diff --git a/internal/poly1305/_asm/go.mod b/internal/poly1305/_asm/go.mod
new file mode 100644
index 0000000000..47f2b758ef
--- /dev/null
+++ b/internal/poly1305/_asm/go.mod
@@ -0,0 +1,15 @@
+module internal/poly1305/_asm
+
+go 1.23
+
+require (
+	github.com/mmcloughlin/avo v0.6.0
+	golang.org/x/crypto v0.26.0
+)
+
+require (
+	golang.org/x/mod v0.20.0 // indirect
+	golang.org/x/sync v0.8.0 // indirect
+	golang.org/x/sys v0.24.0 // indirect
+	golang.org/x/tools v0.24.0 // indirect
+)
diff --git a/internal/poly1305/_asm/go.sum b/internal/poly1305/_asm/go.sum
new file mode 100644
index 0000000000..62ea9dfb70
--- /dev/null
+++ b/internal/poly1305/_asm/go.sum
@@ -0,0 +1,12 @@
+github.com/mmcloughlin/avo v0.6.0 h1:QH6FU8SKoTLaVs80GA8TJuLNkUYl4VokHKlPhVDg4YY=
+github.com/mmcloughlin/avo v0.6.0/go.mod h1:8CoAGaCSYXtCPR+8y18Y9aB/kxb8JSS6FRI7mSkvD+8=
+golang.org/x/crypto v0.26.0 h1:RrRspgV4mU+YwB4FYnuBoKsUapNIL5cohGAmSH3azsw=
+golang.org/x/crypto v0.26.0/go.mod h1:GY7jblb9wI+FOo5y8/S2oY4zWP07AkOJ4+jxCqdqn54=
+golang.org/x/mod v0.20.0 h1:utOm6MM3R3dnawAiJgn0y+xvuYRsm1RKM/4giyfDgV0=
+golang.org/x/mod v0.20.0/go.mod h1:hTbmBsO62+eylJbnUtE2MGJUyE7QWk4xUqPFrRgJ+7c=
+golang.org/x/sync v0.8.0 h1:3NFvSEYkUoMifnESzZl15y791HH1qU2xm6eCJU5ZPXQ=
+golang.org/x/sync v0.8.0/go.mod h1:Czt+wKu1gCyEFDUtn0jG5QVvpJ6rzVqr5aXyt9drQfk=
+golang.org/x/sys v0.24.0 h1:Twjiwq9dn6R1fQcyiK+wQyHWfaz/BJB+YIpzU/Cv3Xg=
+golang.org/x/sys v0.24.0/go.mod h1:/VUhepiaJMQUp4+oa/7Zr1D23ma6VTLIYjOOTFZPUcA=
+golang.org/x/tools v0.24.0 h1:J1shsA93PJUEVaUSaay7UXAyE8aimq3GW0pjlolpa24=
+golang.org/x/tools v0.24.0/go.mod h1:YhNqVBIfWHdzvTLs0d8LCuMhkKUgSUKldakyV7W/WDQ=
diff --git a/internal/poly1305/_asm/sum_amd64_asm.go b/internal/poly1305/_asm/sum_amd64_asm.go
new file mode 100644
index 0000000000..a445c68f01
--- /dev/null
+++ b/internal/poly1305/_asm/sum_amd64_asm.go
@@ -0,0 +1,126 @@
+// Copyright 2024 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.
+
+package main
+
+import (
+	. "github.com/mmcloughlin/avo/build"
+	. "github.com/mmcloughlin/avo/operand"
+	. "github.com/mmcloughlin/avo/reg"
+	_ "golang.org/x/crypto/sha3"
+)
+
+//go:generate go run . -out ../sum_amd64.s -pkg poly1305
+
+func main() {
+	Package("golang.org/x/crypto/internal/poly1305")
+	ConstraintExpr("gc,!purego")
+	update()
+	Generate()
+}
+
+func update() {
+	Implement("update")
+
+	Load(Param("state"), RDI)
+	MOVQ(NewParamAddr("msg_base", 8), RSI)
+	MOVQ(NewParamAddr("msg_len", 16), R15)
+
+	MOVQ(Mem{Base: DI}.Offset(0), R8)   // h0
+	MOVQ(Mem{Base: DI}.Offset(8), R9)   // h1
+	MOVQ(Mem{Base: DI}.Offset(16), R10) // h2
+	MOVQ(Mem{Base: DI}.Offset(24), R11) // r0
+	MOVQ(Mem{Base: DI}.Offset(32), R12) // r1
+
+	CMPQ(R15, Imm(16))
+	JB(LabelRef("bytes_between_0_and_15"))
+
+	Label("loop")
+	POLY1305_ADD(RSI, R8, R9, R10)
+
+	Label("multiply")
+	POLY1305_MUL(R8, R9, R10, R11, R12, RBX, RCX, R13, R14)
+	SUBQ(Imm(16), R15)
+	CMPQ(R15, Imm(16))
+	JAE(LabelRef("loop"))
+
+	Label("bytes_between_0_and_15")
+	TESTQ(R15, R15)
+	JZ(LabelRef("done"))
+	MOVQ(U32(1), RBX)
+	XORQ(RCX, RCX)
+	XORQ(R13, R13)
+	ADDQ(R15, RSI)
+
+	Label("flush_buffer")
+	SHLQ(Imm(8), RBX, RCX)
+	SHLQ(Imm(8), RBX)
+	MOVB(Mem{Base: SI}.Offset(-1), R13B)
+	XORQ(R13, RBX)
+	DECQ(RSI)
+	DECQ(R15)
+	JNZ(LabelRef("flush_buffer"))
+
+	ADDQ(RBX, R8)
+	ADCQ(RCX, R9)
+	ADCQ(Imm(0), R10)
+	MOVQ(U32(16), R15)
+	JMP(LabelRef("multiply"))
+
+	Label("done")
+	MOVQ(R8, Mem{Base: DI}.Offset(0))
+	MOVQ(R9, Mem{Base: DI}.Offset(8))
+	MOVQ(R10, Mem{Base: DI}.Offset(16))
+	RET()
+}
+
+func POLY1305_ADD(msg, h0, h1, h2 GPPhysical) {
+	ADDQ(Mem{Base: msg}.Offset(0), h0)
+	ADCQ(Mem{Base: msg}.Offset(8), h1)
+	ADCQ(Imm(1), h2)
+	LEAQ(Mem{Base: msg}.Offset(16), msg)
+}
+
+func POLY1305_MUL(h0, h1, h2, r0, r1, t0, t1, t2, t3 GPPhysical) {
+	MOVQ(r0, RAX)
+	MULQ(h0)
+	MOVQ(RAX, t0)
+	MOVQ(RDX, t1)
+	MOVQ(r0, RAX)
+	MULQ(h1)
+	ADDQ(RAX, t1)
+	ADCQ(Imm(0), RDX)
+	MOVQ(r0, t2)
+	IMULQ(h2, t2)
+	ADDQ(RDX, t2)
+
+	MOVQ(r1, RAX)
+	MULQ(h0)
+	ADDQ(RAX, t1)
+	ADCQ(Imm(0), RDX)
+	MOVQ(RDX, h0)
+	MOVQ(r1, t3)
+	IMULQ(h2, t3)
+	MOVQ(r1, RAX)
+	MULQ(h1)
+	ADDQ(RAX, t2)
+	ADCQ(RDX, t3)
+	ADDQ(h0, t2)
+	ADCQ(Imm(0), t3)
+
+	MOVQ(t0, h0)
+	MOVQ(t1, h1)
+	MOVQ(t2, h2)
+	ANDQ(Imm(3), h2)
+	MOVQ(t2, t0)
+	ANDQ(I32(-4), t0)
+	ADDQ(t0, h0)
+	ADCQ(t3, h1)
+	ADCQ(Imm(0), h2)
+	SHRQ(Imm(2), t3, t2)
+	SHRQ(Imm(2), t3)
+	ADDQ(t2, h0)
+	ADCQ(t3, h1)
+	ADCQ(Imm(0), h2)
+}
diff --git a/internal/poly1305/sum_amd64.s b/internal/poly1305/sum_amd64.s
index e0d3c64756..133757384b 100644
--- a/internal/poly1305/sum_amd64.s
+++ b/internal/poly1305/sum_amd64.s
@@ -1,108 +1,93 @@
-// Copyright 2012 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.
+// Code generated by command: go run sum_amd64_asm.go -out ../sum_amd64.s -pkg poly1305. DO NOT EDIT.
 
 //go:build gc && !purego
 
-#include "textflag.h"
-
-#define POLY1305_ADD(msg, h0, h1, h2) \
-	ADDQ 0(msg), h0;  \
-	ADCQ 8(msg), h1;  \
-	ADCQ $1, h2;      \
-	LEAQ 16(msg), msg
-
-#define POLY1305_MUL(h0, h1, h2, r0, r1, t0, t1, t2, t3) \
-	MOVQ  r0, AX;                  \
-	MULQ  h0;                      \
-	MOVQ  AX, t0;                  \
-	MOVQ  DX, t1;                  \
-	MOVQ  r0, AX;                  \
-	MULQ  h1;                      \
-	ADDQ  AX, t1;                  \
-	ADCQ  $0, DX;                  \
-	MOVQ  r0, t2;                  \
-	IMULQ h2, t2;                  \
-	ADDQ  DX, t2;                  \
-	                               \
-	MOVQ  r1, AX;                  \
-	MULQ  h0;                      \
-	ADDQ  AX, t1;                  \
-	ADCQ  $0, DX;                  \
-	MOVQ  DX, h0;                  \
-	MOVQ  r1, t3;                  \
-	IMULQ h2, t3;                  \
-	MOVQ  r1, AX;                  \
-	MULQ  h1;                      \
-	ADDQ  AX, t2;                  \
-	ADCQ  DX, t3;                  \
-	ADDQ  h0, t2;                  \
-	ADCQ  $0, t3;                  \
-	                               \
-	MOVQ  t0, h0;                  \
-	MOVQ  t1, h1;                  \
-	MOVQ  t2, h2;                  \
-	ANDQ  $3, h2;                  \
-	MOVQ  t2, t0;                  \
-	ANDQ  $0xFFFFFFFFFFFFFFFC, t0; \
-	ADDQ  t0, h0;                  \
-	ADCQ  t3, h1;                  \
-	ADCQ  $0, h2;                  \
-	SHRQ  $2, t3, t2;              \
-	SHRQ  $2, t3;                  \
-	ADDQ  t2, h0;                  \
-	ADCQ  t3, h1;                  \
-	ADCQ  $0, h2
-
-// func update(state *[7]uint64, msg []byte)
+// func update(state *macState, msg []byte)
 TEXT ·update(SB), $0-32
 	MOVQ state+0(FP), DI
 	MOVQ msg_base+8(FP), SI
 	MOVQ msg_len+16(FP), R15
-
-	MOVQ 0(DI), R8   // h0
-	MOVQ 8(DI), R9   // h1
-	MOVQ 16(DI), R10 // h2
-	MOVQ 24(DI), R11 // r0
-	MOVQ 32(DI), R12 // r1
-
-	CMPQ R15, $16
+	MOVQ (DI), R8
+	MOVQ 8(DI), R9
+	MOVQ 16(DI), R10
+	MOVQ 24(DI), R11
+	MOVQ 32(DI), R12
+	CMPQ R15, $0x10
 	JB   bytes_between_0_and_15
 
 loop:
-	POLY1305_ADD(SI, R8, R9, R10)
+	ADDQ (SI), R8
+	ADCQ 8(SI), R9
+	ADCQ $0x01, R10
+	LEAQ 16(SI), SI
 
 multiply:
-	POLY1305_MUL(R8, R9, R10, R11, R12, BX, CX, R13, R14)
-	SUBQ $16, R15
-	CMPQ R15, $16
-	JAE  loop
+	MOVQ  R11, AX
+	MULQ  R8
+	MOVQ  AX, BX
+	MOVQ  DX, CX
+	MOVQ  R11, AX
+	MULQ  R9
+	ADDQ  AX, CX
+	ADCQ  $0x00, DX
+	MOVQ  R11, R13
+	IMULQ R10, R13
+	ADDQ  DX, R13
+	MOVQ  R12, AX
+	MULQ  R8
+	ADDQ  AX, CX
+	ADCQ  $0x00, DX
+	MOVQ  DX, R8
+	MOVQ  R12, R14
+	IMULQ R10, R14
+	MOVQ  R12, AX
+	MULQ  R9
+	ADDQ  AX, R13
+	ADCQ  DX, R14
+	ADDQ  R8, R13
+	ADCQ  $0x00, R14
+	MOVQ  BX, R8
+	MOVQ  CX, R9
+	MOVQ  R13, R10
+	ANDQ  $0x03, R10
+	MOVQ  R13, BX
+	ANDQ  $-4, BX
+	ADDQ  BX, R8
+	ADCQ  R14, R9
+	ADCQ  $0x00, R10
+	SHRQ  $0x02, R14, R13
+	SHRQ  $0x02, R14
+	ADDQ  R13, R8
+	ADCQ  R14, R9
+	ADCQ  $0x00, R10
+	SUBQ  $0x10, R15
+	CMPQ  R15, $0x10
+	JAE   loop
 
 bytes_between_0_and_15:
 	TESTQ R15, R15
 	JZ    done
-	MOVQ  $1, BX
+	MOVQ  $0x00000001, BX
 	XORQ  CX, CX
 	XORQ  R13, R13
 	ADDQ  R15, SI
 
 flush_buffer:
-	SHLQ $8, BX, CX
-	SHLQ $8, BX
+	SHLQ $0x08, BX, CX
+	SHLQ $0x08, BX
 	MOVB -1(SI), R13
 	XORQ R13, BX
 	DECQ SI
 	DECQ R15
 	JNZ  flush_buffer
-
 	ADDQ BX, R8
 	ADCQ CX, R9
-	ADCQ $0, R10
-	MOVQ $16, R15
+	ADCQ $0x00, R10
+	MOVQ $0x00000010, R15
 	JMP  multiply
 
 done:
-	MOVQ R8, 0(DI)
+	MOVQ R8, (DI)
 	MOVQ R9, 8(DI)
 	MOVQ R10, 16(DI)
 	RET