/
field.go
289 lines (260 loc) · 5.83 KB
/
field.go
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// Copyright 2016 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 ed25519
import (
"encoding/binary"
"fmt"
"math/big"
)
// This file contains field element logic that is independent of the
// representation.
var zero FieldElement
func load3(in []byte) int64 {
var r int64
r = int64(in[0])
r |= int64(in[1]) << 8
r |= int64(in[2]) << 16
return r
}
func load4(in []byte) int64 {
var r int64
r = int64(in[0])
r |= int64(in[1]) << 8
r |= int64(in[2]) << 16
r |= int64(in[3]) << 24
return r
}
func FeZero(fe *FieldElement) {
copy(fe[:], zero[:])
}
func FeOne(fe *FieldElement) {
FeZero(fe)
fe[0] = 1
}
func FeCopy(dst, src *FieldElement) {
copy(dst[:], src[:])
}
func FeIsNegative(f *FieldElement) byte {
var s [32]byte
FeToBytes(&s, f)
return s[0] & 1
}
func FeIsNonZero(f *FieldElement) int32 {
var s [32]byte
FeToBytes(&s, f)
var x uint8
for _, b := range s {
x |= b
}
x |= x >> 4
x |= x >> 2
x |= x >> 1
return int32(x & 1)
}
func FeInvert(out, z *FieldElement) {
var t0, t1, t2, t3 FieldElement
var i int
FeSquare(&t0, z) // 2^1
FeSquare(&t1, &t0) // 2^2
for i = 1; i < 2; i++ { // 2^3
FeSquare(&t1, &t1)
}
FeMul(&t1, z, &t1) // 2^3 + 2^0
FeMul(&t0, &t0, &t1) // 2^3 + 2^1 + 2^0
FeSquare(&t2, &t0) // 2^4 + 2^2 + 2^1
FeMul(&t1, &t1, &t2) // 2^4 + 2^3 + 2^2 + 2^1 + 2^0
FeSquare(&t2, &t1) // 5,4,3,2,1
for i = 1; i < 5; i++ { // 9,8,7,6,5
FeSquare(&t2, &t2)
}
FeMul(&t1, &t2, &t1) // 9,8,7,6,5,4,3,2,1,0
FeSquare(&t2, &t1) // 10..1
for i = 1; i < 10; i++ { // 19..10
FeSquare(&t2, &t2)
}
FeMul(&t2, &t2, &t1) // 19..0
FeSquare(&t3, &t2) // 20..1
for i = 1; i < 20; i++ { // 39..20
FeSquare(&t3, &t3)
}
FeMul(&t2, &t3, &t2) // 39..0
FeSquare(&t2, &t2) // 40..1
for i = 1; i < 10; i++ { // 49..10
FeSquare(&t2, &t2)
}
FeMul(&t1, &t2, &t1) // 49..0
FeSquare(&t2, &t1) // 50..1
for i = 1; i < 50; i++ { // 99..50
FeSquare(&t2, &t2)
}
FeMul(&t2, &t2, &t1) // 99..0
FeSquare(&t3, &t2) // 100..1
for i = 1; i < 100; i++ { // 199..100
FeSquare(&t3, &t3)
}
FeMul(&t2, &t3, &t2) // 199..0
FeSquare(&t2, &t2) // 200..1
for i = 1; i < 50; i++ { // 249..50
FeSquare(&t2, &t2)
}
FeMul(&t1, &t2, &t1) // 249..0
FeSquare(&t1, &t1) // 250..1
for i = 1; i < 5; i++ { // 254..5
FeSquare(&t1, &t1)
}
FeMul(out, &t1, &t0) // 254..5,3,1,0
}
// Returns whether fe equals a.
func (fe *FieldElement) Equals(a *FieldElement) bool {
var b FieldElement
FeSub(&b, fe, a)
return b.IsNonZeroI() == 0
}
// Returns 1 if fe is non-zero, otherwise 0.
func (fe *FieldElement) IsNonZeroI() int32 {
var buf [32]byte
FeToBytes(&buf, fe)
ret := (binary.LittleEndian.Uint64(buf[0:8]) |
binary.LittleEndian.Uint64(buf[8:16]) |
binary.LittleEndian.Uint64(buf[16:24]) |
binary.LittleEndian.Uint64(buf[24:32]))
ret |= ret >> 32
ret |= ret >> 16
ret |= ret >> 8
ret |= ret >> 4
ret |= ret >> 2
ret |= ret >> 1
return int32(ret & 1)
}
// Returns 1 if fe is equal to one, otherwise 0.
func (fe *FieldElement) IsOneI() int32 {
var b, fe1 FieldElement
FeOne(&fe1)
FeSub(&b, fe, &fe1)
return 1 - b.IsNonZeroI()
}
// Returns 1 if fe is negative, otherwise 0.
func (fe *FieldElement) IsNegativeI() int32 {
var buf [32]byte
FeToBytes(&buf, fe)
return int32(buf[0] & 1)
}
// Sets fe to 1/sqrt(a). Requires a to be a square. Returns fe.
func FeInvSqrt(out, a *FieldElement) {
var den2, den3, den4, den6, chk, t, t2 FieldElement
FeSquare(&den2, a)
FeMul(&den3, &den2, a)
FeSquare(&den4, &den2)
FeMul(&den6, &den2, &den4)
FeMul(&t, &den6, a)
fePow22523(&t, &t)
FeMul(&t, &t, &den3)
FeMul(&t2, &t, &sqrtM1)
FeSquare(&chk, &t)
FeMul(&chk, &chk, a)
FeCopy(out, &t)
FeCMove(out, &t2, 1-chk.IsOneI())
}
// Sets fe to sqrt(a). Requires a to be a square. Returns fe.
func FeSqrt(out, a *FieldElement) {
var aCopy FieldElement
FeCopy(&aCopy, a)
FeInvSqrt(out, a)
FeMul(out, out, &aCopy)
var fn FieldElement
FeNeg(&fn, out)
FeCMove(out, &fn, out.IsNegativeI())
}
func fePow22523(out, z *FieldElement) {
var t0, t1, t2 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(&t0, &t0)
for i = 1; i < 1; i++ {
FeSquare(&t0, &t0)
}
FeMul(&t0, &t1, &t0)
FeSquare(&t1, &t0)
for i = 1; i < 5; i++ {
FeSquare(&t1, &t1)
}
FeMul(&t0, &t1, &t0)
FeSquare(&t1, &t0)
for i = 1; i < 10; i++ {
FeSquare(&t1, &t1)
}
FeMul(&t1, &t1, &t0)
FeSquare(&t2, &t1)
for i = 1; i < 20; i++ {
FeSquare(&t2, &t2)
}
FeMul(&t1, &t2, &t1)
FeSquare(&t1, &t1)
for i = 1; i < 10; i++ {
FeSquare(&t1, &t1)
}
FeMul(&t0, &t1, &t0)
FeSquare(&t1, &t0)
for i = 1; i < 50; i++ {
FeSquare(&t1, &t1)
}
FeMul(&t1, &t1, &t0)
FeSquare(&t2, &t1)
for i = 1; i < 100; i++ {
FeSquare(&t2, &t2)
}
FeMul(&t1, &t2, &t1)
FeSquare(&t1, &t1)
for i = 1; i < 50; i++ {
FeSquare(&t1, &t1)
}
FeMul(&t0, &t1, &t0)
FeSquare(&t0, &t0)
for i = 1; i < 2; i++ {
FeSquare(&t0, &t0)
}
FeMul(out, &t0, z)
}
func (fe *FieldElement) String() string {
s := "FieldElement{"
for i := range fe {
if i > 0 {
s += ", "
}
s += fmt.Sprintf("%d", fe[i])
}
s += "}"
return s
}
//
// TESTING PURPOSES ONLY!!
//
func (fe *FieldElement) bigInt() *big.Int {
var ret big.Int
var buf, rBuf [32]byte
FeToBytes(&buf, fe)
for i := 0; i < 32; i++ {
rBuf[i] = buf[31-i]
}
return ret.SetBytes(rBuf[:])
}
func (fe *FieldElement) setBigInt(x *big.Int) {
var v, bi25519 big.Int
bi25519.SetString("7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed", 16)
buf := v.Mod(x, &bi25519).Bytes()
var rBuf [32]byte
for i := 0; i < len(buf) && i < 32; i++ {
rBuf[i] = buf[len(buf)-i-1]
}
FeFromBytes(fe, rBuf[:])
}