diff --git a/sha3/allocations_test.go b/sha3/allocations_test.go
new file mode 100644
index 0000000000..c925099304
--- /dev/null
+++ b/sha3/allocations_test.go
@@ -0,0 +1,53 @@
+// Copyright 2023 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//go:build !noopt
+
+package sha3_test
+
+import (
+	"testing"
+
+	"golang.org/x/crypto/sha3"
+)
+
+var sink byte
+
+func TestAllocations(t *testing.T) {
+	t.Run("New", func(t *testing.T) {
+		if allocs := testing.AllocsPerRun(10, func() {
+			h := sha3.New256()
+			b := []byte("ABC")
+			h.Write(b)
+			out := make([]byte, 0, 32)
+			out = h.Sum(out)
+			sink ^= out[0]
+		}); allocs > 0 {
+			t.Errorf("expected zero allocations, got %0.1f", allocs)
+		}
+	})
+	t.Run("NewShake", func(t *testing.T) {
+		if allocs := testing.AllocsPerRun(10, func() {
+			h := sha3.NewShake128()
+			b := []byte("ABC")
+			h.Write(b)
+			out := make([]byte, 0, 32)
+			out = h.Sum(out)
+			sink ^= out[0]
+			h.Read(out)
+			sink ^= out[0]
+		}); allocs > 0 {
+			t.Errorf("expected zero allocations, got %0.1f", allocs)
+		}
+	})
+	t.Run("Sum", func(t *testing.T) {
+		if allocs := testing.AllocsPerRun(10, func() {
+			b := []byte("ABC")
+			out := sha3.Sum256(b)
+			sink ^= out[0]
+		}); allocs > 0 {
+			t.Errorf("expected zero allocations, got %0.1f", allocs)
+		}
+	})
+}
diff --git a/sha3/sha3.go b/sha3/sha3.go
index 33bd73b0f6..afedde5abf 100644
--- a/sha3/sha3.go
+++ b/sha3/sha3.go
@@ -23,7 +23,6 @@ const (
 type state struct {
 	// Generic sponge components.
 	a    [25]uint64 // main state of the hash
-	buf  []byte     // points into storage
 	rate int        // the number of bytes of state to use
 
 	// dsbyte contains the "domain separation" bits and the first bit of
@@ -40,6 +39,7 @@ type state struct {
 	//      Extendable-Output Functions (May 2014)"
 	dsbyte byte
 
+	i, n    int // storage[i:n] is the buffer, i is only used while squeezing
 	storage [maxRate]byte
 
 	// Specific to SHA-3 and SHAKE.
@@ -54,24 +54,18 @@ func (d *state) BlockSize() int { return d.rate }
 func (d *state) Size() int { return d.outputLen }
 
 // Reset clears the internal state by zeroing the sponge state and
-// the byte buffer, and setting Sponge.state to absorbing.
+// the buffer indexes, and setting Sponge.state to absorbing.
 func (d *state) Reset() {
 	// Zero the permutation's state.
 	for i := range d.a {
 		d.a[i] = 0
 	}
 	d.state = spongeAbsorbing
-	d.buf = d.storage[:0]
+	d.i, d.n = 0, 0
 }
 
 func (d *state) clone() *state {
 	ret := *d
-	if ret.state == spongeAbsorbing {
-		ret.buf = ret.storage[:len(ret.buf)]
-	} else {
-		ret.buf = ret.storage[d.rate-cap(d.buf) : d.rate]
-	}
-
 	return &ret
 }
 
@@ -82,43 +76,40 @@ func (d *state) permute() {
 	case spongeAbsorbing:
 		// If we're absorbing, we need to xor the input into the state
 		// before applying the permutation.
-		xorIn(d, d.buf)
-		d.buf = d.storage[:0]
+		xorIn(d, d.storage[:d.rate])
+		d.n = 0
 		keccakF1600(&d.a)
 	case spongeSqueezing:
 		// If we're squeezing, we need to apply the permutation before
 		// copying more output.
 		keccakF1600(&d.a)
-		d.buf = d.storage[:d.rate]
-		copyOut(d, d.buf)
+		d.i = 0
+		copyOut(d, d.storage[:d.rate])
 	}
 }
 
 // pads appends the domain separation bits in dsbyte, applies
 // the multi-bitrate 10..1 padding rule, and permutes the state.
-func (d *state) padAndPermute(dsbyte byte) {
-	if d.buf == nil {
-		d.buf = d.storage[:0]
-	}
+func (d *state) padAndPermute() {
 	// Pad with this instance's domain-separator bits. We know that there's
 	// at least one byte of space in d.buf because, if it were full,
 	// permute would have been called to empty it. dsbyte also contains the
 	// first one bit for the padding. See the comment in the state struct.
-	d.buf = append(d.buf, dsbyte)
-	zerosStart := len(d.buf)
-	d.buf = d.storage[:d.rate]
-	for i := zerosStart; i < d.rate; i++ {
-		d.buf[i] = 0
+	d.storage[d.n] = d.dsbyte
+	d.n++
+	for d.n < d.rate {
+		d.storage[d.n] = 0
+		d.n++
 	}
 	// This adds the final one bit for the padding. Because of the way that
 	// bits are numbered from the LSB upwards, the final bit is the MSB of
 	// the last byte.
-	d.buf[d.rate-1] ^= 0x80
+	d.storage[d.rate-1] ^= 0x80
 	// Apply the permutation
 	d.permute()
 	d.state = spongeSqueezing
-	d.buf = d.storage[:d.rate]
-	copyOut(d, d.buf)
+	d.n = d.rate
+	copyOut(d, d.storage[:d.rate])
 }
 
 // Write absorbs more data into the hash's state. It panics if any
@@ -127,28 +118,25 @@ func (d *state) Write(p []byte) (written int, err error) {
 	if d.state != spongeAbsorbing {
 		panic("sha3: Write after Read")
 	}
-	if d.buf == nil {
-		d.buf = d.storage[:0]
-	}
 	written = len(p)
 
 	for len(p) > 0 {
-		if len(d.buf) == 0 && len(p) >= d.rate {
+		if d.n == 0 && len(p) >= d.rate {
 			// The fast path; absorb a full "rate" bytes of input and apply the permutation.
 			xorIn(d, p[:d.rate])
 			p = p[d.rate:]
 			keccakF1600(&d.a)
 		} else {
 			// The slow path; buffer the input until we can fill the sponge, and then xor it in.
-			todo := d.rate - len(d.buf)
+			todo := d.rate - d.n
 			if todo > len(p) {
 				todo = len(p)
 			}
-			d.buf = append(d.buf, p[:todo]...)
+			d.n += copy(d.storage[d.n:], p[:todo])
 			p = p[todo:]
 
 			// If the sponge is full, apply the permutation.
-			if len(d.buf) == d.rate {
+			if d.n == d.rate {
 				d.permute()
 			}
 		}
@@ -161,19 +149,19 @@ func (d *state) Write(p []byte) (written int, err error) {
 func (d *state) Read(out []byte) (n int, err error) {
 	// If we're still absorbing, pad and apply the permutation.
 	if d.state == spongeAbsorbing {
-		d.padAndPermute(d.dsbyte)
+		d.padAndPermute()
 	}
 
 	n = len(out)
 
 	// Now, do the squeezing.
 	for len(out) > 0 {
-		n := copy(out, d.buf)
-		d.buf = d.buf[n:]
+		n := copy(out, d.storage[d.i:d.n])
+		d.i += n
 		out = out[n:]
 
 		// Apply the permutation if we've squeezed the sponge dry.
-		if len(d.buf) == 0 {
+		if d.i == d.rate {
 			d.permute()
 		}
 	}