github.com/google/pprof v0.0.0-20210506205249-923b5ab0fc1a
github.com/ianlancetaylor/demangle v0.0.0-20200824232613-28f6c0f3b639 // indirect
golang.org/x/arch v0.0.0-20210502124803-cbf565b21d1e
- golang.org/x/crypto v0.0.0-20210503195802-e9a32991a82e // indirect
+ golang.org/x/crypto v0.0.0-20210817164053-32db794688a5 // indirect
golang.org/x/mod v0.5.1-0.20210827163434-4029241eb1d5
golang.org/x/sys v0.0.0-20210831042530-f4d43177bf5e // indirect
golang.org/x/term v0.0.0-20210503060354-a79de5458b56
github.com/ianlancetaylor/demangle v0.0.0-20200824232613-28f6c0f3b639/go.mod h1:aSSvb/t6k1mPoxDqO4vJh6VOCGPwU4O0C2/Eqndh1Sc=
golang.org/x/arch v0.0.0-20210502124803-cbf565b21d1e h1:pv3V0NlNSh5Q6AX/StwGLBjcLS7UN4m4Gq+V+uSecqM=
golang.org/x/arch v0.0.0-20210502124803-cbf565b21d1e/go.mod h1:5om86z9Hs0C8fWVUuoMHwpExlXzs5Tkyp9hOrfG7pp8=
-golang.org/x/crypto v0.0.0-20210503195802-e9a32991a82e h1:8foAy0aoO5GkqCvAEJ4VC4P3zksTg4X4aJCDpZzmgQI=
-golang.org/x/crypto v0.0.0-20210503195802-e9a32991a82e/go.mod h1:P+XmwS30IXTQdn5tA2iutPOUgjI07+tq3H3K9MVA1s8=
+golang.org/x/crypto v0.0.0-20210817164053-32db794688a5 h1:HWj/xjIHfjYU5nVXpTM0s39J9CbLn7Cc5a7IC5rwsMQ=
+golang.org/x/crypto v0.0.0-20210817164053-32db794688a5/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc=
golang.org/x/mod v0.5.1-0.20210827163434-4029241eb1d5 h1:BJ9Nc92Yf5inqB18HHrMgflMJKHraE07Z29Vjc+Z/Mk=
golang.org/x/mod v0.5.1-0.20210827163434-4029241eb1d5/go.mod h1:5OXOZSfqPIIbmVBIIKWRFfZjPR0E5r58TLhUjH0a2Ro=
golang.org/x/sys v0.0.0-20191204072324-ce4227a45e2e/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
golang.org/x/arch/arm64/arm64asm
golang.org/x/arch/ppc64/ppc64asm
golang.org/x/arch/x86/x86asm
-# golang.org/x/crypto v0.0.0-20210503195802-e9a32991a82e
+# golang.org/x/crypto v0.0.0-20210817164053-32db794688a5
## explicit; go 1.17
golang.org/x/crypto/ed25519
golang.org/x/crypto/ed25519/internal/edwards25519
go 1.18
require (
- golang.org/x/crypto v0.0.0-20210503195802-e9a32991a82e
+ golang.org/x/crypto v0.0.0-20210817164053-32db794688a5
golang.org/x/net v0.0.0-20210825183410-e898025ed96a
golang.org/x/sys v0.0.0-20210831042530-f4d43177bf5e // indirect
golang.org/x/text v0.3.7-0.20210503195748-5c7c50ebbd4f // indirect
-golang.org/x/crypto v0.0.0-20210503195802-e9a32991a82e h1:8foAy0aoO5GkqCvAEJ4VC4P3zksTg4X4aJCDpZzmgQI=
-golang.org/x/crypto v0.0.0-20210503195802-e9a32991a82e/go.mod h1:P+XmwS30IXTQdn5tA2iutPOUgjI07+tq3H3K9MVA1s8=
+golang.org/x/crypto v0.0.0-20210817164053-32db794688a5 h1:HWj/xjIHfjYU5nVXpTM0s39J9CbLn7Cc5a7IC5rwsMQ=
+golang.org/x/crypto v0.0.0-20210817164053-32db794688a5/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc=
golang.org/x/net v0.0.0-20210825183410-e898025ed96a h1:bRuuGXV8wwSdGTB+CtJf+FjgO1APK1CoO39T4BN/XBw=
golang.org/x/net v0.0.0-20210825183410-e898025ed96a/go.mod h1:9nx3DQGgdP8bBQD5qxJ1jj9UTztislL4KSBs9R2vV5Y=
golang.org/x/sys v0.0.0-20210831042530-f4d43177bf5e h1:XMgFehsDnnLGtjvjOfqWSUzt0alpTR1RSEuznObga2c=
< crypto/subtle
< crypto/internal/subtle
< crypto/elliptic/internal/fiat
- < crypto/ed25519/internal/edwards25519/field
+ < crypto/ed25519/internal/edwards25519/field, golang.org/x/crypto/curve25519/internal/field
< crypto/ed25519/internal/edwards25519
< crypto/cipher
< crypto/aes, crypto/des, crypto/hmac, crypto/md5, crypto/rc4,
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
+//go:build go1.11 && gc && !purego
// +build go1.11,gc,!purego
#include "textflag.h"
// The differences in this and the original implementation are
// due to the calling conventions and initialization of constants.
+//go:build gc && !purego
// +build gc,!purego
#include "textflag.h"
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
+//go:build gc && !purego
// +build gc,!purego
#include "go_asm.h"
// This file was originally from https://golang.org/cl/24717 by Vlad Krasnov of CloudFlare.
+//go:build gc && !purego
// +build gc,!purego
#include "textflag.h"
import (
"crypto/subtle"
"fmt"
+
+ "golang.org/x/crypto/curve25519/internal/field"
)
// ScalarMult sets dst to the product scalar * point.
// zeroes, irrespective of the scalar. Instead, use the X25519 function, which
// will return an error.
func ScalarMult(dst, scalar, point *[32]byte) {
- scalarMult(dst, scalar, point)
+ var e [32]byte
+
+ copy(e[:], scalar[:])
+ e[0] &= 248
+ e[31] &= 127
+ e[31] |= 64
+
+ var x1, x2, z2, x3, z3, tmp0, tmp1 field.Element
+ x1.SetBytes(point[:])
+ x2.One()
+ x3.Set(&x1)
+ z3.One()
+
+ swap := 0
+ for pos := 254; pos >= 0; pos-- {
+ b := e[pos/8] >> uint(pos&7)
+ b &= 1
+ swap ^= int(b)
+ x2.Swap(&x3, swap)
+ z2.Swap(&z3, swap)
+ swap = int(b)
+
+ tmp0.Subtract(&x3, &z3)
+ tmp1.Subtract(&x2, &z2)
+ x2.Add(&x2, &z2)
+ z2.Add(&x3, &z3)
+ z3.Multiply(&tmp0, &x2)
+ z2.Multiply(&z2, &tmp1)
+ tmp0.Square(&tmp1)
+ tmp1.Square(&x2)
+ x3.Add(&z3, &z2)
+ z2.Subtract(&z3, &z2)
+ x2.Multiply(&tmp1, &tmp0)
+ tmp1.Subtract(&tmp1, &tmp0)
+ z2.Square(&z2)
+
+ z3.Mult32(&tmp1, 121666)
+ x3.Square(&x3)
+ tmp0.Add(&tmp0, &z3)
+ z3.Multiply(&x1, &z2)
+ z2.Multiply(&tmp1, &tmp0)
+ }
+
+ x2.Swap(&x3, swap)
+ z2.Swap(&z3, swap)
+
+ z2.Invert(&z2)
+ x2.Multiply(&x2, &z2)
+ copy(dst[:], x2.Bytes())
}
// ScalarBaseMult sets dst to the product scalar * base where base is the
+++ /dev/null
-// 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.
-
-//go:build amd64 && gc && !purego
-// +build amd64,gc,!purego
-
-package curve25519
-
-// These functions are implemented in the .s files. The names of the functions
-// in the rest of the file are also taken from the SUPERCOP sources to help
-// people following along.
-
-//go:noescape
-
-func cswap(inout *[5]uint64, v uint64)
-
-//go:noescape
-
-func ladderstep(inout *[5][5]uint64)
-
-//go:noescape
-
-func freeze(inout *[5]uint64)
-
-//go:noescape
-
-func mul(dest, a, b *[5]uint64)
-
-//go:noescape
-
-func square(out, in *[5]uint64)
-
-// mladder uses a Montgomery ladder to calculate (xr/zr) *= s.
-func mladder(xr, zr *[5]uint64, s *[32]byte) {
- var work [5][5]uint64
-
- work[0] = *xr
- setint(&work[1], 1)
- setint(&work[2], 0)
- work[3] = *xr
- setint(&work[4], 1)
-
- j := uint(6)
- var prevbit byte
-
- for i := 31; i >= 0; i-- {
- for j < 8 {
- bit := ((*s)[i] >> j) & 1
- swap := bit ^ prevbit
- prevbit = bit
- cswap(&work[1], uint64(swap))
- ladderstep(&work)
- j--
- }
- j = 7
- }
-
- *xr = work[1]
- *zr = work[2]
-}
-
-func scalarMult(out, in, base *[32]byte) {
- var e [32]byte
- copy(e[:], (*in)[:])
- e[0] &= 248
- e[31] &= 127
- e[31] |= 64
-
- var t, z [5]uint64
- unpack(&t, base)
- mladder(&t, &z, &e)
- invert(&z, &z)
- mul(&t, &t, &z)
- pack(out, &t)
-}
-
-func setint(r *[5]uint64, v uint64) {
- r[0] = v
- r[1] = 0
- r[2] = 0
- r[3] = 0
- r[4] = 0
-}
-
-// unpack sets r = x where r consists of 5, 51-bit limbs in little-endian
-// order.
-func unpack(r *[5]uint64, x *[32]byte) {
- r[0] = uint64(x[0]) |
- uint64(x[1])<<8 |
- uint64(x[2])<<16 |
- uint64(x[3])<<24 |
- uint64(x[4])<<32 |
- uint64(x[5])<<40 |
- uint64(x[6]&7)<<48
-
- r[1] = uint64(x[6])>>3 |
- uint64(x[7])<<5 |
- uint64(x[8])<<13 |
- uint64(x[9])<<21 |
- uint64(x[10])<<29 |
- uint64(x[11])<<37 |
- uint64(x[12]&63)<<45
-
- r[2] = uint64(x[12])>>6 |
- uint64(x[13])<<2 |
- uint64(x[14])<<10 |
- uint64(x[15])<<18 |
- uint64(x[16])<<26 |
- uint64(x[17])<<34 |
- uint64(x[18])<<42 |
- uint64(x[19]&1)<<50
-
- r[3] = uint64(x[19])>>1 |
- uint64(x[20])<<7 |
- uint64(x[21])<<15 |
- uint64(x[22])<<23 |
- uint64(x[23])<<31 |
- uint64(x[24])<<39 |
- uint64(x[25]&15)<<47
-
- r[4] = uint64(x[25])>>4 |
- uint64(x[26])<<4 |
- uint64(x[27])<<12 |
- uint64(x[28])<<20 |
- uint64(x[29])<<28 |
- uint64(x[30])<<36 |
- uint64(x[31]&127)<<44
-}
-
-// pack sets out = x where out is the usual, little-endian form of the 5,
-// 51-bit limbs in x.
-func pack(out *[32]byte, x *[5]uint64) {
- t := *x
- freeze(&t)
-
- out[0] = byte(t[0])
- out[1] = byte(t[0] >> 8)
- out[2] = byte(t[0] >> 16)
- out[3] = byte(t[0] >> 24)
- out[4] = byte(t[0] >> 32)
- out[5] = byte(t[0] >> 40)
- out[6] = byte(t[0] >> 48)
-
- out[6] ^= byte(t[1]<<3) & 0xf8
- out[7] = byte(t[1] >> 5)
- out[8] = byte(t[1] >> 13)
- out[9] = byte(t[1] >> 21)
- out[10] = byte(t[1] >> 29)
- out[11] = byte(t[1] >> 37)
- out[12] = byte(t[1] >> 45)
-
- out[12] ^= byte(t[2]<<6) & 0xc0
- out[13] = byte(t[2] >> 2)
- out[14] = byte(t[2] >> 10)
- out[15] = byte(t[2] >> 18)
- out[16] = byte(t[2] >> 26)
- out[17] = byte(t[2] >> 34)
- out[18] = byte(t[2] >> 42)
- out[19] = byte(t[2] >> 50)
-
- out[19] ^= byte(t[3]<<1) & 0xfe
- out[20] = byte(t[3] >> 7)
- out[21] = byte(t[3] >> 15)
- out[22] = byte(t[3] >> 23)
- out[23] = byte(t[3] >> 31)
- out[24] = byte(t[3] >> 39)
- out[25] = byte(t[3] >> 47)
-
- out[25] ^= byte(t[4]<<4) & 0xf0
- out[26] = byte(t[4] >> 4)
- out[27] = byte(t[4] >> 12)
- out[28] = byte(t[4] >> 20)
- out[29] = byte(t[4] >> 28)
- out[30] = byte(t[4] >> 36)
- out[31] = byte(t[4] >> 44)
-}
-
-// invert calculates r = x^-1 mod p using Fermat's little theorem.
-func invert(r *[5]uint64, x *[5]uint64) {
- var z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t [5]uint64
-
- square(&z2, x) /* 2 */
- square(&t, &z2) /* 4 */
- square(&t, &t) /* 8 */
- mul(&z9, &t, x) /* 9 */
- mul(&z11, &z9, &z2) /* 11 */
- square(&t, &z11) /* 22 */
- mul(&z2_5_0, &t, &z9) /* 2^5 - 2^0 = 31 */
-
- square(&t, &z2_5_0) /* 2^6 - 2^1 */
- for i := 1; i < 5; i++ { /* 2^20 - 2^10 */
- square(&t, &t)
- }
- mul(&z2_10_0, &t, &z2_5_0) /* 2^10 - 2^0 */
-
- square(&t, &z2_10_0) /* 2^11 - 2^1 */
- for i := 1; i < 10; i++ { /* 2^20 - 2^10 */
- square(&t, &t)
- }
- mul(&z2_20_0, &t, &z2_10_0) /* 2^20 - 2^0 */
-
- square(&t, &z2_20_0) /* 2^21 - 2^1 */
- for i := 1; i < 20; i++ { /* 2^40 - 2^20 */
- square(&t, &t)
- }
- mul(&t, &t, &z2_20_0) /* 2^40 - 2^0 */
-
- square(&t, &t) /* 2^41 - 2^1 */
- for i := 1; i < 10; i++ { /* 2^50 - 2^10 */
- square(&t, &t)
- }
- mul(&z2_50_0, &t, &z2_10_0) /* 2^50 - 2^0 */
-
- square(&t, &z2_50_0) /* 2^51 - 2^1 */
- for i := 1; i < 50; i++ { /* 2^100 - 2^50 */
- square(&t, &t)
- }
- mul(&z2_100_0, &t, &z2_50_0) /* 2^100 - 2^0 */
-
- square(&t, &z2_100_0) /* 2^101 - 2^1 */
- for i := 1; i < 100; i++ { /* 2^200 - 2^100 */
- square(&t, &t)
- }
- mul(&t, &t, &z2_100_0) /* 2^200 - 2^0 */
-
- square(&t, &t) /* 2^201 - 2^1 */
- for i := 1; i < 50; i++ { /* 2^250 - 2^50 */
- square(&t, &t)
- }
- mul(&t, &t, &z2_50_0) /* 2^250 - 2^0 */
-
- square(&t, &t) /* 2^251 - 2^1 */
- square(&t, &t) /* 2^252 - 2^2 */
- square(&t, &t) /* 2^253 - 2^3 */
-
- square(&t, &t) /* 2^254 - 2^4 */
-
- square(&t, &t) /* 2^255 - 2^5 */
- mul(r, &t, &z11) /* 2^255 - 21 */
-}
+++ /dev/null
-// 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.
-
-// This code was translated into a form compatible with 6a from the public
-// domain sources in SUPERCOP: https://bench.cr.yp.to/supercop.html
-
-// +build amd64,gc,!purego
-
-#define REDMASK51 0x0007FFFFFFFFFFFF
-
-// These constants cannot be encoded in non-MOVQ immediates.
-// We access them directly from memory instead.
-
-DATA ·_121666_213(SB)/8, $996687872
-GLOBL ·_121666_213(SB), 8, $8
-
-DATA ·_2P0(SB)/8, $0xFFFFFFFFFFFDA
-GLOBL ·_2P0(SB), 8, $8
-
-DATA ·_2P1234(SB)/8, $0xFFFFFFFFFFFFE
-GLOBL ·_2P1234(SB), 8, $8
-
-// func freeze(inout *[5]uint64)
-TEXT ·freeze(SB),7,$0-8
- MOVQ inout+0(FP), DI
-
- MOVQ 0(DI),SI
- MOVQ 8(DI),DX
- MOVQ 16(DI),CX
- MOVQ 24(DI),R8
- MOVQ 32(DI),R9
- MOVQ $REDMASK51,AX
- MOVQ AX,R10
- SUBQ $18,R10
- MOVQ $3,R11
-REDUCELOOP:
- MOVQ SI,R12
- SHRQ $51,R12
- ANDQ AX,SI
- ADDQ R12,DX
- MOVQ DX,R12
- SHRQ $51,R12
- ANDQ AX,DX
- ADDQ R12,CX
- MOVQ CX,R12
- SHRQ $51,R12
- ANDQ AX,CX
- ADDQ R12,R8
- MOVQ R8,R12
- SHRQ $51,R12
- ANDQ AX,R8
- ADDQ R12,R9
- MOVQ R9,R12
- SHRQ $51,R12
- ANDQ AX,R9
- IMUL3Q $19,R12,R12
- ADDQ R12,SI
- SUBQ $1,R11
- JA REDUCELOOP
- MOVQ $1,R12
- CMPQ R10,SI
- CMOVQLT R11,R12
- CMPQ AX,DX
- CMOVQNE R11,R12
- CMPQ AX,CX
- CMOVQNE R11,R12
- CMPQ AX,R8
- CMOVQNE R11,R12
- CMPQ AX,R9
- CMOVQNE R11,R12
- NEGQ R12
- ANDQ R12,AX
- ANDQ R12,R10
- SUBQ R10,SI
- SUBQ AX,DX
- SUBQ AX,CX
- SUBQ AX,R8
- SUBQ AX,R9
- MOVQ SI,0(DI)
- MOVQ DX,8(DI)
- MOVQ CX,16(DI)
- MOVQ R8,24(DI)
- MOVQ R9,32(DI)
- RET
-
-// func ladderstep(inout *[5][5]uint64)
-TEXT ·ladderstep(SB),0,$296-8
- MOVQ inout+0(FP),DI
-
- MOVQ 40(DI),SI
- MOVQ 48(DI),DX
- MOVQ 56(DI),CX
- MOVQ 64(DI),R8
- MOVQ 72(DI),R9
- MOVQ SI,AX
- MOVQ DX,R10
- MOVQ CX,R11
- MOVQ R8,R12
- MOVQ R9,R13
- ADDQ ·_2P0(SB),AX
- ADDQ ·_2P1234(SB),R10
- ADDQ ·_2P1234(SB),R11
- ADDQ ·_2P1234(SB),R12
- ADDQ ·_2P1234(SB),R13
- ADDQ 80(DI),SI
- ADDQ 88(DI),DX
- ADDQ 96(DI),CX
- ADDQ 104(DI),R8
- ADDQ 112(DI),R9
- SUBQ 80(DI),AX
- SUBQ 88(DI),R10
- SUBQ 96(DI),R11
- SUBQ 104(DI),R12
- SUBQ 112(DI),R13
- MOVQ SI,0(SP)
- MOVQ DX,8(SP)
- MOVQ CX,16(SP)
- MOVQ R8,24(SP)
- MOVQ R9,32(SP)
- MOVQ AX,40(SP)
- MOVQ R10,48(SP)
- MOVQ R11,56(SP)
- MOVQ R12,64(SP)
- MOVQ R13,72(SP)
- MOVQ 40(SP),AX
- MULQ 40(SP)
- MOVQ AX,SI
- MOVQ DX,CX
- MOVQ 40(SP),AX
- SHLQ $1,AX
- MULQ 48(SP)
- MOVQ AX,R8
- MOVQ DX,R9
- MOVQ 40(SP),AX
- SHLQ $1,AX
- MULQ 56(SP)
- MOVQ AX,R10
- MOVQ DX,R11
- MOVQ 40(SP),AX
- SHLQ $1,AX
- MULQ 64(SP)
- MOVQ AX,R12
- MOVQ DX,R13
- MOVQ 40(SP),AX
- SHLQ $1,AX
- MULQ 72(SP)
- MOVQ AX,R14
- MOVQ DX,R15
- MOVQ 48(SP),AX
- MULQ 48(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 48(SP),AX
- SHLQ $1,AX
- MULQ 56(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 48(SP),AX
- SHLQ $1,AX
- MULQ 64(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 48(SP),DX
- IMUL3Q $38,DX,AX
- MULQ 72(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 56(SP),AX
- MULQ 56(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 56(SP),DX
- IMUL3Q $38,DX,AX
- MULQ 64(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 56(SP),DX
- IMUL3Q $38,DX,AX
- MULQ 72(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 64(SP),DX
- IMUL3Q $19,DX,AX
- MULQ 64(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 64(SP),DX
- IMUL3Q $38,DX,AX
- MULQ 72(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 72(SP),DX
- IMUL3Q $19,DX,AX
- MULQ 72(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ $REDMASK51,DX
- SHLQ $13,SI,CX
- ANDQ DX,SI
- SHLQ $13,R8,R9
- ANDQ DX,R8
- ADDQ CX,R8
- SHLQ $13,R10,R11
- ANDQ DX,R10
- ADDQ R9,R10
- SHLQ $13,R12,R13
- ANDQ DX,R12
- ADDQ R11,R12
- SHLQ $13,R14,R15
- ANDQ DX,R14
- ADDQ R13,R14
- IMUL3Q $19,R15,CX
- ADDQ CX,SI
- MOVQ SI,CX
- SHRQ $51,CX
- ADDQ R8,CX
- ANDQ DX,SI
- MOVQ CX,R8
- SHRQ $51,CX
- ADDQ R10,CX
- ANDQ DX,R8
- MOVQ CX,R9
- SHRQ $51,CX
- ADDQ R12,CX
- ANDQ DX,R9
- MOVQ CX,AX
- SHRQ $51,CX
- ADDQ R14,CX
- ANDQ DX,AX
- MOVQ CX,R10
- SHRQ $51,CX
- IMUL3Q $19,CX,CX
- ADDQ CX,SI
- ANDQ DX,R10
- MOVQ SI,80(SP)
- MOVQ R8,88(SP)
- MOVQ R9,96(SP)
- MOVQ AX,104(SP)
- MOVQ R10,112(SP)
- MOVQ 0(SP),AX
- MULQ 0(SP)
- MOVQ AX,SI
- MOVQ DX,CX
- MOVQ 0(SP),AX
- SHLQ $1,AX
- MULQ 8(SP)
- MOVQ AX,R8
- MOVQ DX,R9
- MOVQ 0(SP),AX
- SHLQ $1,AX
- MULQ 16(SP)
- MOVQ AX,R10
- MOVQ DX,R11
- MOVQ 0(SP),AX
- SHLQ $1,AX
- MULQ 24(SP)
- MOVQ AX,R12
- MOVQ DX,R13
- MOVQ 0(SP),AX
- SHLQ $1,AX
- MULQ 32(SP)
- MOVQ AX,R14
- MOVQ DX,R15
- MOVQ 8(SP),AX
- MULQ 8(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 8(SP),AX
- SHLQ $1,AX
- MULQ 16(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 8(SP),AX
- SHLQ $1,AX
- MULQ 24(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 8(SP),DX
- IMUL3Q $38,DX,AX
- MULQ 32(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 16(SP),AX
- MULQ 16(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 16(SP),DX
- IMUL3Q $38,DX,AX
- MULQ 24(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 16(SP),DX
- IMUL3Q $38,DX,AX
- MULQ 32(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 24(SP),DX
- IMUL3Q $19,DX,AX
- MULQ 24(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 24(SP),DX
- IMUL3Q $38,DX,AX
- MULQ 32(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 32(SP),DX
- IMUL3Q $19,DX,AX
- MULQ 32(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ $REDMASK51,DX
- SHLQ $13,SI,CX
- ANDQ DX,SI
- SHLQ $13,R8,R9
- ANDQ DX,R8
- ADDQ CX,R8
- SHLQ $13,R10,R11
- ANDQ DX,R10
- ADDQ R9,R10
- SHLQ $13,R12,R13
- ANDQ DX,R12
- ADDQ R11,R12
- SHLQ $13,R14,R15
- ANDQ DX,R14
- ADDQ R13,R14
- IMUL3Q $19,R15,CX
- ADDQ CX,SI
- MOVQ SI,CX
- SHRQ $51,CX
- ADDQ R8,CX
- ANDQ DX,SI
- MOVQ CX,R8
- SHRQ $51,CX
- ADDQ R10,CX
- ANDQ DX,R8
- MOVQ CX,R9
- SHRQ $51,CX
- ADDQ R12,CX
- ANDQ DX,R9
- MOVQ CX,AX
- SHRQ $51,CX
- ADDQ R14,CX
- ANDQ DX,AX
- MOVQ CX,R10
- SHRQ $51,CX
- IMUL3Q $19,CX,CX
- ADDQ CX,SI
- ANDQ DX,R10
- MOVQ SI,120(SP)
- MOVQ R8,128(SP)
- MOVQ R9,136(SP)
- MOVQ AX,144(SP)
- MOVQ R10,152(SP)
- MOVQ SI,SI
- MOVQ R8,DX
- MOVQ R9,CX
- MOVQ AX,R8
- MOVQ R10,R9
- ADDQ ·_2P0(SB),SI
- ADDQ ·_2P1234(SB),DX
- ADDQ ·_2P1234(SB),CX
- ADDQ ·_2P1234(SB),R8
- ADDQ ·_2P1234(SB),R9
- SUBQ 80(SP),SI
- SUBQ 88(SP),DX
- SUBQ 96(SP),CX
- SUBQ 104(SP),R8
- SUBQ 112(SP),R9
- MOVQ SI,160(SP)
- MOVQ DX,168(SP)
- MOVQ CX,176(SP)
- MOVQ R8,184(SP)
- MOVQ R9,192(SP)
- MOVQ 120(DI),SI
- MOVQ 128(DI),DX
- MOVQ 136(DI),CX
- MOVQ 144(DI),R8
- MOVQ 152(DI),R9
- MOVQ SI,AX
- MOVQ DX,R10
- MOVQ CX,R11
- MOVQ R8,R12
- MOVQ R9,R13
- ADDQ ·_2P0(SB),AX
- ADDQ ·_2P1234(SB),R10
- ADDQ ·_2P1234(SB),R11
- ADDQ ·_2P1234(SB),R12
- ADDQ ·_2P1234(SB),R13
- ADDQ 160(DI),SI
- ADDQ 168(DI),DX
- ADDQ 176(DI),CX
- ADDQ 184(DI),R8
- ADDQ 192(DI),R9
- SUBQ 160(DI),AX
- SUBQ 168(DI),R10
- SUBQ 176(DI),R11
- SUBQ 184(DI),R12
- SUBQ 192(DI),R13
- MOVQ SI,200(SP)
- MOVQ DX,208(SP)
- MOVQ CX,216(SP)
- MOVQ R8,224(SP)
- MOVQ R9,232(SP)
- MOVQ AX,240(SP)
- MOVQ R10,248(SP)
- MOVQ R11,256(SP)
- MOVQ R12,264(SP)
- MOVQ R13,272(SP)
- MOVQ 224(SP),SI
- IMUL3Q $19,SI,AX
- MOVQ AX,280(SP)
- MULQ 56(SP)
- MOVQ AX,SI
- MOVQ DX,CX
- MOVQ 232(SP),DX
- IMUL3Q $19,DX,AX
- MOVQ AX,288(SP)
- MULQ 48(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 200(SP),AX
- MULQ 40(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 200(SP),AX
- MULQ 48(SP)
- MOVQ AX,R8
- MOVQ DX,R9
- MOVQ 200(SP),AX
- MULQ 56(SP)
- MOVQ AX,R10
- MOVQ DX,R11
- MOVQ 200(SP),AX
- MULQ 64(SP)
- MOVQ AX,R12
- MOVQ DX,R13
- MOVQ 200(SP),AX
- MULQ 72(SP)
- MOVQ AX,R14
- MOVQ DX,R15
- MOVQ 208(SP),AX
- MULQ 40(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 208(SP),AX
- MULQ 48(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 208(SP),AX
- MULQ 56(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 208(SP),AX
- MULQ 64(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 208(SP),DX
- IMUL3Q $19,DX,AX
- MULQ 72(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 216(SP),AX
- MULQ 40(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 216(SP),AX
- MULQ 48(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 216(SP),AX
- MULQ 56(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 216(SP),DX
- IMUL3Q $19,DX,AX
- MULQ 64(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 216(SP),DX
- IMUL3Q $19,DX,AX
- MULQ 72(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 224(SP),AX
- MULQ 40(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 224(SP),AX
- MULQ 48(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 280(SP),AX
- MULQ 64(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 280(SP),AX
- MULQ 72(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 232(SP),AX
- MULQ 40(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 288(SP),AX
- MULQ 56(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 288(SP),AX
- MULQ 64(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 288(SP),AX
- MULQ 72(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ $REDMASK51,DX
- SHLQ $13,SI,CX
- ANDQ DX,SI
- SHLQ $13,R8,R9
- ANDQ DX,R8
- ADDQ CX,R8
- SHLQ $13,R10,R11
- ANDQ DX,R10
- ADDQ R9,R10
- SHLQ $13,R12,R13
- ANDQ DX,R12
- ADDQ R11,R12
- SHLQ $13,R14,R15
- ANDQ DX,R14
- ADDQ R13,R14
- IMUL3Q $19,R15,CX
- ADDQ CX,SI
- MOVQ SI,CX
- SHRQ $51,CX
- ADDQ R8,CX
- MOVQ CX,R8
- SHRQ $51,CX
- ANDQ DX,SI
- ADDQ R10,CX
- MOVQ CX,R9
- SHRQ $51,CX
- ANDQ DX,R8
- ADDQ R12,CX
- MOVQ CX,AX
- SHRQ $51,CX
- ANDQ DX,R9
- ADDQ R14,CX
- MOVQ CX,R10
- SHRQ $51,CX
- ANDQ DX,AX
- IMUL3Q $19,CX,CX
- ADDQ CX,SI
- ANDQ DX,R10
- MOVQ SI,40(SP)
- MOVQ R8,48(SP)
- MOVQ R9,56(SP)
- MOVQ AX,64(SP)
- MOVQ R10,72(SP)
- MOVQ 264(SP),SI
- IMUL3Q $19,SI,AX
- MOVQ AX,200(SP)
- MULQ 16(SP)
- MOVQ AX,SI
- MOVQ DX,CX
- MOVQ 272(SP),DX
- IMUL3Q $19,DX,AX
- MOVQ AX,208(SP)
- MULQ 8(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 240(SP),AX
- MULQ 0(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 240(SP),AX
- MULQ 8(SP)
- MOVQ AX,R8
- MOVQ DX,R9
- MOVQ 240(SP),AX
- MULQ 16(SP)
- MOVQ AX,R10
- MOVQ DX,R11
- MOVQ 240(SP),AX
- MULQ 24(SP)
- MOVQ AX,R12
- MOVQ DX,R13
- MOVQ 240(SP),AX
- MULQ 32(SP)
- MOVQ AX,R14
- MOVQ DX,R15
- MOVQ 248(SP),AX
- MULQ 0(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 248(SP),AX
- MULQ 8(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 248(SP),AX
- MULQ 16(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 248(SP),AX
- MULQ 24(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 248(SP),DX
- IMUL3Q $19,DX,AX
- MULQ 32(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 256(SP),AX
- MULQ 0(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 256(SP),AX
- MULQ 8(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 256(SP),AX
- MULQ 16(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 256(SP),DX
- IMUL3Q $19,DX,AX
- MULQ 24(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 256(SP),DX
- IMUL3Q $19,DX,AX
- MULQ 32(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 264(SP),AX
- MULQ 0(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 264(SP),AX
- MULQ 8(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 200(SP),AX
- MULQ 24(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 200(SP),AX
- MULQ 32(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 272(SP),AX
- MULQ 0(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 208(SP),AX
- MULQ 16(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 208(SP),AX
- MULQ 24(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 208(SP),AX
- MULQ 32(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ $REDMASK51,DX
- SHLQ $13,SI,CX
- ANDQ DX,SI
- SHLQ $13,R8,R9
- ANDQ DX,R8
- ADDQ CX,R8
- SHLQ $13,R10,R11
- ANDQ DX,R10
- ADDQ R9,R10
- SHLQ $13,R12,R13
- ANDQ DX,R12
- ADDQ R11,R12
- SHLQ $13,R14,R15
- ANDQ DX,R14
- ADDQ R13,R14
- IMUL3Q $19,R15,CX
- ADDQ CX,SI
- MOVQ SI,CX
- SHRQ $51,CX
- ADDQ R8,CX
- MOVQ CX,R8
- SHRQ $51,CX
- ANDQ DX,SI
- ADDQ R10,CX
- MOVQ CX,R9
- SHRQ $51,CX
- ANDQ DX,R8
- ADDQ R12,CX
- MOVQ CX,AX
- SHRQ $51,CX
- ANDQ DX,R9
- ADDQ R14,CX
- MOVQ CX,R10
- SHRQ $51,CX
- ANDQ DX,AX
- IMUL3Q $19,CX,CX
- ADDQ CX,SI
- ANDQ DX,R10
- MOVQ SI,DX
- MOVQ R8,CX
- MOVQ R9,R11
- MOVQ AX,R12
- MOVQ R10,R13
- ADDQ ·_2P0(SB),DX
- ADDQ ·_2P1234(SB),CX
- ADDQ ·_2P1234(SB),R11
- ADDQ ·_2P1234(SB),R12
- ADDQ ·_2P1234(SB),R13
- ADDQ 40(SP),SI
- ADDQ 48(SP),R8
- ADDQ 56(SP),R9
- ADDQ 64(SP),AX
- ADDQ 72(SP),R10
- SUBQ 40(SP),DX
- SUBQ 48(SP),CX
- SUBQ 56(SP),R11
- SUBQ 64(SP),R12
- SUBQ 72(SP),R13
- MOVQ SI,120(DI)
- MOVQ R8,128(DI)
- MOVQ R9,136(DI)
- MOVQ AX,144(DI)
- MOVQ R10,152(DI)
- MOVQ DX,160(DI)
- MOVQ CX,168(DI)
- MOVQ R11,176(DI)
- MOVQ R12,184(DI)
- MOVQ R13,192(DI)
- MOVQ 120(DI),AX
- MULQ 120(DI)
- MOVQ AX,SI
- MOVQ DX,CX
- MOVQ 120(DI),AX
- SHLQ $1,AX
- MULQ 128(DI)
- MOVQ AX,R8
- MOVQ DX,R9
- MOVQ 120(DI),AX
- SHLQ $1,AX
- MULQ 136(DI)
- MOVQ AX,R10
- MOVQ DX,R11
- MOVQ 120(DI),AX
- SHLQ $1,AX
- MULQ 144(DI)
- MOVQ AX,R12
- MOVQ DX,R13
- MOVQ 120(DI),AX
- SHLQ $1,AX
- MULQ 152(DI)
- MOVQ AX,R14
- MOVQ DX,R15
- MOVQ 128(DI),AX
- MULQ 128(DI)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 128(DI),AX
- SHLQ $1,AX
- MULQ 136(DI)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 128(DI),AX
- SHLQ $1,AX
- MULQ 144(DI)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 128(DI),DX
- IMUL3Q $38,DX,AX
- MULQ 152(DI)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 136(DI),AX
- MULQ 136(DI)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 136(DI),DX
- IMUL3Q $38,DX,AX
- MULQ 144(DI)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 136(DI),DX
- IMUL3Q $38,DX,AX
- MULQ 152(DI)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 144(DI),DX
- IMUL3Q $19,DX,AX
- MULQ 144(DI)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 144(DI),DX
- IMUL3Q $38,DX,AX
- MULQ 152(DI)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 152(DI),DX
- IMUL3Q $19,DX,AX
- MULQ 152(DI)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ $REDMASK51,DX
- SHLQ $13,SI,CX
- ANDQ DX,SI
- SHLQ $13,R8,R9
- ANDQ DX,R8
- ADDQ CX,R8
- SHLQ $13,R10,R11
- ANDQ DX,R10
- ADDQ R9,R10
- SHLQ $13,R12,R13
- ANDQ DX,R12
- ADDQ R11,R12
- SHLQ $13,R14,R15
- ANDQ DX,R14
- ADDQ R13,R14
- IMUL3Q $19,R15,CX
- ADDQ CX,SI
- MOVQ SI,CX
- SHRQ $51,CX
- ADDQ R8,CX
- ANDQ DX,SI
- MOVQ CX,R8
- SHRQ $51,CX
- ADDQ R10,CX
- ANDQ DX,R8
- MOVQ CX,R9
- SHRQ $51,CX
- ADDQ R12,CX
- ANDQ DX,R9
- MOVQ CX,AX
- SHRQ $51,CX
- ADDQ R14,CX
- ANDQ DX,AX
- MOVQ CX,R10
- SHRQ $51,CX
- IMUL3Q $19,CX,CX
- ADDQ CX,SI
- ANDQ DX,R10
- MOVQ SI,120(DI)
- MOVQ R8,128(DI)
- MOVQ R9,136(DI)
- MOVQ AX,144(DI)
- MOVQ R10,152(DI)
- MOVQ 160(DI),AX
- MULQ 160(DI)
- MOVQ AX,SI
- MOVQ DX,CX
- MOVQ 160(DI),AX
- SHLQ $1,AX
- MULQ 168(DI)
- MOVQ AX,R8
- MOVQ DX,R9
- MOVQ 160(DI),AX
- SHLQ $1,AX
- MULQ 176(DI)
- MOVQ AX,R10
- MOVQ DX,R11
- MOVQ 160(DI),AX
- SHLQ $1,AX
- MULQ 184(DI)
- MOVQ AX,R12
- MOVQ DX,R13
- MOVQ 160(DI),AX
- SHLQ $1,AX
- MULQ 192(DI)
- MOVQ AX,R14
- MOVQ DX,R15
- MOVQ 168(DI),AX
- MULQ 168(DI)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 168(DI),AX
- SHLQ $1,AX
- MULQ 176(DI)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 168(DI),AX
- SHLQ $1,AX
- MULQ 184(DI)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 168(DI),DX
- IMUL3Q $38,DX,AX
- MULQ 192(DI)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 176(DI),AX
- MULQ 176(DI)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 176(DI),DX
- IMUL3Q $38,DX,AX
- MULQ 184(DI)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 176(DI),DX
- IMUL3Q $38,DX,AX
- MULQ 192(DI)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 184(DI),DX
- IMUL3Q $19,DX,AX
- MULQ 184(DI)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 184(DI),DX
- IMUL3Q $38,DX,AX
- MULQ 192(DI)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 192(DI),DX
- IMUL3Q $19,DX,AX
- MULQ 192(DI)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ $REDMASK51,DX
- SHLQ $13,SI,CX
- ANDQ DX,SI
- SHLQ $13,R8,R9
- ANDQ DX,R8
- ADDQ CX,R8
- SHLQ $13,R10,R11
- ANDQ DX,R10
- ADDQ R9,R10
- SHLQ $13,R12,R13
- ANDQ DX,R12
- ADDQ R11,R12
- SHLQ $13,R14,R15
- ANDQ DX,R14
- ADDQ R13,R14
- IMUL3Q $19,R15,CX
- ADDQ CX,SI
- MOVQ SI,CX
- SHRQ $51,CX
- ADDQ R8,CX
- ANDQ DX,SI
- MOVQ CX,R8
- SHRQ $51,CX
- ADDQ R10,CX
- ANDQ DX,R8
- MOVQ CX,R9
- SHRQ $51,CX
- ADDQ R12,CX
- ANDQ DX,R9
- MOVQ CX,AX
- SHRQ $51,CX
- ADDQ R14,CX
- ANDQ DX,AX
- MOVQ CX,R10
- SHRQ $51,CX
- IMUL3Q $19,CX,CX
- ADDQ CX,SI
- ANDQ DX,R10
- MOVQ SI,160(DI)
- MOVQ R8,168(DI)
- MOVQ R9,176(DI)
- MOVQ AX,184(DI)
- MOVQ R10,192(DI)
- MOVQ 184(DI),SI
- IMUL3Q $19,SI,AX
- MOVQ AX,0(SP)
- MULQ 16(DI)
- MOVQ AX,SI
- MOVQ DX,CX
- MOVQ 192(DI),DX
- IMUL3Q $19,DX,AX
- MOVQ AX,8(SP)
- MULQ 8(DI)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 160(DI),AX
- MULQ 0(DI)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 160(DI),AX
- MULQ 8(DI)
- MOVQ AX,R8
- MOVQ DX,R9
- MOVQ 160(DI),AX
- MULQ 16(DI)
- MOVQ AX,R10
- MOVQ DX,R11
- MOVQ 160(DI),AX
- MULQ 24(DI)
- MOVQ AX,R12
- MOVQ DX,R13
- MOVQ 160(DI),AX
- MULQ 32(DI)
- MOVQ AX,R14
- MOVQ DX,R15
- MOVQ 168(DI),AX
- MULQ 0(DI)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 168(DI),AX
- MULQ 8(DI)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 168(DI),AX
- MULQ 16(DI)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 168(DI),AX
- MULQ 24(DI)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 168(DI),DX
- IMUL3Q $19,DX,AX
- MULQ 32(DI)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 176(DI),AX
- MULQ 0(DI)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 176(DI),AX
- MULQ 8(DI)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 176(DI),AX
- MULQ 16(DI)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 176(DI),DX
- IMUL3Q $19,DX,AX
- MULQ 24(DI)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 176(DI),DX
- IMUL3Q $19,DX,AX
- MULQ 32(DI)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 184(DI),AX
- MULQ 0(DI)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 184(DI),AX
- MULQ 8(DI)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 0(SP),AX
- MULQ 24(DI)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 0(SP),AX
- MULQ 32(DI)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 192(DI),AX
- MULQ 0(DI)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 8(SP),AX
- MULQ 16(DI)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 8(SP),AX
- MULQ 24(DI)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 8(SP),AX
- MULQ 32(DI)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ $REDMASK51,DX
- SHLQ $13,SI,CX
- ANDQ DX,SI
- SHLQ $13,R8,R9
- ANDQ DX,R8
- ADDQ CX,R8
- SHLQ $13,R10,R11
- ANDQ DX,R10
- ADDQ R9,R10
- SHLQ $13,R12,R13
- ANDQ DX,R12
- ADDQ R11,R12
- SHLQ $13,R14,R15
- ANDQ DX,R14
- ADDQ R13,R14
- IMUL3Q $19,R15,CX
- ADDQ CX,SI
- MOVQ SI,CX
- SHRQ $51,CX
- ADDQ R8,CX
- MOVQ CX,R8
- SHRQ $51,CX
- ANDQ DX,SI
- ADDQ R10,CX
- MOVQ CX,R9
- SHRQ $51,CX
- ANDQ DX,R8
- ADDQ R12,CX
- MOVQ CX,AX
- SHRQ $51,CX
- ANDQ DX,R9
- ADDQ R14,CX
- MOVQ CX,R10
- SHRQ $51,CX
- ANDQ DX,AX
- IMUL3Q $19,CX,CX
- ADDQ CX,SI
- ANDQ DX,R10
- MOVQ SI,160(DI)
- MOVQ R8,168(DI)
- MOVQ R9,176(DI)
- MOVQ AX,184(DI)
- MOVQ R10,192(DI)
- MOVQ 144(SP),SI
- IMUL3Q $19,SI,AX
- MOVQ AX,0(SP)
- MULQ 96(SP)
- MOVQ AX,SI
- MOVQ DX,CX
- MOVQ 152(SP),DX
- IMUL3Q $19,DX,AX
- MOVQ AX,8(SP)
- MULQ 88(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 120(SP),AX
- MULQ 80(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 120(SP),AX
- MULQ 88(SP)
- MOVQ AX,R8
- MOVQ DX,R9
- MOVQ 120(SP),AX
- MULQ 96(SP)
- MOVQ AX,R10
- MOVQ DX,R11
- MOVQ 120(SP),AX
- MULQ 104(SP)
- MOVQ AX,R12
- MOVQ DX,R13
- MOVQ 120(SP),AX
- MULQ 112(SP)
- MOVQ AX,R14
- MOVQ DX,R15
- MOVQ 128(SP),AX
- MULQ 80(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 128(SP),AX
- MULQ 88(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 128(SP),AX
- MULQ 96(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 128(SP),AX
- MULQ 104(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 128(SP),DX
- IMUL3Q $19,DX,AX
- MULQ 112(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 136(SP),AX
- MULQ 80(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 136(SP),AX
- MULQ 88(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 136(SP),AX
- MULQ 96(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 136(SP),DX
- IMUL3Q $19,DX,AX
- MULQ 104(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 136(SP),DX
- IMUL3Q $19,DX,AX
- MULQ 112(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 144(SP),AX
- MULQ 80(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 144(SP),AX
- MULQ 88(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 0(SP),AX
- MULQ 104(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 0(SP),AX
- MULQ 112(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 152(SP),AX
- MULQ 80(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 8(SP),AX
- MULQ 96(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 8(SP),AX
- MULQ 104(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 8(SP),AX
- MULQ 112(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ $REDMASK51,DX
- SHLQ $13,SI,CX
- ANDQ DX,SI
- SHLQ $13,R8,R9
- ANDQ DX,R8
- ADDQ CX,R8
- SHLQ $13,R10,R11
- ANDQ DX,R10
- ADDQ R9,R10
- SHLQ $13,R12,R13
- ANDQ DX,R12
- ADDQ R11,R12
- SHLQ $13,R14,R15
- ANDQ DX,R14
- ADDQ R13,R14
- IMUL3Q $19,R15,CX
- ADDQ CX,SI
- MOVQ SI,CX
- SHRQ $51,CX
- ADDQ R8,CX
- MOVQ CX,R8
- SHRQ $51,CX
- ANDQ DX,SI
- ADDQ R10,CX
- MOVQ CX,R9
- SHRQ $51,CX
- ANDQ DX,R8
- ADDQ R12,CX
- MOVQ CX,AX
- SHRQ $51,CX
- ANDQ DX,R9
- ADDQ R14,CX
- MOVQ CX,R10
- SHRQ $51,CX
- ANDQ DX,AX
- IMUL3Q $19,CX,CX
- ADDQ CX,SI
- ANDQ DX,R10
- MOVQ SI,40(DI)
- MOVQ R8,48(DI)
- MOVQ R9,56(DI)
- MOVQ AX,64(DI)
- MOVQ R10,72(DI)
- MOVQ 160(SP),AX
- MULQ ·_121666_213(SB)
- SHRQ $13,AX
- MOVQ AX,SI
- MOVQ DX,CX
- MOVQ 168(SP),AX
- MULQ ·_121666_213(SB)
- SHRQ $13,AX
- ADDQ AX,CX
- MOVQ DX,R8
- MOVQ 176(SP),AX
- MULQ ·_121666_213(SB)
- SHRQ $13,AX
- ADDQ AX,R8
- MOVQ DX,R9
- MOVQ 184(SP),AX
- MULQ ·_121666_213(SB)
- SHRQ $13,AX
- ADDQ AX,R9
- MOVQ DX,R10
- MOVQ 192(SP),AX
- MULQ ·_121666_213(SB)
- SHRQ $13,AX
- ADDQ AX,R10
- IMUL3Q $19,DX,DX
- ADDQ DX,SI
- ADDQ 80(SP),SI
- ADDQ 88(SP),CX
- ADDQ 96(SP),R8
- ADDQ 104(SP),R9
- ADDQ 112(SP),R10
- MOVQ SI,80(DI)
- MOVQ CX,88(DI)
- MOVQ R8,96(DI)
- MOVQ R9,104(DI)
- MOVQ R10,112(DI)
- MOVQ 104(DI),SI
- IMUL3Q $19,SI,AX
- MOVQ AX,0(SP)
- MULQ 176(SP)
- MOVQ AX,SI
- MOVQ DX,CX
- MOVQ 112(DI),DX
- IMUL3Q $19,DX,AX
- MOVQ AX,8(SP)
- MULQ 168(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 80(DI),AX
- MULQ 160(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 80(DI),AX
- MULQ 168(SP)
- MOVQ AX,R8
- MOVQ DX,R9
- MOVQ 80(DI),AX
- MULQ 176(SP)
- MOVQ AX,R10
- MOVQ DX,R11
- MOVQ 80(DI),AX
- MULQ 184(SP)
- MOVQ AX,R12
- MOVQ DX,R13
- MOVQ 80(DI),AX
- MULQ 192(SP)
- MOVQ AX,R14
- MOVQ DX,R15
- MOVQ 88(DI),AX
- MULQ 160(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 88(DI),AX
- MULQ 168(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 88(DI),AX
- MULQ 176(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 88(DI),AX
- MULQ 184(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 88(DI),DX
- IMUL3Q $19,DX,AX
- MULQ 192(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 96(DI),AX
- MULQ 160(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 96(DI),AX
- MULQ 168(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 96(DI),AX
- MULQ 176(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 96(DI),DX
- IMUL3Q $19,DX,AX
- MULQ 184(SP)
- ADDQ AX,SI
- ADCQ DX,CX
- MOVQ 96(DI),DX
- IMUL3Q $19,DX,AX
- MULQ 192(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 104(DI),AX
- MULQ 160(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 104(DI),AX
- MULQ 168(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 0(SP),AX
- MULQ 184(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 0(SP),AX
- MULQ 192(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 112(DI),AX
- MULQ 160(SP)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 8(SP),AX
- MULQ 176(SP)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 8(SP),AX
- MULQ 184(SP)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 8(SP),AX
- MULQ 192(SP)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ $REDMASK51,DX
- SHLQ $13,SI,CX
- ANDQ DX,SI
- SHLQ $13,R8,R9
- ANDQ DX,R8
- ADDQ CX,R8
- SHLQ $13,R10,R11
- ANDQ DX,R10
- ADDQ R9,R10
- SHLQ $13,R12,R13
- ANDQ DX,R12
- ADDQ R11,R12
- SHLQ $13,R14,R15
- ANDQ DX,R14
- ADDQ R13,R14
- IMUL3Q $19,R15,CX
- ADDQ CX,SI
- MOVQ SI,CX
- SHRQ $51,CX
- ADDQ R8,CX
- MOVQ CX,R8
- SHRQ $51,CX
- ANDQ DX,SI
- ADDQ R10,CX
- MOVQ CX,R9
- SHRQ $51,CX
- ANDQ DX,R8
- ADDQ R12,CX
- MOVQ CX,AX
- SHRQ $51,CX
- ANDQ DX,R9
- ADDQ R14,CX
- MOVQ CX,R10
- SHRQ $51,CX
- ANDQ DX,AX
- IMUL3Q $19,CX,CX
- ADDQ CX,SI
- ANDQ DX,R10
- MOVQ SI,80(DI)
- MOVQ R8,88(DI)
- MOVQ R9,96(DI)
- MOVQ AX,104(DI)
- MOVQ R10,112(DI)
- RET
-
-// func cswap(inout *[4][5]uint64, v uint64)
-TEXT ·cswap(SB),7,$0
- MOVQ inout+0(FP),DI
- MOVQ v+8(FP),SI
-
- SUBQ $1, SI
- NOTQ SI
- MOVQ SI, X15
- PSHUFD $0x44, X15, X15
-
- MOVOU 0(DI), X0
- MOVOU 16(DI), X2
- MOVOU 32(DI), X4
- MOVOU 48(DI), X6
- MOVOU 64(DI), X8
- MOVOU 80(DI), X1
- MOVOU 96(DI), X3
- MOVOU 112(DI), X5
- MOVOU 128(DI), X7
- MOVOU 144(DI), X9
-
- MOVO X1, X10
- MOVO X3, X11
- MOVO X5, X12
- MOVO X7, X13
- MOVO X9, X14
-
- PXOR X0, X10
- PXOR X2, X11
- PXOR X4, X12
- PXOR X6, X13
- PXOR X8, X14
- PAND X15, X10
- PAND X15, X11
- PAND X15, X12
- PAND X15, X13
- PAND X15, X14
- PXOR X10, X0
- PXOR X10, X1
- PXOR X11, X2
- PXOR X11, X3
- PXOR X12, X4
- PXOR X12, X5
- PXOR X13, X6
- PXOR X13, X7
- PXOR X14, X8
- PXOR X14, X9
-
- MOVOU X0, 0(DI)
- MOVOU X2, 16(DI)
- MOVOU X4, 32(DI)
- MOVOU X6, 48(DI)
- MOVOU X8, 64(DI)
- MOVOU X1, 80(DI)
- MOVOU X3, 96(DI)
- MOVOU X5, 112(DI)
- MOVOU X7, 128(DI)
- MOVOU X9, 144(DI)
- RET
-
-// func mul(dest, a, b *[5]uint64)
-TEXT ·mul(SB),0,$16-24
- MOVQ dest+0(FP), DI
- MOVQ a+8(FP), SI
- MOVQ b+16(FP), DX
-
- MOVQ DX,CX
- MOVQ 24(SI),DX
- IMUL3Q $19,DX,AX
- MOVQ AX,0(SP)
- MULQ 16(CX)
- MOVQ AX,R8
- MOVQ DX,R9
- MOVQ 32(SI),DX
- IMUL3Q $19,DX,AX
- MOVQ AX,8(SP)
- MULQ 8(CX)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 0(SI),AX
- MULQ 0(CX)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 0(SI),AX
- MULQ 8(CX)
- MOVQ AX,R10
- MOVQ DX,R11
- MOVQ 0(SI),AX
- MULQ 16(CX)
- MOVQ AX,R12
- MOVQ DX,R13
- MOVQ 0(SI),AX
- MULQ 24(CX)
- MOVQ AX,R14
- MOVQ DX,R15
- MOVQ 0(SI),AX
- MULQ 32(CX)
- MOVQ AX,BX
- MOVQ DX,BP
- MOVQ 8(SI),AX
- MULQ 0(CX)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 8(SI),AX
- MULQ 8(CX)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 8(SI),AX
- MULQ 16(CX)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 8(SI),AX
- MULQ 24(CX)
- ADDQ AX,BX
- ADCQ DX,BP
- MOVQ 8(SI),DX
- IMUL3Q $19,DX,AX
- MULQ 32(CX)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 16(SI),AX
- MULQ 0(CX)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 16(SI),AX
- MULQ 8(CX)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 16(SI),AX
- MULQ 16(CX)
- ADDQ AX,BX
- ADCQ DX,BP
- MOVQ 16(SI),DX
- IMUL3Q $19,DX,AX
- MULQ 24(CX)
- ADDQ AX,R8
- ADCQ DX,R9
- MOVQ 16(SI),DX
- IMUL3Q $19,DX,AX
- MULQ 32(CX)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 24(SI),AX
- MULQ 0(CX)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ 24(SI),AX
- MULQ 8(CX)
- ADDQ AX,BX
- ADCQ DX,BP
- MOVQ 0(SP),AX
- MULQ 24(CX)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 0(SP),AX
- MULQ 32(CX)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 32(SI),AX
- MULQ 0(CX)
- ADDQ AX,BX
- ADCQ DX,BP
- MOVQ 8(SP),AX
- MULQ 16(CX)
- ADDQ AX,R10
- ADCQ DX,R11
- MOVQ 8(SP),AX
- MULQ 24(CX)
- ADDQ AX,R12
- ADCQ DX,R13
- MOVQ 8(SP),AX
- MULQ 32(CX)
- ADDQ AX,R14
- ADCQ DX,R15
- MOVQ $REDMASK51,SI
- SHLQ $13,R8,R9
- ANDQ SI,R8
- SHLQ $13,R10,R11
- ANDQ SI,R10
- ADDQ R9,R10
- SHLQ $13,R12,R13
- ANDQ SI,R12
- ADDQ R11,R12
- SHLQ $13,R14,R15
- ANDQ SI,R14
- ADDQ R13,R14
- SHLQ $13,BX,BP
- ANDQ SI,BX
- ADDQ R15,BX
- IMUL3Q $19,BP,DX
- ADDQ DX,R8
- MOVQ R8,DX
- SHRQ $51,DX
- ADDQ R10,DX
- MOVQ DX,CX
- SHRQ $51,DX
- ANDQ SI,R8
- ADDQ R12,DX
- MOVQ DX,R9
- SHRQ $51,DX
- ANDQ SI,CX
- ADDQ R14,DX
- MOVQ DX,AX
- SHRQ $51,DX
- ANDQ SI,R9
- ADDQ BX,DX
- MOVQ DX,R10
- SHRQ $51,DX
- ANDQ SI,AX
- IMUL3Q $19,DX,DX
- ADDQ DX,R8
- ANDQ SI,R10
- MOVQ R8,0(DI)
- MOVQ CX,8(DI)
- MOVQ R9,16(DI)
- MOVQ AX,24(DI)
- MOVQ R10,32(DI)
- RET
-
-// func square(out, in *[5]uint64)
-TEXT ·square(SB),7,$0-16
- MOVQ out+0(FP), DI
- MOVQ in+8(FP), SI
-
- MOVQ 0(SI),AX
- MULQ 0(SI)
- MOVQ AX,CX
- MOVQ DX,R8
- MOVQ 0(SI),AX
- SHLQ $1,AX
- MULQ 8(SI)
- MOVQ AX,R9
- MOVQ DX,R10
- MOVQ 0(SI),AX
- SHLQ $1,AX
- MULQ 16(SI)
- MOVQ AX,R11
- MOVQ DX,R12
- MOVQ 0(SI),AX
- SHLQ $1,AX
- MULQ 24(SI)
- MOVQ AX,R13
- MOVQ DX,R14
- MOVQ 0(SI),AX
- SHLQ $1,AX
- MULQ 32(SI)
- MOVQ AX,R15
- MOVQ DX,BX
- MOVQ 8(SI),AX
- MULQ 8(SI)
- ADDQ AX,R11
- ADCQ DX,R12
- MOVQ 8(SI),AX
- SHLQ $1,AX
- MULQ 16(SI)
- ADDQ AX,R13
- ADCQ DX,R14
- MOVQ 8(SI),AX
- SHLQ $1,AX
- MULQ 24(SI)
- ADDQ AX,R15
- ADCQ DX,BX
- MOVQ 8(SI),DX
- IMUL3Q $38,DX,AX
- MULQ 32(SI)
- ADDQ AX,CX
- ADCQ DX,R8
- MOVQ 16(SI),AX
- MULQ 16(SI)
- ADDQ AX,R15
- ADCQ DX,BX
- MOVQ 16(SI),DX
- IMUL3Q $38,DX,AX
- MULQ 24(SI)
- ADDQ AX,CX
- ADCQ DX,R8
- MOVQ 16(SI),DX
- IMUL3Q $38,DX,AX
- MULQ 32(SI)
- ADDQ AX,R9
- ADCQ DX,R10
- MOVQ 24(SI),DX
- IMUL3Q $19,DX,AX
- MULQ 24(SI)
- ADDQ AX,R9
- ADCQ DX,R10
- MOVQ 24(SI),DX
- IMUL3Q $38,DX,AX
- MULQ 32(SI)
- ADDQ AX,R11
- ADCQ DX,R12
- MOVQ 32(SI),DX
- IMUL3Q $19,DX,AX
- MULQ 32(SI)
- ADDQ AX,R13
- ADCQ DX,R14
- MOVQ $REDMASK51,SI
- SHLQ $13,CX,R8
- ANDQ SI,CX
- SHLQ $13,R9,R10
- ANDQ SI,R9
- ADDQ R8,R9
- SHLQ $13,R11,R12
- ANDQ SI,R11
- ADDQ R10,R11
- SHLQ $13,R13,R14
- ANDQ SI,R13
- ADDQ R12,R13
- SHLQ $13,R15,BX
- ANDQ SI,R15
- ADDQ R14,R15
- IMUL3Q $19,BX,DX
- ADDQ DX,CX
- MOVQ CX,DX
- SHRQ $51,DX
- ADDQ R9,DX
- ANDQ SI,CX
- MOVQ DX,R8
- SHRQ $51,DX
- ADDQ R11,DX
- ANDQ SI,R8
- MOVQ DX,R9
- SHRQ $51,DX
- ADDQ R13,DX
- ANDQ SI,R9
- MOVQ DX,AX
- SHRQ $51,DX
- ADDQ R15,DX
- ANDQ SI,AX
- MOVQ DX,R10
- SHRQ $51,DX
- IMUL3Q $19,DX,DX
- ADDQ DX,CX
- ANDQ SI,R10
- MOVQ CX,0(DI)
- MOVQ R8,8(DI)
- MOVQ R9,16(DI)
- MOVQ AX,24(DI)
- MOVQ R10,32(DI)
- RET
+++ /dev/null
-// Copyright 2013 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 curve25519
-
-import "encoding/binary"
-
-// This code is a port of the public domain, "ref10" implementation of
-// curve25519 from SUPERCOP 20130419 by D. J. Bernstein.
-
-// fieldElement represents an element of the field GF(2^255 - 19). An element
-// t, entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
-// t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
-// context.
-type fieldElement [10]int32
-
-func feZero(fe *fieldElement) {
- for i := range fe {
- fe[i] = 0
- }
-}
-
-func feOne(fe *fieldElement) {
- feZero(fe)
- fe[0] = 1
-}
-
-func feAdd(dst, a, b *fieldElement) {
- for i := range dst {
- dst[i] = a[i] + b[i]
- }
-}
-
-func feSub(dst, a, b *fieldElement) {
- for i := range dst {
- dst[i] = a[i] - b[i]
- }
-}
-
-func feCopy(dst, src *fieldElement) {
- for i := range dst {
- dst[i] = src[i]
- }
-}
-
-// feCSwap replaces (f,g) with (g,f) if b == 1; replaces (f,g) with (f,g) if b == 0.
-//
-// Preconditions: b in {0,1}.
-func feCSwap(f, g *fieldElement, b int32) {
- b = -b
- for i := range f {
- t := b & (f[i] ^ g[i])
- f[i] ^= t
- g[i] ^= t
- }
-}
-
-// load3 reads a 24-bit, little-endian value from in.
-func load3(in []byte) int64 {
- var r int64
- r = int64(in[0])
- r |= int64(in[1]) << 8
- r |= int64(in[2]) << 16
- return r
-}
-
-// load4 reads a 32-bit, little-endian value from in.
-func load4(in []byte) int64 {
- return int64(binary.LittleEndian.Uint32(in))
-}
-
-func feFromBytes(dst *fieldElement, src *[32]byte) {
- h0 := load4(src[:])
- h1 := load3(src[4:]) << 6
- h2 := load3(src[7:]) << 5
- h3 := load3(src[10:]) << 3
- h4 := load3(src[13:]) << 2
- h5 := load4(src[16:])
- h6 := load3(src[20:]) << 7
- h7 := load3(src[23:]) << 5
- h8 := load3(src[26:]) << 4
- h9 := (load3(src[29:]) & 0x7fffff) << 2
-
- var carry [10]int64
- carry[9] = (h9 + 1<<24) >> 25
- h0 += carry[9] * 19
- h9 -= carry[9] << 25
- carry[1] = (h1 + 1<<24) >> 25
- h2 += carry[1]
- h1 -= carry[1] << 25
- carry[3] = (h3 + 1<<24) >> 25
- h4 += carry[3]
- h3 -= carry[3] << 25
- carry[5] = (h5 + 1<<24) >> 25
- h6 += carry[5]
- h5 -= carry[5] << 25
- carry[7] = (h7 + 1<<24) >> 25
- h8 += carry[7]
- h7 -= carry[7] << 25
-
- carry[0] = (h0 + 1<<25) >> 26
- h1 += carry[0]
- h0 -= carry[0] << 26
- carry[2] = (h2 + 1<<25) >> 26
- h3 += carry[2]
- h2 -= carry[2] << 26
- carry[4] = (h4 + 1<<25) >> 26
- h5 += carry[4]
- h4 -= carry[4] << 26
- carry[6] = (h6 + 1<<25) >> 26
- h7 += carry[6]
- h6 -= carry[6] << 26
- carry[8] = (h8 + 1<<25) >> 26
- h9 += carry[8]
- h8 -= carry[8] << 26
-
- dst[0] = int32(h0)
- dst[1] = int32(h1)
- dst[2] = int32(h2)
- dst[3] = int32(h3)
- dst[4] = int32(h4)
- dst[5] = int32(h5)
- dst[6] = int32(h6)
- dst[7] = int32(h7)
- dst[8] = int32(h8)
- dst[9] = int32(h9)
-}
-
-// feToBytes marshals h to s.
-// Preconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-//
-// Write p=2^255-19; q=floor(h/p).
-// Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
-//
-// Proof:
-// Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
-// Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4.
-//
-// Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
-// Then 0<y<1.
-//
-// Write r=h-pq.
-// Have 0<=r<=p-1=2^255-20.
-// Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
-//
-// Write x=r+19(2^-255)r+y.
-// Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
-//
-// Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
-// so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
-func feToBytes(s *[32]byte, h *fieldElement) {
- var carry [10]int32
-
- q := (19*h[9] + (1 << 24)) >> 25
- q = (h[0] + q) >> 26
- q = (h[1] + q) >> 25
- q = (h[2] + q) >> 26
- q = (h[3] + q) >> 25
- q = (h[4] + q) >> 26
- q = (h[5] + q) >> 25
- q = (h[6] + q) >> 26
- q = (h[7] + q) >> 25
- q = (h[8] + q) >> 26
- q = (h[9] + q) >> 25
-
- // Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20.
- h[0] += 19 * q
- // Goal: Output h-2^255 q, which is between 0 and 2^255-20.
-
- carry[0] = h[0] >> 26
- h[1] += carry[0]
- h[0] -= carry[0] << 26
- carry[1] = h[1] >> 25
- h[2] += carry[1]
- h[1] -= carry[1] << 25
- carry[2] = h[2] >> 26
- h[3] += carry[2]
- h[2] -= carry[2] << 26
- carry[3] = h[3] >> 25
- h[4] += carry[3]
- h[3] -= carry[3] << 25
- carry[4] = h[4] >> 26
- h[5] += carry[4]
- h[4] -= carry[4] << 26
- carry[5] = h[5] >> 25
- h[6] += carry[5]
- h[5] -= carry[5] << 25
- carry[6] = h[6] >> 26
- h[7] += carry[6]
- h[6] -= carry[6] << 26
- carry[7] = h[7] >> 25
- h[8] += carry[7]
- h[7] -= carry[7] << 25
- carry[8] = h[8] >> 26
- h[9] += carry[8]
- h[8] -= carry[8] << 26
- carry[9] = h[9] >> 25
- h[9] -= carry[9] << 25
- // h10 = carry9
-
- // Goal: Output h[0]+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
- // Have h[0]+...+2^230 h[9] between 0 and 2^255-1;
- // evidently 2^255 h10-2^255 q = 0.
- // Goal: Output h[0]+...+2^230 h[9].
-
- s[0] = byte(h[0] >> 0)
- s[1] = byte(h[0] >> 8)
- s[2] = byte(h[0] >> 16)
- s[3] = byte((h[0] >> 24) | (h[1] << 2))
- s[4] = byte(h[1] >> 6)
- s[5] = byte(h[1] >> 14)
- s[6] = byte((h[1] >> 22) | (h[2] << 3))
- s[7] = byte(h[2] >> 5)
- s[8] = byte(h[2] >> 13)
- s[9] = byte((h[2] >> 21) | (h[3] << 5))
- s[10] = byte(h[3] >> 3)
- s[11] = byte(h[3] >> 11)
- s[12] = byte((h[3] >> 19) | (h[4] << 6))
- s[13] = byte(h[4] >> 2)
- s[14] = byte(h[4] >> 10)
- s[15] = byte(h[4] >> 18)
- s[16] = byte(h[5] >> 0)
- s[17] = byte(h[5] >> 8)
- s[18] = byte(h[5] >> 16)
- s[19] = byte((h[5] >> 24) | (h[6] << 1))
- s[20] = byte(h[6] >> 7)
- s[21] = byte(h[6] >> 15)
- s[22] = byte((h[6] >> 23) | (h[7] << 3))
- s[23] = byte(h[7] >> 5)
- s[24] = byte(h[7] >> 13)
- s[25] = byte((h[7] >> 21) | (h[8] << 4))
- s[26] = byte(h[8] >> 4)
- s[27] = byte(h[8] >> 12)
- s[28] = byte((h[8] >> 20) | (h[9] << 6))
- s[29] = byte(h[9] >> 2)
- s[30] = byte(h[9] >> 10)
- s[31] = byte(h[9] >> 18)
-}
-
-// feMul calculates h = f * g
-// Can overlap h with f or g.
-//
-// Preconditions:
-// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-// |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//
-// Postconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-//
-// Notes on implementation strategy:
-//
-// Using schoolbook multiplication.
-// Karatsuba would save a little in some cost models.
-//
-// Most multiplications by 2 and 19 are 32-bit precomputations;
-// cheaper than 64-bit postcomputations.
-//
-// There is one remaining multiplication by 19 in the carry chain;
-// one *19 precomputation can be merged into this,
-// but the resulting data flow is considerably less clean.
-//
-// There are 12 carries below.
-// 10 of them are 2-way parallelizable and vectorizable.
-// Can get away with 11 carries, but then data flow is much deeper.
-//
-// With tighter constraints on inputs can squeeze carries into int32.
-func feMul(h, f, g *fieldElement) {
- f0 := f[0]
- f1 := f[1]
- f2 := f[2]
- f3 := f[3]
- f4 := f[4]
- f5 := f[5]
- f6 := f[6]
- f7 := f[7]
- f8 := f[8]
- f9 := f[9]
- g0 := g[0]
- g1 := g[1]
- g2 := g[2]
- g3 := g[3]
- g4 := g[4]
- g5 := g[5]
- g6 := g[6]
- g7 := g[7]
- g8 := g[8]
- g9 := g[9]
- g1_19 := 19 * g1 // 1.4*2^29
- g2_19 := 19 * g2 // 1.4*2^30; still ok
- g3_19 := 19 * g3
- g4_19 := 19 * g4
- g5_19 := 19 * g5
- g6_19 := 19 * g6
- g7_19 := 19 * g7
- g8_19 := 19 * g8
- g9_19 := 19 * g9
- f1_2 := 2 * f1
- f3_2 := 2 * f3
- f5_2 := 2 * f5
- f7_2 := 2 * f7
- f9_2 := 2 * f9
- f0g0 := int64(f0) * int64(g0)
- f0g1 := int64(f0) * int64(g1)
- f0g2 := int64(f0) * int64(g2)
- f0g3 := int64(f0) * int64(g3)
- f0g4 := int64(f0) * int64(g4)
- f0g5 := int64(f0) * int64(g5)
- f0g6 := int64(f0) * int64(g6)
- f0g7 := int64(f0) * int64(g7)
- f0g8 := int64(f0) * int64(g8)
- f0g9 := int64(f0) * int64(g9)
- f1g0 := int64(f1) * int64(g0)
- f1g1_2 := int64(f1_2) * int64(g1)
- f1g2 := int64(f1) * int64(g2)
- f1g3_2 := int64(f1_2) * int64(g3)
- f1g4 := int64(f1) * int64(g4)
- f1g5_2 := int64(f1_2) * int64(g5)
- f1g6 := int64(f1) * int64(g6)
- f1g7_2 := int64(f1_2) * int64(g7)
- f1g8 := int64(f1) * int64(g8)
- f1g9_38 := int64(f1_2) * int64(g9_19)
- f2g0 := int64(f2) * int64(g0)
- f2g1 := int64(f2) * int64(g1)
- f2g2 := int64(f2) * int64(g2)
- f2g3 := int64(f2) * int64(g3)
- f2g4 := int64(f2) * int64(g4)
- f2g5 := int64(f2) * int64(g5)
- f2g6 := int64(f2) * int64(g6)
- f2g7 := int64(f2) * int64(g7)
- f2g8_19 := int64(f2) * int64(g8_19)
- f2g9_19 := int64(f2) * int64(g9_19)
- f3g0 := int64(f3) * int64(g0)
- f3g1_2 := int64(f3_2) * int64(g1)
- f3g2 := int64(f3) * int64(g2)
- f3g3_2 := int64(f3_2) * int64(g3)
- f3g4 := int64(f3) * int64(g4)
- f3g5_2 := int64(f3_2) * int64(g5)
- f3g6 := int64(f3) * int64(g6)
- f3g7_38 := int64(f3_2) * int64(g7_19)
- f3g8_19 := int64(f3) * int64(g8_19)
- f3g9_38 := int64(f3_2) * int64(g9_19)
- f4g0 := int64(f4) * int64(g0)
- f4g1 := int64(f4) * int64(g1)
- f4g2 := int64(f4) * int64(g2)
- f4g3 := int64(f4) * int64(g3)
- f4g4 := int64(f4) * int64(g4)
- f4g5 := int64(f4) * int64(g5)
- f4g6_19 := int64(f4) * int64(g6_19)
- f4g7_19 := int64(f4) * int64(g7_19)
- f4g8_19 := int64(f4) * int64(g8_19)
- f4g9_19 := int64(f4) * int64(g9_19)
- f5g0 := int64(f5) * int64(g0)
- f5g1_2 := int64(f5_2) * int64(g1)
- f5g2 := int64(f5) * int64(g2)
- f5g3_2 := int64(f5_2) * int64(g3)
- f5g4 := int64(f5) * int64(g4)
- f5g5_38 := int64(f5_2) * int64(g5_19)
- f5g6_19 := int64(f5) * int64(g6_19)
- f5g7_38 := int64(f5_2) * int64(g7_19)
- f5g8_19 := int64(f5) * int64(g8_19)
- f5g9_38 := int64(f5_2) * int64(g9_19)
- f6g0 := int64(f6) * int64(g0)
- f6g1 := int64(f6) * int64(g1)
- f6g2 := int64(f6) * int64(g2)
- f6g3 := int64(f6) * int64(g3)
- f6g4_19 := int64(f6) * int64(g4_19)
- f6g5_19 := int64(f6) * int64(g5_19)
- f6g6_19 := int64(f6) * int64(g6_19)
- f6g7_19 := int64(f6) * int64(g7_19)
- f6g8_19 := int64(f6) * int64(g8_19)
- f6g9_19 := int64(f6) * int64(g9_19)
- f7g0 := int64(f7) * int64(g0)
- f7g1_2 := int64(f7_2) * int64(g1)
- f7g2 := int64(f7) * int64(g2)
- f7g3_38 := int64(f7_2) * int64(g3_19)
- f7g4_19 := int64(f7) * int64(g4_19)
- f7g5_38 := int64(f7_2) * int64(g5_19)
- f7g6_19 := int64(f7) * int64(g6_19)
- f7g7_38 := int64(f7_2) * int64(g7_19)
- f7g8_19 := int64(f7) * int64(g8_19)
- f7g9_38 := int64(f7_2) * int64(g9_19)
- f8g0 := int64(f8) * int64(g0)
- f8g1 := int64(f8) * int64(g1)
- f8g2_19 := int64(f8) * int64(g2_19)
- f8g3_19 := int64(f8) * int64(g3_19)
- f8g4_19 := int64(f8) * int64(g4_19)
- f8g5_19 := int64(f8) * int64(g5_19)
- f8g6_19 := int64(f8) * int64(g6_19)
- f8g7_19 := int64(f8) * int64(g7_19)
- f8g8_19 := int64(f8) * int64(g8_19)
- f8g9_19 := int64(f8) * int64(g9_19)
- f9g0 := int64(f9) * int64(g0)
- f9g1_38 := int64(f9_2) * int64(g1_19)
- f9g2_19 := int64(f9) * int64(g2_19)
- f9g3_38 := int64(f9_2) * int64(g3_19)
- f9g4_19 := int64(f9) * int64(g4_19)
- f9g5_38 := int64(f9_2) * int64(g5_19)
- f9g6_19 := int64(f9) * int64(g6_19)
- f9g7_38 := int64(f9_2) * int64(g7_19)
- f9g8_19 := int64(f9) * int64(g8_19)
- f9g9_38 := int64(f9_2) * int64(g9_19)
- h0 := f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38
- h1 := f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19
- h2 := f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38
- h3 := f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19
- h4 := f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38
- h5 := f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19
- h6 := f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38
- h7 := f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19
- h8 := f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38
- h9 := f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0
- var carry [10]int64
-
- // |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38))
- // i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8
- // |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19))
- // i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9
-
- carry[0] = (h0 + (1 << 25)) >> 26
- h1 += carry[0]
- h0 -= carry[0] << 26
- carry[4] = (h4 + (1 << 25)) >> 26
- h5 += carry[4]
- h4 -= carry[4] << 26
- // |h0| <= 2^25
- // |h4| <= 2^25
- // |h1| <= 1.51*2^58
- // |h5| <= 1.51*2^58
-
- carry[1] = (h1 + (1 << 24)) >> 25
- h2 += carry[1]
- h1 -= carry[1] << 25
- carry[5] = (h5 + (1 << 24)) >> 25
- h6 += carry[5]
- h5 -= carry[5] << 25
- // |h1| <= 2^24; from now on fits into int32
- // |h5| <= 2^24; from now on fits into int32
- // |h2| <= 1.21*2^59
- // |h6| <= 1.21*2^59
-
- carry[2] = (h2 + (1 << 25)) >> 26
- h3 += carry[2]
- h2 -= carry[2] << 26
- carry[6] = (h6 + (1 << 25)) >> 26
- h7 += carry[6]
- h6 -= carry[6] << 26
- // |h2| <= 2^25; from now on fits into int32 unchanged
- // |h6| <= 2^25; from now on fits into int32 unchanged
- // |h3| <= 1.51*2^58
- // |h7| <= 1.51*2^58
-
- carry[3] = (h3 + (1 << 24)) >> 25
- h4 += carry[3]
- h3 -= carry[3] << 25
- carry[7] = (h7 + (1 << 24)) >> 25
- h8 += carry[7]
- h7 -= carry[7] << 25
- // |h3| <= 2^24; from now on fits into int32 unchanged
- // |h7| <= 2^24; from now on fits into int32 unchanged
- // |h4| <= 1.52*2^33
- // |h8| <= 1.52*2^33
-
- carry[4] = (h4 + (1 << 25)) >> 26
- h5 += carry[4]
- h4 -= carry[4] << 26
- carry[8] = (h8 + (1 << 25)) >> 26
- h9 += carry[8]
- h8 -= carry[8] << 26
- // |h4| <= 2^25; from now on fits into int32 unchanged
- // |h8| <= 2^25; from now on fits into int32 unchanged
- // |h5| <= 1.01*2^24
- // |h9| <= 1.51*2^58
-
- carry[9] = (h9 + (1 << 24)) >> 25
- h0 += carry[9] * 19
- h9 -= carry[9] << 25
- // |h9| <= 2^24; from now on fits into int32 unchanged
- // |h0| <= 1.8*2^37
-
- carry[0] = (h0 + (1 << 25)) >> 26
- h1 += carry[0]
- h0 -= carry[0] << 26
- // |h0| <= 2^25; from now on fits into int32 unchanged
- // |h1| <= 1.01*2^24
-
- h[0] = int32(h0)
- h[1] = int32(h1)
- h[2] = int32(h2)
- h[3] = int32(h3)
- h[4] = int32(h4)
- h[5] = int32(h5)
- h[6] = int32(h6)
- h[7] = int32(h7)
- h[8] = int32(h8)
- h[9] = int32(h9)
-}
-
-// feSquare calculates h = f*f. Can overlap h with f.
-//
-// Preconditions:
-// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//
-// Postconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-func feSquare(h, f *fieldElement) {
- f0 := f[0]
- f1 := f[1]
- f2 := f[2]
- f3 := f[3]
- f4 := f[4]
- f5 := f[5]
- f6 := f[6]
- f7 := f[7]
- f8 := f[8]
- f9 := f[9]
- f0_2 := 2 * f0
- f1_2 := 2 * f1
- f2_2 := 2 * f2
- f3_2 := 2 * f3
- f4_2 := 2 * f4
- f5_2 := 2 * f5
- f6_2 := 2 * f6
- f7_2 := 2 * f7
- f5_38 := 38 * f5 // 1.31*2^30
- f6_19 := 19 * f6 // 1.31*2^30
- f7_38 := 38 * f7 // 1.31*2^30
- f8_19 := 19 * f8 // 1.31*2^30
- f9_38 := 38 * f9 // 1.31*2^30
- f0f0 := int64(f0) * int64(f0)
- f0f1_2 := int64(f0_2) * int64(f1)
- f0f2_2 := int64(f0_2) * int64(f2)
- f0f3_2 := int64(f0_2) * int64(f3)
- f0f4_2 := int64(f0_2) * int64(f4)
- f0f5_2 := int64(f0_2) * int64(f5)
- f0f6_2 := int64(f0_2) * int64(f6)
- f0f7_2 := int64(f0_2) * int64(f7)
- f0f8_2 := int64(f0_2) * int64(f8)
- f0f9_2 := int64(f0_2) * int64(f9)
- f1f1_2 := int64(f1_2) * int64(f1)
- f1f2_2 := int64(f1_2) * int64(f2)
- f1f3_4 := int64(f1_2) * int64(f3_2)
- f1f4_2 := int64(f1_2) * int64(f4)
- f1f5_4 := int64(f1_2) * int64(f5_2)
- f1f6_2 := int64(f1_2) * int64(f6)
- f1f7_4 := int64(f1_2) * int64(f7_2)
- f1f8_2 := int64(f1_2) * int64(f8)
- f1f9_76 := int64(f1_2) * int64(f9_38)
- f2f2 := int64(f2) * int64(f2)
- f2f3_2 := int64(f2_2) * int64(f3)
- f2f4_2 := int64(f2_2) * int64(f4)
- f2f5_2 := int64(f2_2) * int64(f5)
- f2f6_2 := int64(f2_2) * int64(f6)
- f2f7_2 := int64(f2_2) * int64(f7)
- f2f8_38 := int64(f2_2) * int64(f8_19)
- f2f9_38 := int64(f2) * int64(f9_38)
- f3f3_2 := int64(f3_2) * int64(f3)
- f3f4_2 := int64(f3_2) * int64(f4)
- f3f5_4 := int64(f3_2) * int64(f5_2)
- f3f6_2 := int64(f3_2) * int64(f6)
- f3f7_76 := int64(f3_2) * int64(f7_38)
- f3f8_38 := int64(f3_2) * int64(f8_19)
- f3f9_76 := int64(f3_2) * int64(f9_38)
- f4f4 := int64(f4) * int64(f4)
- f4f5_2 := int64(f4_2) * int64(f5)
- f4f6_38 := int64(f4_2) * int64(f6_19)
- f4f7_38 := int64(f4) * int64(f7_38)
- f4f8_38 := int64(f4_2) * int64(f8_19)
- f4f9_38 := int64(f4) * int64(f9_38)
- f5f5_38 := int64(f5) * int64(f5_38)
- f5f6_38 := int64(f5_2) * int64(f6_19)
- f5f7_76 := int64(f5_2) * int64(f7_38)
- f5f8_38 := int64(f5_2) * int64(f8_19)
- f5f9_76 := int64(f5_2) * int64(f9_38)
- f6f6_19 := int64(f6) * int64(f6_19)
- f6f7_38 := int64(f6) * int64(f7_38)
- f6f8_38 := int64(f6_2) * int64(f8_19)
- f6f9_38 := int64(f6) * int64(f9_38)
- f7f7_38 := int64(f7) * int64(f7_38)
- f7f8_38 := int64(f7_2) * int64(f8_19)
- f7f9_76 := int64(f7_2) * int64(f9_38)
- f8f8_19 := int64(f8) * int64(f8_19)
- f8f9_38 := int64(f8) * int64(f9_38)
- f9f9_38 := int64(f9) * int64(f9_38)
- h0 := f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38
- h1 := f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38
- h2 := f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19
- h3 := f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38
- h4 := f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38
- h5 := f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38
- h6 := f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19
- h7 := f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38
- h8 := f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38
- h9 := f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2
- var carry [10]int64
-
- carry[0] = (h0 + (1 << 25)) >> 26
- h1 += carry[0]
- h0 -= carry[0] << 26
- carry[4] = (h4 + (1 << 25)) >> 26
- h5 += carry[4]
- h4 -= carry[4] << 26
-
- carry[1] = (h1 + (1 << 24)) >> 25
- h2 += carry[1]
- h1 -= carry[1] << 25
- carry[5] = (h5 + (1 << 24)) >> 25
- h6 += carry[5]
- h5 -= carry[5] << 25
-
- carry[2] = (h2 + (1 << 25)) >> 26
- h3 += carry[2]
- h2 -= carry[2] << 26
- carry[6] = (h6 + (1 << 25)) >> 26
- h7 += carry[6]
- h6 -= carry[6] << 26
-
- carry[3] = (h3 + (1 << 24)) >> 25
- h4 += carry[3]
- h3 -= carry[3] << 25
- carry[7] = (h7 + (1 << 24)) >> 25
- h8 += carry[7]
- h7 -= carry[7] << 25
-
- carry[4] = (h4 + (1 << 25)) >> 26
- h5 += carry[4]
- h4 -= carry[4] << 26
- carry[8] = (h8 + (1 << 25)) >> 26
- h9 += carry[8]
- h8 -= carry[8] << 26
-
- carry[9] = (h9 + (1 << 24)) >> 25
- h0 += carry[9] * 19
- h9 -= carry[9] << 25
-
- carry[0] = (h0 + (1 << 25)) >> 26
- h1 += carry[0]
- h0 -= carry[0] << 26
-
- h[0] = int32(h0)
- h[1] = int32(h1)
- h[2] = int32(h2)
- h[3] = int32(h3)
- h[4] = int32(h4)
- h[5] = int32(h5)
- h[6] = int32(h6)
- h[7] = int32(h7)
- h[8] = int32(h8)
- h[9] = int32(h9)
-}
-
-// feMul121666 calculates h = f * 121666. Can overlap h with f.
-//
-// Preconditions:
-// |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//
-// Postconditions:
-// |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-func feMul121666(h, f *fieldElement) {
- h0 := int64(f[0]) * 121666
- h1 := int64(f[1]) * 121666
- h2 := int64(f[2]) * 121666
- h3 := int64(f[3]) * 121666
- h4 := int64(f[4]) * 121666
- h5 := int64(f[5]) * 121666
- h6 := int64(f[6]) * 121666
- h7 := int64(f[7]) * 121666
- h8 := int64(f[8]) * 121666
- h9 := int64(f[9]) * 121666
- var carry [10]int64
-
- carry[9] = (h9 + (1 << 24)) >> 25
- h0 += carry[9] * 19
- h9 -= carry[9] << 25
- carry[1] = (h1 + (1 << 24)) >> 25
- h2 += carry[1]
- h1 -= carry[1] << 25
- carry[3] = (h3 + (1 << 24)) >> 25
- h4 += carry[3]
- h3 -= carry[3] << 25
- carry[5] = (h5 + (1 << 24)) >> 25
- h6 += carry[5]
- h5 -= carry[5] << 25
- carry[7] = (h7 + (1 << 24)) >> 25
- h8 += carry[7]
- h7 -= carry[7] << 25
-
- carry[0] = (h0 + (1 << 25)) >> 26
- h1 += carry[0]
- h0 -= carry[0] << 26
- carry[2] = (h2 + (1 << 25)) >> 26
- h3 += carry[2]
- h2 -= carry[2] << 26
- carry[4] = (h4 + (1 << 25)) >> 26
- h5 += carry[4]
- h4 -= carry[4] << 26
- carry[6] = (h6 + (1 << 25)) >> 26
- h7 += carry[6]
- h6 -= carry[6] << 26
- carry[8] = (h8 + (1 << 25)) >> 26
- h9 += carry[8]
- h8 -= carry[8] << 26
-
- h[0] = int32(h0)
- h[1] = int32(h1)
- h[2] = int32(h2)
- h[3] = int32(h3)
- h[4] = int32(h4)
- h[5] = int32(h5)
- h[6] = int32(h6)
- h[7] = int32(h7)
- h[8] = int32(h8)
- h[9] = int32(h9)
-}
-
-// feInvert sets out = z^-1.
-func feInvert(out, z *fieldElement) {
- var t0, t1, t2, t3 fieldElement
- var i int
-
- feSquare(&t0, z)
- for i = 1; i < 1; i++ {
- feSquare(&t0, &t0)
- }
- feSquare(&t1, &t0)
- for i = 1; i < 2; i++ {
- feSquare(&t1, &t1)
- }
- feMul(&t1, z, &t1)
- feMul(&t0, &t0, &t1)
- feSquare(&t2, &t0)
- for i = 1; i < 1; i++ {
- feSquare(&t2, &t2)
- }
- feMul(&t1, &t1, &t2)
- feSquare(&t2, &t1)
- for i = 1; i < 5; i++ {
- feSquare(&t2, &t2)
- }
- feMul(&t1, &t2, &t1)
- feSquare(&t2, &t1)
- for i = 1; i < 10; i++ {
- feSquare(&t2, &t2)
- }
- feMul(&t2, &t2, &t1)
- feSquare(&t3, &t2)
- for i = 1; i < 20; i++ {
- feSquare(&t3, &t3)
- }
- feMul(&t2, &t3, &t2)
- feSquare(&t2, &t2)
- for i = 1; i < 10; i++ {
- feSquare(&t2, &t2)
- }
- feMul(&t1, &t2, &t1)
- feSquare(&t2, &t1)
- for i = 1; i < 50; i++ {
- feSquare(&t2, &t2)
- }
- feMul(&t2, &t2, &t1)
- feSquare(&t3, &t2)
- for i = 1; i < 100; i++ {
- feSquare(&t3, &t3)
- }
- feMul(&t2, &t3, &t2)
- feSquare(&t2, &t2)
- for i = 1; i < 50; i++ {
- feSquare(&t2, &t2)
- }
- feMul(&t1, &t2, &t1)
- feSquare(&t1, &t1)
- for i = 1; i < 5; i++ {
- feSquare(&t1, &t1)
- }
- feMul(out, &t1, &t0)
-}
-
-func scalarMultGeneric(out, in, base *[32]byte) {
- var e [32]byte
-
- copy(e[:], in[:])
- e[0] &= 248
- e[31] &= 127
- e[31] |= 64
-
- var x1, x2, z2, x3, z3, tmp0, tmp1 fieldElement
- feFromBytes(&x1, base)
- feOne(&x2)
- feCopy(&x3, &x1)
- feOne(&z3)
-
- swap := int32(0)
- for pos := 254; pos >= 0; pos-- {
- b := e[pos/8] >> uint(pos&7)
- b &= 1
- swap ^= int32(b)
- feCSwap(&x2, &x3, swap)
- feCSwap(&z2, &z3, swap)
- swap = int32(b)
-
- feSub(&tmp0, &x3, &z3)
- feSub(&tmp1, &x2, &z2)
- feAdd(&x2, &x2, &z2)
- feAdd(&z2, &x3, &z3)
- feMul(&z3, &tmp0, &x2)
- feMul(&z2, &z2, &tmp1)
- feSquare(&tmp0, &tmp1)
- feSquare(&tmp1, &x2)
- feAdd(&x3, &z3, &z2)
- feSub(&z2, &z3, &z2)
- feMul(&x2, &tmp1, &tmp0)
- feSub(&tmp1, &tmp1, &tmp0)
- feSquare(&z2, &z2)
- feMul121666(&z3, &tmp1)
- feSquare(&x3, &x3)
- feAdd(&tmp0, &tmp0, &z3)
- feMul(&z3, &x1, &z2)
- feMul(&z2, &tmp1, &tmp0)
- }
-
- feCSwap(&x2, &x3, swap)
- feCSwap(&z2, &z3, swap)
-
- feInvert(&z2, &z2)
- feMul(&x2, &x2, &z2)
- feToBytes(out, &x2)
-}
+++ /dev/null
-// Copyright 2019 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 !amd64 || !gc || purego
-// +build !amd64 !gc purego
-
-package curve25519
-
-func scalarMult(out, in, base *[32]byte) {
- scalarMultGeneric(out, in, base)
-}
--- /dev/null
+This package is kept in sync with crypto/ed25519/internal/edwards25519/field in
+the standard library.
+
+If there are any changes in the standard library that need to be synced to this
+package, run sync.sh. It will not overwrite any local changes made since the
+previous sync, so it's ok to land changes in this package first, and then sync
+to the standard library later.
--- /dev/null
+// Copyright (c) 2017 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 field implements fast arithmetic modulo 2^255-19.
+package field
+
+import (
+ "crypto/subtle"
+ "encoding/binary"
+ "math/bits"
+)
+
+// Element represents an element of the field GF(2^255-19). Note that this
+// is not a cryptographically secure group, and should only be used to interact
+// with edwards25519.Point coordinates.
+//
+// This type works similarly to math/big.Int, and all arguments and receivers
+// are allowed to alias.
+//
+// The zero value is a valid zero element.
+type Element struct {
+ // An element t represents the integer
+ // t.l0 + t.l1*2^51 + t.l2*2^102 + t.l3*2^153 + t.l4*2^204
+ //
+ // Between operations, all limbs are expected to be lower than 2^52.
+ l0 uint64
+ l1 uint64
+ l2 uint64
+ l3 uint64
+ l4 uint64
+}
+
+const maskLow51Bits uint64 = (1 << 51) - 1
+
+var feZero = &Element{0, 0, 0, 0, 0}
+
+// Zero sets v = 0, and returns v.
+func (v *Element) Zero() *Element {
+ *v = *feZero
+ return v
+}
+
+var feOne = &Element{1, 0, 0, 0, 0}
+
+// One sets v = 1, and returns v.
+func (v *Element) One() *Element {
+ *v = *feOne
+ return v
+}
+
+// reduce reduces v modulo 2^255 - 19 and returns it.
+func (v *Element) reduce() *Element {
+ v.carryPropagate()
+
+ // After the light reduction we now have a field element representation
+ // v < 2^255 + 2^13 * 19, but need v < 2^255 - 19.
+
+ // If v >= 2^255 - 19, then v + 19 >= 2^255, which would overflow 2^255 - 1,
+ // generating a carry. That is, c will be 0 if v < 2^255 - 19, and 1 otherwise.
+ c := (v.l0 + 19) >> 51
+ c = (v.l1 + c) >> 51
+ c = (v.l2 + c) >> 51
+ c = (v.l3 + c) >> 51
+ c = (v.l4 + c) >> 51
+
+ // If v < 2^255 - 19 and c = 0, this will be a no-op. Otherwise, it's
+ // effectively applying the reduction identity to the carry.
+ v.l0 += 19 * c
+
+ v.l1 += v.l0 >> 51
+ v.l0 = v.l0 & maskLow51Bits
+ v.l2 += v.l1 >> 51
+ v.l1 = v.l1 & maskLow51Bits
+ v.l3 += v.l2 >> 51
+ v.l2 = v.l2 & maskLow51Bits
+ v.l4 += v.l3 >> 51
+ v.l3 = v.l3 & maskLow51Bits
+ // no additional carry
+ v.l4 = v.l4 & maskLow51Bits
+
+ return v
+}
+
+// Add sets v = a + b, and returns v.
+func (v *Element) Add(a, b *Element) *Element {
+ v.l0 = a.l0 + b.l0
+ v.l1 = a.l1 + b.l1
+ v.l2 = a.l2 + b.l2
+ v.l3 = a.l3 + b.l3
+ v.l4 = a.l4 + b.l4
+ // Using the generic implementation here is actually faster than the
+ // assembly. Probably because the body of this function is so simple that
+ // the compiler can figure out better optimizations by inlining the carry
+ // propagation. TODO
+ return v.carryPropagateGeneric()
+}
+
+// Subtract sets v = a - b, and returns v.
+func (v *Element) Subtract(a, b *Element) *Element {
+ // We first add 2 * p, to guarantee the subtraction won't underflow, and
+ // then subtract b (which can be up to 2^255 + 2^13 * 19).
+ v.l0 = (a.l0 + 0xFFFFFFFFFFFDA) - b.l0
+ v.l1 = (a.l1 + 0xFFFFFFFFFFFFE) - b.l1
+ v.l2 = (a.l2 + 0xFFFFFFFFFFFFE) - b.l2
+ v.l3 = (a.l3 + 0xFFFFFFFFFFFFE) - b.l3
+ v.l4 = (a.l4 + 0xFFFFFFFFFFFFE) - b.l4
+ return v.carryPropagate()
+}
+
+// Negate sets v = -a, and returns v.
+func (v *Element) Negate(a *Element) *Element {
+ return v.Subtract(feZero, a)
+}
+
+// Invert sets v = 1/z mod p, and returns v.
+//
+// If z == 0, Invert returns v = 0.
+func (v *Element) Invert(z *Element) *Element {
+ // Inversion is implemented as exponentiation with exponent p − 2. It uses the
+ // same sequence of 255 squarings and 11 multiplications as [Curve25519].
+ var z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t Element
+
+ z2.Square(z) // 2
+ t.Square(&z2) // 4
+ t.Square(&t) // 8
+ z9.Multiply(&t, z) // 9
+ z11.Multiply(&z9, &z2) // 11
+ t.Square(&z11) // 22
+ z2_5_0.Multiply(&t, &z9) // 31 = 2^5 - 2^0
+
+ t.Square(&z2_5_0) // 2^6 - 2^1
+ for i := 0; i < 4; i++ {
+ t.Square(&t) // 2^10 - 2^5
+ }
+ z2_10_0.Multiply(&t, &z2_5_0) // 2^10 - 2^0
+
+ t.Square(&z2_10_0) // 2^11 - 2^1
+ for i := 0; i < 9; i++ {
+ t.Square(&t) // 2^20 - 2^10
+ }
+ z2_20_0.Multiply(&t, &z2_10_0) // 2^20 - 2^0
+
+ t.Square(&z2_20_0) // 2^21 - 2^1
+ for i := 0; i < 19; i++ {
+ t.Square(&t) // 2^40 - 2^20
+ }
+ t.Multiply(&t, &z2_20_0) // 2^40 - 2^0
+
+ t.Square(&t) // 2^41 - 2^1
+ for i := 0; i < 9; i++ {
+ t.Square(&t) // 2^50 - 2^10
+ }
+ z2_50_0.Multiply(&t, &z2_10_0) // 2^50 - 2^0
+
+ t.Square(&z2_50_0) // 2^51 - 2^1
+ for i := 0; i < 49; i++ {
+ t.Square(&t) // 2^100 - 2^50
+ }
+ z2_100_0.Multiply(&t, &z2_50_0) // 2^100 - 2^0
+
+ t.Square(&z2_100_0) // 2^101 - 2^1
+ for i := 0; i < 99; i++ {
+ t.Square(&t) // 2^200 - 2^100
+ }
+ t.Multiply(&t, &z2_100_0) // 2^200 - 2^0
+
+ t.Square(&t) // 2^201 - 2^1
+ for i := 0; i < 49; i++ {
+ t.Square(&t) // 2^250 - 2^50
+ }
+ t.Multiply(&t, &z2_50_0) // 2^250 - 2^0
+
+ t.Square(&t) // 2^251 - 2^1
+ t.Square(&t) // 2^252 - 2^2
+ t.Square(&t) // 2^253 - 2^3
+ t.Square(&t) // 2^254 - 2^4
+ t.Square(&t) // 2^255 - 2^5
+
+ return v.Multiply(&t, &z11) // 2^255 - 21
+}
+
+// Set sets v = a, and returns v.
+func (v *Element) Set(a *Element) *Element {
+ *v = *a
+ return v
+}
+
+// SetBytes sets v to x, which must be a 32-byte little-endian encoding.
+//
+// Consistent with RFC 7748, the most significant bit (the high bit of the
+// last byte) is ignored, and non-canonical values (2^255-19 through 2^255-1)
+// are accepted. Note that this is laxer than specified by RFC 8032.
+func (v *Element) SetBytes(x []byte) *Element {
+ if len(x) != 32 {
+ panic("edwards25519: invalid field element input size")
+ }
+
+ // Bits 0:51 (bytes 0:8, bits 0:64, shift 0, mask 51).
+ v.l0 = binary.LittleEndian.Uint64(x[0:8])
+ v.l0 &= maskLow51Bits
+ // Bits 51:102 (bytes 6:14, bits 48:112, shift 3, mask 51).
+ v.l1 = binary.LittleEndian.Uint64(x[6:14]) >> 3
+ v.l1 &= maskLow51Bits
+ // Bits 102:153 (bytes 12:20, bits 96:160, shift 6, mask 51).
+ v.l2 = binary.LittleEndian.Uint64(x[12:20]) >> 6
+ v.l2 &= maskLow51Bits
+ // Bits 153:204 (bytes 19:27, bits 152:216, shift 1, mask 51).
+ v.l3 = binary.LittleEndian.Uint64(x[19:27]) >> 1
+ v.l3 &= maskLow51Bits
+ // Bits 204:251 (bytes 24:32, bits 192:256, shift 12, mask 51).
+ // Note: not bytes 25:33, shift 4, to avoid overread.
+ v.l4 = binary.LittleEndian.Uint64(x[24:32]) >> 12
+ v.l4 &= maskLow51Bits
+
+ return v
+}
+
+// Bytes returns the canonical 32-byte little-endian encoding of v.
+func (v *Element) Bytes() []byte {
+ // This function is outlined to make the allocations inline in the caller
+ // rather than happen on the heap.
+ var out [32]byte
+ return v.bytes(&out)
+}
+
+func (v *Element) bytes(out *[32]byte) []byte {
+ t := *v
+ t.reduce()
+
+ var buf [8]byte
+ for i, l := range [5]uint64{t.l0, t.l1, t.l2, t.l3, t.l4} {
+ bitsOffset := i * 51
+ binary.LittleEndian.PutUint64(buf[:], l<<uint(bitsOffset%8))
+ for i, bb := range buf {
+ off := bitsOffset/8 + i
+ if off >= len(out) {
+ break
+ }
+ out[off] |= bb
+ }
+ }
+
+ return out[:]
+}
+
+// Equal returns 1 if v and u are equal, and 0 otherwise.
+func (v *Element) Equal(u *Element) int {
+ sa, sv := u.Bytes(), v.Bytes()
+ return subtle.ConstantTimeCompare(sa, sv)
+}
+
+// mask64Bits returns 0xffffffff if cond is 1, and 0 otherwise.
+func mask64Bits(cond int) uint64 { return ^(uint64(cond) - 1) }
+
+// Select sets v to a if cond == 1, and to b if cond == 0.
+func (v *Element) Select(a, b *Element, cond int) *Element {
+ m := mask64Bits(cond)
+ v.l0 = (m & a.l0) | (^m & b.l0)
+ v.l1 = (m & a.l1) | (^m & b.l1)
+ v.l2 = (m & a.l2) | (^m & b.l2)
+ v.l3 = (m & a.l3) | (^m & b.l3)
+ v.l4 = (m & a.l4) | (^m & b.l4)
+ return v
+}
+
+// Swap swaps v and u if cond == 1 or leaves them unchanged if cond == 0, and returns v.
+func (v *Element) Swap(u *Element, cond int) {
+ m := mask64Bits(cond)
+ t := m & (v.l0 ^ u.l0)
+ v.l0 ^= t
+ u.l0 ^= t
+ t = m & (v.l1 ^ u.l1)
+ v.l1 ^= t
+ u.l1 ^= t
+ t = m & (v.l2 ^ u.l2)
+ v.l2 ^= t
+ u.l2 ^= t
+ t = m & (v.l3 ^ u.l3)
+ v.l3 ^= t
+ u.l3 ^= t
+ t = m & (v.l4 ^ u.l4)
+ v.l4 ^= t
+ u.l4 ^= t
+}
+
+// IsNegative returns 1 if v is negative, and 0 otherwise.
+func (v *Element) IsNegative() int {
+ return int(v.Bytes()[0] & 1)
+}
+
+// Absolute sets v to |u|, and returns v.
+func (v *Element) Absolute(u *Element) *Element {
+ return v.Select(new(Element).Negate(u), u, u.IsNegative())
+}
+
+// Multiply sets v = x * y, and returns v.
+func (v *Element) Multiply(x, y *Element) *Element {
+ feMul(v, x, y)
+ return v
+}
+
+// Square sets v = x * x, and returns v.
+func (v *Element) Square(x *Element) *Element {
+ feSquare(v, x)
+ return v
+}
+
+// Mult32 sets v = x * y, and returns v.
+func (v *Element) Mult32(x *Element, y uint32) *Element {
+ x0lo, x0hi := mul51(x.l0, y)
+ x1lo, x1hi := mul51(x.l1, y)
+ x2lo, x2hi := mul51(x.l2, y)
+ x3lo, x3hi := mul51(x.l3, y)
+ x4lo, x4hi := mul51(x.l4, y)
+ v.l0 = x0lo + 19*x4hi // carried over per the reduction identity
+ v.l1 = x1lo + x0hi
+ v.l2 = x2lo + x1hi
+ v.l3 = x3lo + x2hi
+ v.l4 = x4lo + x3hi
+ // The hi portions are going to be only 32 bits, plus any previous excess,
+ // so we can skip the carry propagation.
+ return v
+}
+
+// mul51 returns lo + hi * 2⁵¹ = a * b.
+func mul51(a uint64, b uint32) (lo uint64, hi uint64) {
+ mh, ml := bits.Mul64(a, uint64(b))
+ lo = ml & maskLow51Bits
+ hi = (mh << 13) | (ml >> 51)
+ return
+}
+
+// Pow22523 set v = x^((p-5)/8), and returns v. (p-5)/8 is 2^252-3.
+func (v *Element) Pow22523(x *Element) *Element {
+ var t0, t1, t2 Element
+
+ t0.Square(x) // x^2
+ t1.Square(&t0) // x^4
+ t1.Square(&t1) // x^8
+ t1.Multiply(x, &t1) // x^9
+ t0.Multiply(&t0, &t1) // x^11
+ t0.Square(&t0) // x^22
+ t0.Multiply(&t1, &t0) // x^31
+ t1.Square(&t0) // x^62
+ for i := 1; i < 5; i++ { // x^992
+ t1.Square(&t1)
+ }
+ t0.Multiply(&t1, &t0) // x^1023 -> 1023 = 2^10 - 1
+ t1.Square(&t0) // 2^11 - 2
+ for i := 1; i < 10; i++ { // 2^20 - 2^10
+ t1.Square(&t1)
+ }
+ t1.Multiply(&t1, &t0) // 2^20 - 1
+ t2.Square(&t1) // 2^21 - 2
+ for i := 1; i < 20; i++ { // 2^40 - 2^20
+ t2.Square(&t2)
+ }
+ t1.Multiply(&t2, &t1) // 2^40 - 1
+ t1.Square(&t1) // 2^41 - 2
+ for i := 1; i < 10; i++ { // 2^50 - 2^10
+ t1.Square(&t1)
+ }
+ t0.Multiply(&t1, &t0) // 2^50 - 1
+ t1.Square(&t0) // 2^51 - 2
+ for i := 1; i < 50; i++ { // 2^100 - 2^50
+ t1.Square(&t1)
+ }
+ t1.Multiply(&t1, &t0) // 2^100 - 1
+ t2.Square(&t1) // 2^101 - 2
+ for i := 1; i < 100; i++ { // 2^200 - 2^100
+ t2.Square(&t2)
+ }
+ t1.Multiply(&t2, &t1) // 2^200 - 1
+ t1.Square(&t1) // 2^201 - 2
+ for i := 1; i < 50; i++ { // 2^250 - 2^50
+ t1.Square(&t1)
+ }
+ t0.Multiply(&t1, &t0) // 2^250 - 1
+ t0.Square(&t0) // 2^251 - 2
+ t0.Square(&t0) // 2^252 - 4
+ return v.Multiply(&t0, x) // 2^252 - 3 -> x^(2^252-3)
+}
+
+// sqrtM1 is 2^((p-1)/4), which squared is equal to -1 by Euler's Criterion.
+var sqrtM1 = &Element{1718705420411056, 234908883556509,
+ 2233514472574048, 2117202627021982, 765476049583133}
+
+// SqrtRatio sets r to the non-negative square root of the ratio of u and v.
+//
+// If u/v is square, SqrtRatio returns r and 1. If u/v is not square, SqrtRatio
+// sets r according to Section 4.3 of draft-irtf-cfrg-ristretto255-decaf448-00,
+// and returns r and 0.
+func (r *Element) SqrtRatio(u, v *Element) (rr *Element, wasSquare int) {
+ var a, b Element
+
+ // r = (u * v3) * (u * v7)^((p-5)/8)
+ v2 := a.Square(v)
+ uv3 := b.Multiply(u, b.Multiply(v2, v))
+ uv7 := a.Multiply(uv3, a.Square(v2))
+ r.Multiply(uv3, r.Pow22523(uv7))
+
+ check := a.Multiply(v, a.Square(r)) // check = v * r^2
+
+ uNeg := b.Negate(u)
+ correctSignSqrt := check.Equal(u)
+ flippedSignSqrt := check.Equal(uNeg)
+ flippedSignSqrtI := check.Equal(uNeg.Multiply(uNeg, sqrtM1))
+
+ rPrime := b.Multiply(r, sqrtM1) // r_prime = SQRT_M1 * r
+ // r = CT_SELECT(r_prime IF flipped_sign_sqrt | flipped_sign_sqrt_i ELSE r)
+ r.Select(rPrime, r, flippedSignSqrt|flippedSignSqrtI)
+
+ r.Absolute(r) // Choose the nonnegative square root.
+ return r, correctSignSqrt | flippedSignSqrt
+}
--- /dev/null
+// Code generated by command: go run fe_amd64_asm.go -out ../fe_amd64.s -stubs ../fe_amd64.go -pkg field. DO NOT EDIT.
+
+// +build amd64,gc,!purego
+
+package field
+
+// feMul sets out = a * b. It works like feMulGeneric.
+//go:noescape
+func feMul(out *Element, a *Element, b *Element)
+
+// feSquare sets out = a * a. It works like feSquareGeneric.
+//go:noescape
+func feSquare(out *Element, a *Element)
--- /dev/null
+// Code generated by command: go run fe_amd64_asm.go -out ../fe_amd64.s -stubs ../fe_amd64.go -pkg field. DO NOT EDIT.
+
+//go:build amd64 && gc && !purego
+// +build amd64,gc,!purego
+
+#include "textflag.h"
+
+// func feMul(out *Element, a *Element, b *Element)
+TEXT ·feMul(SB), NOSPLIT, $0-24
+ MOVQ a+8(FP), CX
+ MOVQ b+16(FP), BX
+
+ // r0 = a0×b0
+ MOVQ (CX), AX
+ MULQ (BX)
+ MOVQ AX, DI
+ MOVQ DX, SI
+
+ // r0 += 19×a1×b4
+ MOVQ 8(CX), AX
+ IMUL3Q $0x13, AX, AX
+ MULQ 32(BX)
+ ADDQ AX, DI
+ ADCQ DX, SI
+
+ // r0 += 19×a2×b3
+ MOVQ 16(CX), AX
+ IMUL3Q $0x13, AX, AX
+ MULQ 24(BX)
+ ADDQ AX, DI
+ ADCQ DX, SI
+
+ // r0 += 19×a3×b2
+ MOVQ 24(CX), AX
+ IMUL3Q $0x13, AX, AX
+ MULQ 16(BX)
+ ADDQ AX, DI
+ ADCQ DX, SI
+
+ // r0 += 19×a4×b1
+ MOVQ 32(CX), AX
+ IMUL3Q $0x13, AX, AX
+ MULQ 8(BX)
+ ADDQ AX, DI
+ ADCQ DX, SI
+
+ // r1 = a0×b1
+ MOVQ (CX), AX
+ MULQ 8(BX)
+ MOVQ AX, R9
+ MOVQ DX, R8
+
+ // r1 += a1×b0
+ MOVQ 8(CX), AX
+ MULQ (BX)
+ ADDQ AX, R9
+ ADCQ DX, R8
+
+ // r1 += 19×a2×b4
+ MOVQ 16(CX), AX
+ IMUL3Q $0x13, AX, AX
+ MULQ 32(BX)
+ ADDQ AX, R9
+ ADCQ DX, R8
+
+ // r1 += 19×a3×b3
+ MOVQ 24(CX), AX
+ IMUL3Q $0x13, AX, AX
+ MULQ 24(BX)
+ ADDQ AX, R9
+ ADCQ DX, R8
+
+ // r1 += 19×a4×b2
+ MOVQ 32(CX), AX
+ IMUL3Q $0x13, AX, AX
+ MULQ 16(BX)
+ ADDQ AX, R9
+ ADCQ DX, R8
+
+ // r2 = a0×b2
+ MOVQ (CX), AX
+ MULQ 16(BX)
+ MOVQ AX, R11
+ MOVQ DX, R10
+
+ // r2 += a1×b1
+ MOVQ 8(CX), AX
+ MULQ 8(BX)
+ ADDQ AX, R11
+ ADCQ DX, R10
+
+ // r2 += a2×b0
+ MOVQ 16(CX), AX
+ MULQ (BX)
+ ADDQ AX, R11
+ ADCQ DX, R10
+
+ // r2 += 19×a3×b4
+ MOVQ 24(CX), AX
+ IMUL3Q $0x13, AX, AX
+ MULQ 32(BX)
+ ADDQ AX, R11
+ ADCQ DX, R10
+
+ // r2 += 19×a4×b3
+ MOVQ 32(CX), AX
+ IMUL3Q $0x13, AX, AX
+ MULQ 24(BX)
+ ADDQ AX, R11
+ ADCQ DX, R10
+
+ // r3 = a0×b3
+ MOVQ (CX), AX
+ MULQ 24(BX)
+ MOVQ AX, R13
+ MOVQ DX, R12
+
+ // r3 += a1×b2
+ MOVQ 8(CX), AX
+ MULQ 16(BX)
+ ADDQ AX, R13
+ ADCQ DX, R12
+
+ // r3 += a2×b1
+ MOVQ 16(CX), AX
+ MULQ 8(BX)
+ ADDQ AX, R13
+ ADCQ DX, R12
+
+ // r3 += a3×b0
+ MOVQ 24(CX), AX
+ MULQ (BX)
+ ADDQ AX, R13
+ ADCQ DX, R12
+
+ // r3 += 19×a4×b4
+ MOVQ 32(CX), AX
+ IMUL3Q $0x13, AX, AX
+ MULQ 32(BX)
+ ADDQ AX, R13
+ ADCQ DX, R12
+
+ // r4 = a0×b4
+ MOVQ (CX), AX
+ MULQ 32(BX)
+ MOVQ AX, R15
+ MOVQ DX, R14
+
+ // r4 += a1×b3
+ MOVQ 8(CX), AX
+ MULQ 24(BX)
+ ADDQ AX, R15
+ ADCQ DX, R14
+
+ // r4 += a2×b2
+ MOVQ 16(CX), AX
+ MULQ 16(BX)
+ ADDQ AX, R15
+ ADCQ DX, R14
+
+ // r4 += a3×b1
+ MOVQ 24(CX), AX
+ MULQ 8(BX)
+ ADDQ AX, R15
+ ADCQ DX, R14
+
+ // r4 += a4×b0
+ MOVQ 32(CX), AX
+ MULQ (BX)
+ ADDQ AX, R15
+ ADCQ DX, R14
+
+ // First reduction chain
+ MOVQ $0x0007ffffffffffff, AX
+ SHLQ $0x0d, DI, SI
+ SHLQ $0x0d, R9, R8
+ SHLQ $0x0d, R11, R10
+ SHLQ $0x0d, R13, R12
+ SHLQ $0x0d, R15, R14
+ ANDQ AX, DI
+ IMUL3Q $0x13, R14, R14
+ ADDQ R14, DI
+ ANDQ AX, R9
+ ADDQ SI, R9
+ ANDQ AX, R11
+ ADDQ R8, R11
+ ANDQ AX, R13
+ ADDQ R10, R13
+ ANDQ AX, R15
+ ADDQ R12, R15
+
+ // Second reduction chain (carryPropagate)
+ MOVQ DI, SI
+ SHRQ $0x33, SI
+ MOVQ R9, R8
+ SHRQ $0x33, R8
+ MOVQ R11, R10
+ SHRQ $0x33, R10
+ MOVQ R13, R12
+ SHRQ $0x33, R12
+ MOVQ R15, R14
+ SHRQ $0x33, R14
+ ANDQ AX, DI
+ IMUL3Q $0x13, R14, R14
+ ADDQ R14, DI
+ ANDQ AX, R9
+ ADDQ SI, R9
+ ANDQ AX, R11
+ ADDQ R8, R11
+ ANDQ AX, R13
+ ADDQ R10, R13
+ ANDQ AX, R15
+ ADDQ R12, R15
+
+ // Store output
+ MOVQ out+0(FP), AX
+ MOVQ DI, (AX)
+ MOVQ R9, 8(AX)
+ MOVQ R11, 16(AX)
+ MOVQ R13, 24(AX)
+ MOVQ R15, 32(AX)
+ RET
+
+// func feSquare(out *Element, a *Element)
+TEXT ·feSquare(SB), NOSPLIT, $0-16
+ MOVQ a+8(FP), CX
+
+ // r0 = l0×l0
+ MOVQ (CX), AX
+ MULQ (CX)
+ MOVQ AX, SI
+ MOVQ DX, BX
+
+ // r0 += 38×l1×l4
+ MOVQ 8(CX), AX
+ IMUL3Q $0x26, AX, AX
+ MULQ 32(CX)
+ ADDQ AX, SI
+ ADCQ DX, BX
+
+ // r0 += 38×l2×l3
+ MOVQ 16(CX), AX
+ IMUL3Q $0x26, AX, AX
+ MULQ 24(CX)
+ ADDQ AX, SI
+ ADCQ DX, BX
+
+ // r1 = 2×l0×l1
+ MOVQ (CX), AX
+ SHLQ $0x01, AX
+ MULQ 8(CX)
+ MOVQ AX, R8
+ MOVQ DX, DI
+
+ // r1 += 38×l2×l4
+ MOVQ 16(CX), AX
+ IMUL3Q $0x26, AX, AX
+ MULQ 32(CX)
+ ADDQ AX, R8
+ ADCQ DX, DI
+
+ // r1 += 19×l3×l3
+ MOVQ 24(CX), AX
+ IMUL3Q $0x13, AX, AX
+ MULQ 24(CX)
+ ADDQ AX, R8
+ ADCQ DX, DI
+
+ // r2 = 2×l0×l2
+ MOVQ (CX), AX
+ SHLQ $0x01, AX
+ MULQ 16(CX)
+ MOVQ AX, R10
+ MOVQ DX, R9
+
+ // r2 += l1×l1
+ MOVQ 8(CX), AX
+ MULQ 8(CX)
+ ADDQ AX, R10
+ ADCQ DX, R9
+
+ // r2 += 38×l3×l4
+ MOVQ 24(CX), AX
+ IMUL3Q $0x26, AX, AX
+ MULQ 32(CX)
+ ADDQ AX, R10
+ ADCQ DX, R9
+
+ // r3 = 2×l0×l3
+ MOVQ (CX), AX
+ SHLQ $0x01, AX
+ MULQ 24(CX)
+ MOVQ AX, R12
+ MOVQ DX, R11
+
+ // r3 += 2×l1×l2
+ MOVQ 8(CX), AX
+ IMUL3Q $0x02, AX, AX
+ MULQ 16(CX)
+ ADDQ AX, R12
+ ADCQ DX, R11
+
+ // r3 += 19×l4×l4
+ MOVQ 32(CX), AX
+ IMUL3Q $0x13, AX, AX
+ MULQ 32(CX)
+ ADDQ AX, R12
+ ADCQ DX, R11
+
+ // r4 = 2×l0×l4
+ MOVQ (CX), AX
+ SHLQ $0x01, AX
+ MULQ 32(CX)
+ MOVQ AX, R14
+ MOVQ DX, R13
+
+ // r4 += 2×l1×l3
+ MOVQ 8(CX), AX
+ IMUL3Q $0x02, AX, AX
+ MULQ 24(CX)
+ ADDQ AX, R14
+ ADCQ DX, R13
+
+ // r4 += l2×l2
+ MOVQ 16(CX), AX
+ MULQ 16(CX)
+ ADDQ AX, R14
+ ADCQ DX, R13
+
+ // First reduction chain
+ MOVQ $0x0007ffffffffffff, AX
+ SHLQ $0x0d, SI, BX
+ SHLQ $0x0d, R8, DI
+ SHLQ $0x0d, R10, R9
+ SHLQ $0x0d, R12, R11
+ SHLQ $0x0d, R14, R13
+ ANDQ AX, SI
+ IMUL3Q $0x13, R13, R13
+ ADDQ R13, SI
+ ANDQ AX, R8
+ ADDQ BX, R8
+ ANDQ AX, R10
+ ADDQ DI, R10
+ ANDQ AX, R12
+ ADDQ R9, R12
+ ANDQ AX, R14
+ ADDQ R11, R14
+
+ // Second reduction chain (carryPropagate)
+ MOVQ SI, BX
+ SHRQ $0x33, BX
+ MOVQ R8, DI
+ SHRQ $0x33, DI
+ MOVQ R10, R9
+ SHRQ $0x33, R9
+ MOVQ R12, R11
+ SHRQ $0x33, R11
+ MOVQ R14, R13
+ SHRQ $0x33, R13
+ ANDQ AX, SI
+ IMUL3Q $0x13, R13, R13
+ ADDQ R13, SI
+ ANDQ AX, R8
+ ADDQ BX, R8
+ ANDQ AX, R10
+ ADDQ DI, R10
+ ANDQ AX, R12
+ ADDQ R9, R12
+ ANDQ AX, R14
+ ADDQ R11, R14
+
+ // Store output
+ MOVQ out+0(FP), AX
+ MOVQ SI, (AX)
+ MOVQ R8, 8(AX)
+ MOVQ R10, 16(AX)
+ MOVQ R12, 24(AX)
+ MOVQ R14, 32(AX)
+ RET
--- /dev/null
+// Copyright (c) 2019 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 !amd64 || !gc || purego
+// +build !amd64 !gc purego
+
+package field
+
+func feMul(v, x, y *Element) { feMulGeneric(v, x, y) }
+
+func feSquare(v, x *Element) { feSquareGeneric(v, x) }
--- /dev/null
+// Copyright (c) 2020 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 arm64 && gc && !purego
+// +build arm64,gc,!purego
+
+package field
+
+//go:noescape
+func carryPropagate(v *Element)
+
+func (v *Element) carryPropagate() *Element {
+ carryPropagate(v)
+ return v
+}
--- /dev/null
+// Copyright (c) 2020 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 arm64 && gc && !purego
+// +build arm64,gc,!purego
+
+#include "textflag.h"
+
+// carryPropagate works exactly like carryPropagateGeneric and uses the
+// same AND, ADD, and LSR+MADD instructions emitted by the compiler, but
+// avoids loading R0-R4 twice and uses LDP and STP.
+//
+// See https://golang.org/issues/43145 for the main compiler issue.
+//
+// func carryPropagate(v *Element)
+TEXT ·carryPropagate(SB),NOFRAME|NOSPLIT,$0-8
+ MOVD v+0(FP), R20
+
+ LDP 0(R20), (R0, R1)
+ LDP 16(R20), (R2, R3)
+ MOVD 32(R20), R4
+
+ AND $0x7ffffffffffff, R0, R10
+ AND $0x7ffffffffffff, R1, R11
+ AND $0x7ffffffffffff, R2, R12
+ AND $0x7ffffffffffff, R3, R13
+ AND $0x7ffffffffffff, R4, R14
+
+ ADD R0>>51, R11, R11
+ ADD R1>>51, R12, R12
+ ADD R2>>51, R13, R13
+ ADD R3>>51, R14, R14
+ // R4>>51 * 19 + R10 -> R10
+ LSR $51, R4, R21
+ MOVD $19, R22
+ MADD R22, R10, R21, R10
+
+ STP (R10, R11), 0(R20)
+ STP (R12, R13), 16(R20)
+ MOVD R14, 32(R20)
+
+ RET
--- /dev/null
+// Copyright (c) 2021 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 !arm64 || !gc || purego
+// +build !arm64 !gc purego
+
+package field
+
+func (v *Element) carryPropagate() *Element {
+ return v.carryPropagateGeneric()
+}
--- /dev/null
+// Copyright (c) 2017 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 field
+
+import "math/bits"
+
+// uint128 holds a 128-bit number as two 64-bit limbs, for use with the
+// bits.Mul64 and bits.Add64 intrinsics.
+type uint128 struct {
+ lo, hi uint64
+}
+
+// mul64 returns a * b.
+func mul64(a, b uint64) uint128 {
+ hi, lo := bits.Mul64(a, b)
+ return uint128{lo, hi}
+}
+
+// addMul64 returns v + a * b.
+func addMul64(v uint128, a, b uint64) uint128 {
+ hi, lo := bits.Mul64(a, b)
+ lo, c := bits.Add64(lo, v.lo, 0)
+ hi, _ = bits.Add64(hi, v.hi, c)
+ return uint128{lo, hi}
+}
+
+// shiftRightBy51 returns a >> 51. a is assumed to be at most 115 bits.
+func shiftRightBy51(a uint128) uint64 {
+ return (a.hi << (64 - 51)) | (a.lo >> 51)
+}
+
+func feMulGeneric(v, a, b *Element) {
+ a0 := a.l0
+ a1 := a.l1
+ a2 := a.l2
+ a3 := a.l3
+ a4 := a.l4
+
+ b0 := b.l0
+ b1 := b.l1
+ b2 := b.l2
+ b3 := b.l3
+ b4 := b.l4
+
+ // Limb multiplication works like pen-and-paper columnar multiplication, but
+ // with 51-bit limbs instead of digits.
+ //
+ // a4 a3 a2 a1 a0 x
+ // b4 b3 b2 b1 b0 =
+ // ------------------------
+ // a4b0 a3b0 a2b0 a1b0 a0b0 +
+ // a4b1 a3b1 a2b1 a1b1 a0b1 +
+ // a4b2 a3b2 a2b2 a1b2 a0b2 +
+ // a4b3 a3b3 a2b3 a1b3 a0b3 +
+ // a4b4 a3b4 a2b4 a1b4 a0b4 =
+ // ----------------------------------------------
+ // r8 r7 r6 r5 r4 r3 r2 r1 r0
+ //
+ // We can then use the reduction identity (a * 2²⁵⁵ + b = a * 19 + b) to
+ // reduce the limbs that would overflow 255 bits. r5 * 2²⁵⁵ becomes 19 * r5,
+ // r6 * 2³⁰⁶ becomes 19 * r6 * 2⁵¹, etc.
+ //
+ // Reduction can be carried out simultaneously to multiplication. For
+ // example, we do not compute r5: whenever the result of a multiplication
+ // belongs to r5, like a1b4, we multiply it by 19 and add the result to r0.
+ //
+ // a4b0 a3b0 a2b0 a1b0 a0b0 +
+ // a3b1 a2b1 a1b1 a0b1 19×a4b1 +
+ // a2b2 a1b2 a0b2 19×a4b2 19×a3b2 +
+ // a1b3 a0b3 19×a4b3 19×a3b3 19×a2b3 +
+ // a0b4 19×a4b4 19×a3b4 19×a2b4 19×a1b4 =
+ // --------------------------------------
+ // r4 r3 r2 r1 r0
+ //
+ // Finally we add up the columns into wide, overlapping limbs.
+
+ a1_19 := a1 * 19
+ a2_19 := a2 * 19
+ a3_19 := a3 * 19
+ a4_19 := a4 * 19
+
+ // r0 = a0×b0 + 19×(a1×b4 + a2×b3 + a3×b2 + a4×b1)
+ r0 := mul64(a0, b0)
+ r0 = addMul64(r0, a1_19, b4)
+ r0 = addMul64(r0, a2_19, b3)
+ r0 = addMul64(r0, a3_19, b2)
+ r0 = addMul64(r0, a4_19, b1)
+
+ // r1 = a0×b1 + a1×b0 + 19×(a2×b4 + a3×b3 + a4×b2)
+ r1 := mul64(a0, b1)
+ r1 = addMul64(r1, a1, b0)
+ r1 = addMul64(r1, a2_19, b4)
+ r1 = addMul64(r1, a3_19, b3)
+ r1 = addMul64(r1, a4_19, b2)
+
+ // r2 = a0×b2 + a1×b1 + a2×b0 + 19×(a3×b4 + a4×b3)
+ r2 := mul64(a0, b2)
+ r2 = addMul64(r2, a1, b1)
+ r2 = addMul64(r2, a2, b0)
+ r2 = addMul64(r2, a3_19, b4)
+ r2 = addMul64(r2, a4_19, b3)
+
+ // r3 = a0×b3 + a1×b2 + a2×b1 + a3×b0 + 19×a4×b4
+ r3 := mul64(a0, b3)
+ r3 = addMul64(r3, a1, b2)
+ r3 = addMul64(r3, a2, b1)
+ r3 = addMul64(r3, a3, b0)
+ r3 = addMul64(r3, a4_19, b4)
+
+ // r4 = a0×b4 + a1×b3 + a2×b2 + a3×b1 + a4×b0
+ r4 := mul64(a0, b4)
+ r4 = addMul64(r4, a1, b3)
+ r4 = addMul64(r4, a2, b2)
+ r4 = addMul64(r4, a3, b1)
+ r4 = addMul64(r4, a4, b0)
+
+ // After the multiplication, we need to reduce (carry) the five coefficients
+ // to obtain a result with limbs that are at most slightly larger than 2⁵¹,
+ // to respect the Element invariant.
+ //
+ // Overall, the reduction works the same as carryPropagate, except with
+ // wider inputs: we take the carry for each coefficient by shifting it right
+ // by 51, and add it to the limb above it. The top carry is multiplied by 19
+ // according to the reduction identity and added to the lowest limb.
+ //
+ // The largest coefficient (r0) will be at most 111 bits, which guarantees
+ // that all carries are at most 111 - 51 = 60 bits, which fits in a uint64.
+ //
+ // r0 = a0×b0 + 19×(a1×b4 + a2×b3 + a3×b2 + a4×b1)
+ // r0 < 2⁵²×2⁵² + 19×(2⁵²×2⁵² + 2⁵²×2⁵² + 2⁵²×2⁵² + 2⁵²×2⁵²)
+ // r0 < (1 + 19 × 4) × 2⁵² × 2⁵²
+ // r0 < 2⁷ × 2⁵² × 2⁵²
+ // r0 < 2¹¹¹
+ //
+ // Moreover, the top coefficient (r4) is at most 107 bits, so c4 is at most
+ // 56 bits, and c4 * 19 is at most 61 bits, which again fits in a uint64 and
+ // allows us to easily apply the reduction identity.
+ //
+ // r4 = a0×b4 + a1×b3 + a2×b2 + a3×b1 + a4×b0
+ // r4 < 5 × 2⁵² × 2⁵²
+ // r4 < 2¹⁰⁷
+ //
+
+ c0 := shiftRightBy51(r0)
+ c1 := shiftRightBy51(r1)
+ c2 := shiftRightBy51(r2)
+ c3 := shiftRightBy51(r3)
+ c4 := shiftRightBy51(r4)
+
+ rr0 := r0.lo&maskLow51Bits + c4*19
+ rr1 := r1.lo&maskLow51Bits + c0
+ rr2 := r2.lo&maskLow51Bits + c1
+ rr3 := r3.lo&maskLow51Bits + c2
+ rr4 := r4.lo&maskLow51Bits + c3
+
+ // Now all coefficients fit into 64-bit registers but are still too large to
+ // be passed around as a Element. We therefore do one last carry chain,
+ // where the carries will be small enough to fit in the wiggle room above 2⁵¹.
+ *v = Element{rr0, rr1, rr2, rr3, rr4}
+ v.carryPropagate()
+}
+
+func feSquareGeneric(v, a *Element) {
+ l0 := a.l0
+ l1 := a.l1
+ l2 := a.l2
+ l3 := a.l3
+ l4 := a.l4
+
+ // Squaring works precisely like multiplication above, but thanks to its
+ // symmetry we get to group a few terms together.
+ //
+ // l4 l3 l2 l1 l0 x
+ // l4 l3 l2 l1 l0 =
+ // ------------------------
+ // l4l0 l3l0 l2l0 l1l0 l0l0 +
+ // l4l1 l3l1 l2l1 l1l1 l0l1 +
+ // l4l2 l3l2 l2l2 l1l2 l0l2 +
+ // l4l3 l3l3 l2l3 l1l3 l0l3 +
+ // l4l4 l3l4 l2l4 l1l4 l0l4 =
+ // ----------------------------------------------
+ // r8 r7 r6 r5 r4 r3 r2 r1 r0
+ //
+ // l4l0 l3l0 l2l0 l1l0 l0l0 +
+ // l3l1 l2l1 l1l1 l0l1 19×l4l1 +
+ // l2l2 l1l2 l0l2 19×l4l2 19×l3l2 +
+ // l1l3 l0l3 19×l4l3 19×l3l3 19×l2l3 +
+ // l0l4 19×l4l4 19×l3l4 19×l2l4 19×l1l4 =
+ // --------------------------------------
+ // r4 r3 r2 r1 r0
+ //
+ // With precomputed 2×, 19×, and 2×19× terms, we can compute each limb with
+ // only three Mul64 and four Add64, instead of five and eight.
+
+ l0_2 := l0 * 2
+ l1_2 := l1 * 2
+
+ l1_38 := l1 * 38
+ l2_38 := l2 * 38
+ l3_38 := l3 * 38
+
+ l3_19 := l3 * 19
+ l4_19 := l4 * 19
+
+ // r0 = l0×l0 + 19×(l1×l4 + l2×l3 + l3×l2 + l4×l1) = l0×l0 + 19×2×(l1×l4 + l2×l3)
+ r0 := mul64(l0, l0)
+ r0 = addMul64(r0, l1_38, l4)
+ r0 = addMul64(r0, l2_38, l3)
+
+ // r1 = l0×l1 + l1×l0 + 19×(l2×l4 + l3×l3 + l4×l2) = 2×l0×l1 + 19×2×l2×l4 + 19×l3×l3
+ r1 := mul64(l0_2, l1)
+ r1 = addMul64(r1, l2_38, l4)
+ r1 = addMul64(r1, l3_19, l3)
+
+ // r2 = l0×l2 + l1×l1 + l2×l0 + 19×(l3×l4 + l4×l3) = 2×l0×l2 + l1×l1 + 19×2×l3×l4
+ r2 := mul64(l0_2, l2)
+ r2 = addMul64(r2, l1, l1)
+ r2 = addMul64(r2, l3_38, l4)
+
+ // r3 = l0×l3 + l1×l2 + l2×l1 + l3×l0 + 19×l4×l4 = 2×l0×l3 + 2×l1×l2 + 19×l4×l4
+ r3 := mul64(l0_2, l3)
+ r3 = addMul64(r3, l1_2, l2)
+ r3 = addMul64(r3, l4_19, l4)
+
+ // r4 = l0×l4 + l1×l3 + l2×l2 + l3×l1 + l4×l0 = 2×l0×l4 + 2×l1×l3 + l2×l2
+ r4 := mul64(l0_2, l4)
+ r4 = addMul64(r4, l1_2, l3)
+ r4 = addMul64(r4, l2, l2)
+
+ c0 := shiftRightBy51(r0)
+ c1 := shiftRightBy51(r1)
+ c2 := shiftRightBy51(r2)
+ c3 := shiftRightBy51(r3)
+ c4 := shiftRightBy51(r4)
+
+ rr0 := r0.lo&maskLow51Bits + c4*19
+ rr1 := r1.lo&maskLow51Bits + c0
+ rr2 := r2.lo&maskLow51Bits + c1
+ rr3 := r3.lo&maskLow51Bits + c2
+ rr4 := r4.lo&maskLow51Bits + c3
+
+ *v = Element{rr0, rr1, rr2, rr3, rr4}
+ v.carryPropagate()
+}
+
+// carryPropagate brings the limbs below 52 bits by applying the reduction
+// identity (a * 2²⁵⁵ + b = a * 19 + b) to the l4 carry. TODO inline
+func (v *Element) carryPropagateGeneric() *Element {
+ c0 := v.l0 >> 51
+ c1 := v.l1 >> 51
+ c2 := v.l2 >> 51
+ c3 := v.l3 >> 51
+ c4 := v.l4 >> 51
+
+ v.l0 = v.l0&maskLow51Bits + c4*19
+ v.l1 = v.l1&maskLow51Bits + c0
+ v.l2 = v.l2&maskLow51Bits + c1
+ v.l3 = v.l3&maskLow51Bits + c2
+ v.l4 = v.l4&maskLow51Bits + c3
+
+ return v
+}
--- /dev/null
+b0c49ae9f59d233526f8934262c5bbbe14d4358d
--- /dev/null
+#! /bin/bash
+set -euo pipefail
+
+cd "$(git rev-parse --show-toplevel)"
+
+STD_PATH=src/crypto/ed25519/internal/edwards25519/field
+LOCAL_PATH=curve25519/internal/field
+LAST_SYNC_REF=$(cat $LOCAL_PATH/sync.checkpoint)
+
+git fetch https://go.googlesource.com/go master
+
+if git diff --quiet $LAST_SYNC_REF:$STD_PATH FETCH_HEAD:$STD_PATH; then
+ echo "No changes."
+else
+ NEW_REF=$(git rev-parse FETCH_HEAD | tee $LOCAL_PATH/sync.checkpoint)
+ echo "Applying changes from $LAST_SYNC_REF to $NEW_REF..."
+ git diff $LAST_SYNC_REF:$STD_PATH FETCH_HEAD:$STD_PATH | \
+ git apply -3 --directory=$LOCAL_PATH
+fi
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
+//go:build gc && !purego
// +build gc,!purego
#include "textflag.h"
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
+//go:build gc && !purego
// +build gc,!purego
#include "textflag.h"
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
+//go:build gc && !purego
// +build gc,!purego
#include "textflag.h"
-# golang.org/x/crypto v0.0.0-20210503195802-e9a32991a82e
+# golang.org/x/crypto v0.0.0-20210817164053-32db794688a5
## explicit; go 1.17
golang.org/x/crypto/chacha20
golang.org/x/crypto/chacha20poly1305
golang.org/x/crypto/cryptobyte
golang.org/x/crypto/cryptobyte/asn1
golang.org/x/crypto/curve25519
+golang.org/x/crypto/curve25519/internal/field
golang.org/x/crypto/hkdf
golang.org/x/crypto/internal/subtle
golang.org/x/crypto/poly1305