[2], y[4]) add128(c, mul) mul64x64_128(mul, x[3], y[3]) add128(c, mul)
f = lo128(c); q1[1] |= (f << 32) & 0xffffffffffffff; q1[2] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
mul64x64_128(c, x[4], y[3]) add128_64(c, f) mul64x64_128(mul, x[3], y[4]) add128(c, mul)
f = lo128(c); q1[2] |= (f << 32) & 0xffffffffffffff; q1[3] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
mul64x64_128(c, x[4], y[4]) add128_64(c, f)
f = lo128(c); q1[3] |= (f << 32) & 0xffffffffffffff; q1[4] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
q1[4] |= (f << 32);
barrett_reduce256_modm(r, q1, r1);
}
void
expand256_modm(bignum256modm out, const byte *in, size_t len) {
byte work[64] = {0};
bignum256modm_element_t x[16];
bignum256modm q1;
memcpy(work, in, len);
x[0] = U8TO64_LE(work + 0);
x[1] = U8TO64_LE(work + 8);
x[2] = U8TO64_LE(work + 16);
x[3] = U8TO64_LE(work + 24);
x[4] = U8TO64_LE(work + 32);
x[5] = U8TO64_LE(work + 40);
x[6] = U8TO64_LE(work + 48);
x[7] = U8TO64_LE(work + 56);
/* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1) */
out[0] = ( x[0]) & 0xffffffffffffff;
out[1] = ((x[ 0] >> 56) | (x[ 1] << 8)) & 0xffffffffffffff;
out[2] = ((x[ 1] >> 48) | (x[ 2] << 16)) & 0xffffffffffffff;
out[3] = ((x[ 2] >> 40) | (x[ 3] << 24)) & 0xffffffffffffff;
out[4] = ((x[ 3] >> 32) | (x[ 4] << 32)) & 0x0000ffffffffff;
/* under 252 bits, no need to reduce */
if (len < 32)
return;