}
return b
}
+
+func BenchmarkEncodingDecoding(b *testing.B) {
+ p := new(Point).Set(dalekScalarBasepoint)
+ for i := 0; i < b.N; i++ {
+ buf := p.Bytes()
+ _, err := p.SetBytes(buf)
+ if err != nil {
+ b.Fatal(err)
+ }
+ }
+}
module asm
-go 1.16
+go 1.19
-require github.com/mmcloughlin/avo v0.2.0
+require github.com/mmcloughlin/avo v0.4.0
+
+require (
+ golang.org/x/mod v0.4.2 // indirect
+ golang.org/x/sys v0.0.0-20211030160813-b3129d9d1021 // indirect
+ golang.org/x/tools v0.1.7 // indirect
+ golang.org/x/xerrors v0.0.0-20200804184101-5ec99f83aff1 // indirect
+)
-github.com/mmcloughlin/avo v0.2.0 h1:6vhoSaKtxb6f4RiH+LK2qL6GSMpFzhEwJYTTSZNy09w=
-github.com/mmcloughlin/avo v0.2.0/go.mod h1:5tidO2Z9Z7N6X7UMcGg+1KTj51O8OxYDCMHxCZTVpEA=
-github.com/yuin/goldmark v1.2.1/go.mod h1:3hX8gzYuyVAZsxl0MRgGTJEmQBFcNTphYh9decYSb74=
-golang.org/x/arch v0.0.0-20210405154355-08b684f594a5/go.mod h1:flIaEI6LNU6xOCD5PaJvn9wGP0agmIOqjrtsKGRguv4=
+github.com/mmcloughlin/avo v0.4.0 h1:jeHDRktVD+578ULxWpQHkilor6pkdLF7u7EiTzDbfcU=
+github.com/mmcloughlin/avo v0.4.0/go.mod h1:RW9BfYA3TgO9uCdNrKU2h6J8cPD8ZLznvfgHAeszb1s=
+github.com/yuin/goldmark v1.4.0/go.mod h1:mwnBkeHKe2W/ZEtQ+71ViKU8L12m81fl3OWwC1Zlc8k=
+golang.org/x/arch v0.0.0-20210923205945-b76863e36670/go.mod h1:5om86z9Hs0C8fWVUuoMHwpExlXzs5Tkyp9hOrfG7pp8=
golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
golang.org/x/crypto v0.0.0-20191011191535-87dc89f01550/go.mod h1:yigFU9vqHzYiE8UmvKecakEJjdnWj3jj499lnFckfCI=
-golang.org/x/crypto v0.0.0-20200622213623-75b288015ac9/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto=
-golang.org/x/mod v0.3.0 h1:RM4zey1++hCTbCVQfnWeKs9/IEsaBLA8vTkd0WVtmH4=
-golang.org/x/mod v0.3.0/go.mod h1:s0Qsj1ACt9ePp/hMypM3fl4fZqREWJwdYDEqhRiZZUA=
+golang.org/x/mod v0.4.2 h1:Gz96sIWK3OalVv/I/qNygP42zyoKp3xptRVCWRFEBvo=
+golang.org/x/mod v0.4.2/go.mod h1:s0Qsj1ACt9ePp/hMypM3fl4fZqREWJwdYDEqhRiZZUA=
golang.org/x/net v0.0.0-20190404232315-eb5bcb51f2a3/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
golang.org/x/net v0.0.0-20190620200207-3b0461eec859/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s=
-golang.org/x/net v0.0.0-20201021035429-f5854403a974/go.mod h1:sp8m0HH+o8qH0wwXwYZr8TS3Oi6o0r6Gce1SSxlDquU=
+golang.org/x/net v0.0.0-20210805182204-aaa1db679c0d/go.mod h1:9nx3DQGgdP8bBQD5qxJ1jj9UTztislL4KSBs9R2vV5Y=
golang.org/x/sync v0.0.0-20190423024810-112230192c58/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
-golang.org/x/sync v0.0.0-20201020160332-67f06af15bc9/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
+golang.org/x/sync v0.0.0-20210220032951-036812b2e83c/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
golang.org/x/sys v0.0.0-20190412213103-97732733099d/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
-golang.org/x/sys v0.0.0-20200930185726-fdedc70b468f/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
-golang.org/x/sys v0.0.0-20210119212857-b64e53b001e4/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
-golang.org/x/sys v0.0.0-20210403161142-5e06dd20ab57 h1:F5Gozwx4I1xtr/sr/8CFbb57iKi3297KFs0QDbGN60A=
-golang.org/x/sys v0.0.0-20210403161142-5e06dd20ab57/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
+golang.org/x/sys v0.0.0-20201119102817-f84b799fce68/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
+golang.org/x/sys v0.0.0-20210423082822-04245dca01da/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
+golang.org/x/sys v0.0.0-20210809222454-d867a43fc93e/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
+golang.org/x/sys v0.0.0-20211030160813-b3129d9d1021 h1:giLT+HuUP/gXYrG2Plg9WTjj4qhfgaW424ZIFog3rlk=
+golang.org/x/sys v0.0.0-20211030160813-b3129d9d1021/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
+golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo=
golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
-golang.org/x/text v0.3.3/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
+golang.org/x/text v0.3.6/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
golang.org/x/tools v0.0.0-20191119224855-298f0cb1881e/go.mod h1:b+2E5dAYhXwXZwtnZ6UAqBI28+e2cm9otk0dWdXHAEo=
-golang.org/x/tools v0.1.0 h1:po9/4sTYwZU9lPhi1tOrb4hCv3qrhiQ77LZfGa2OjwY=
-golang.org/x/tools v0.1.0/go.mod h1:xkSsbof2nBLbhDlRMhhhyNLN/zl3eTqcnHD5viDpcZ0=
+golang.org/x/tools v0.1.7 h1:6j8CgantCy3yc8JGBqkDLMKWqZ0RDU2g1HVgacojGWQ=
+golang.org/x/tools v0.1.7/go.mod h1:LGqMHiF4EqQNHR1JncWGqT5BVaXmza+X+BDGol+dOxo=
golang.org/x/xerrors v0.0.0-20190717185122-a985d3407aa7/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
golang.org/x/xerrors v0.0.0-20191011141410-1b5146add898/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
golang.org/x/xerrors v0.0.0-20200804184101-5ec99f83aff1 h1:go1bK/D/BFZV2I8cIQd1NKEZ+0owSTG1fDTci4IqFcE=
// 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
+//go:build amd64 && gc && !purego
#include "textflag.h"
import "testing"
func BenchmarkAdd(b *testing.B) {
- var x, y Element
- x.One()
- y.Add(feOne, feOne)
+ x := new(Element).One()
+ y := new(Element).Add(x, x)
b.ResetTimer()
for i := 0; i < b.N; i++ {
- x.Add(&x, &y)
+ x.Add(x, y)
}
}
func BenchmarkMultiply(b *testing.B) {
- var x, y Element
- x.One()
- y.Add(feOne, feOne)
+ x := new(Element).One()
+ y := new(Element).Add(x, x)
b.ResetTimer()
for i := 0; i < b.N; i++ {
- x.Multiply(&x, &y)
+ x.Multiply(x, y)
+ }
+}
+
+func BenchmarkSquare(b *testing.B) {
+ x := new(Element).Add(feOne, feOne)
+ b.ResetTimer()
+ for i := 0; i < b.N; i++ {
+ x.Square(x)
+ }
+}
+
+func BenchmarkInvert(b *testing.B) {
+ x := new(Element).Add(feOne, feOne)
+ b.ResetTimer()
+ for i := 0; i < b.N; i++ {
+ x.Invert(x)
}
}
func BenchmarkMult32(b *testing.B) {
- var x Element
- x.One()
+ x := new(Element).One()
b.ResetTimer()
for i := 0; i < b.N; i++ {
- x.Mult32(&x, 0xaa42aa42)
+ x.Mult32(x, 0xaa42aa42)
}
}
package edwards25519
import (
- "crypto/subtle"
"encoding/binary"
"errors"
)
//
// The zero value is a valid zero element.
type Scalar struct {
- // s is the Scalar value in little-endian. The value is always reduced
- // modulo l between operations.
- s [32]byte
+ // s is the scalar in the Montgomery domain, in the format of the
+ // fiat-crypto implementation.
+ s fiatScalarMontgomeryDomainFieldElement
}
-var (
- scZero = Scalar{[32]byte{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}
-
- scOne = Scalar{[32]byte{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}
-
- scMinusOne = Scalar{[32]byte{236, 211, 245, 92, 26, 99, 18, 88, 214, 156, 247, 162, 222, 249, 222, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16}}
-)
+// The field implementation in scalar_fiat.go is generated by the fiat-crypto
+// project (https://github.com/mit-plv/fiat-crypto) at version v0.0.9 (23d2dbc)
+// from a formally verified model.
+//
+// fiat-crypto code comes under the following license.
+//
+// Copyright (c) 2015-2020 The fiat-crypto Authors. All rights reserved.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+// 1. Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//
+// THIS SOFTWARE IS PROVIDED BY the fiat-crypto authors "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
+// THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL Berkeley Software Design,
+// Inc. BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
// NewScalar returns a new zero Scalar.
func NewScalar() *Scalar {
return &Scalar{}
}
-// MultiplyAdd sets s = x * y + z mod l, and returns s.
+// MultiplyAdd sets s = x * y + z mod l, and returns s. It is equivalent to
+// using Multiply and then Add.
func (s *Scalar) MultiplyAdd(x, y, z *Scalar) *Scalar {
- scMulAdd(&s.s, &x.s, &y.s, &z.s)
- return s
+ // Make a copy of z in case it aliases s.
+ zCopy := new(Scalar).Set(z)
+ return s.Multiply(x, y).Add(s, zCopy)
}
// Add sets s = x + y mod l, and returns s.
func (s *Scalar) Add(x, y *Scalar) *Scalar {
// s = 1 * x + y mod l
- scMulAdd(&s.s, &scOne.s, &x.s, &y.s)
+ fiatScalarAdd(&s.s, &x.s, &y.s)
return s
}
// Subtract sets s = x - y mod l, and returns s.
func (s *Scalar) Subtract(x, y *Scalar) *Scalar {
// s = -1 * y + x mod l
- scMulAdd(&s.s, &scMinusOne.s, &y.s, &x.s)
+ fiatScalarSub(&s.s, &x.s, &y.s)
return s
}
// Negate sets s = -x mod l, and returns s.
func (s *Scalar) Negate(x *Scalar) *Scalar {
// s = -1 * x + 0 mod l
- scMulAdd(&s.s, &scMinusOne.s, &x.s, &scZero.s)
+ fiatScalarOpp(&s.s, &x.s)
return s
}
// Multiply sets s = x * y mod l, and returns s.
func (s *Scalar) Multiply(x, y *Scalar) *Scalar {
// s = x * y + 0 mod l
- scMulAdd(&s.s, &x.s, &y.s, &scZero.s)
+ fiatScalarMul(&s.s, &x.s, &y.s)
return s
}
if len(x) != 64 {
return nil, errors.New("edwards25519: invalid SetUniformBytes input length")
}
- var wideBytes [64]byte
- copy(wideBytes[:], x[:])
- scReduce(&s.s, &wideBytes)
+
+ // We have a value x of 512 bits, but our fiatScalarFromBytes function
+ // expects an input lower than l, which is a little over 252 bits.
+ //
+ // Instead of writing a reduction function that operates on wider inputs, we
+ // can interpret x as the sum of three shorter values a, b, and c.
+ //
+ // x = a + b * 2^168 + c * 2^336 mod l
+ //
+ // We then precompute 2^168 and 2^336 modulo l, and perform the reduction
+ // with two multiplications and two additions.
+
+ s.setShortBytes(x[:21])
+ t := new(Scalar).setShortBytes(x[21:42])
+ s.Add(s, t.Multiply(t, scalarTwo168))
+ t.setShortBytes(x[42:])
+ s.Add(s, t.Multiply(t, scalarTwo336))
+
return s, nil
}
+// scalarTwo168 and scalarTwo336 are 2^168 and 2^336 modulo l, encoded as a
+// fiatScalarMontgomeryDomainFieldElement, which is a little-endian 4-limb value
+// in the 2^256 Montgomery domain.
+var scalarTwo168 = &Scalar{s: [4]uint64{0x5b8ab432eac74798, 0x38afddd6de59d5d7,
+ 0xa2c131b399411b7c, 0x6329a7ed9ce5a30}}
+var scalarTwo336 = &Scalar{s: [4]uint64{0xbd3d108e2b35ecc5, 0x5c3a3718bdf9c90b,
+ 0x63aa97a331b4f2ee, 0x3d217f5be65cb5c}}
+
+// setShortBytes sets s = x mod l, where x is a little-endian integer shorter
+// than 32 bytes.
+func (s *Scalar) setShortBytes(x []byte) *Scalar {
+ if len(x) >= 32 {
+ panic("edwards25519: internal error: setShortBytes called with a long string")
+ }
+ var buf [32]byte
+ copy(buf[:], x)
+ fiatScalarFromBytes((*[4]uint64)(&s.s), &buf)
+ fiatScalarToMontgomery(&s.s, (*fiatScalarNonMontgomeryDomainFieldElement)(&s.s))
+ return s
+}
+
// SetCanonicalBytes sets s = x, where x is a 32-byte little-endian encoding of
// s, and returns s. If x is not a canonical encoding of s, SetCanonicalBytes
// returns nil and an error, and the receiver is unchanged.
if len(x) != 32 {
return nil, errors.New("invalid scalar length")
}
- ss := &Scalar{}
- copy(ss.s[:], x)
- if !isReduced(ss) {
+ if !isReduced(x) {
return nil, errors.New("invalid scalar encoding")
}
- s.s = ss.s
+
+ fiatScalarFromBytes((*[4]uint64)(&s.s), (*[32]byte)(x))
+ fiatScalarToMontgomery(&s.s, (*fiatScalarNonMontgomeryDomainFieldElement)(&s.s))
+
return s, nil
}
-// isReduced returns whether the given scalar is reduced modulo l.
-func isReduced(s *Scalar) bool {
- for i := len(s.s) - 1; i >= 0; i-- {
+// scalarMinusOneBytes is l - 1 in little endian.
+var scalarMinusOneBytes = [32]byte{236, 211, 245, 92, 26, 99, 18, 88, 214, 156, 247, 162, 222, 249, 222, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16}
+
+// isReduced returns whether the given scalar in 32-byte little endian encoded
+// form is reduced modulo l.
+func isReduced(s []byte) bool {
+ if len(s) != 32 {
+ return false
+ }
+
+ for i := len(s) - 1; i >= 0; i-- {
switch {
- case s.s[i] > scMinusOne.s[i]:
+ case s[i] > scalarMinusOneBytes[i]:
return false
- case s.s[i] < scMinusOne.s[i]:
+ case s[i] < scalarMinusOneBytes[i]:
return true
}
}
if len(x) != 32 {
return nil, errors.New("edwards25519: invalid SetBytesWithClamping input length")
}
+
+ // We need to use the wide reduction from SetUniformBytes, since clamping
+ // sets the 2^254 bit, making the value higher than the order.
var wideBytes [64]byte
copy(wideBytes[:], x[:])
wideBytes[0] &= 248
wideBytes[31] &= 63
wideBytes[31] |= 64
- scReduce(&s.s, &wideBytes)
- return s, nil
+ return s.SetUniformBytes(wideBytes[:])
}
// Bytes returns the canonical 32-byte little-endian encoding of s.
func (s *Scalar) Bytes() []byte {
- buf := make([]byte, 32)
- copy(buf, s.s[:])
- return buf
-}
-
-// Equal returns 1 if s and t are equal, and 0 otherwise.
-func (s *Scalar) Equal(t *Scalar) int {
- return subtle.ConstantTimeCompare(s.s[:], t.s[:])
-}
-
-// scMulAdd and scReduce are ported from the public domain, “ref10”
-// implementation of ed25519 from SUPERCOP.
-
-func load3(in []byte) int64 {
- r := int64(in[0])
- r |= int64(in[1]) << 8
- r |= int64(in[2]) << 16
- return r
-}
-
-func load4(in []byte) int64 {
- r := int64(in[0])
- r |= int64(in[1]) << 8
- r |= int64(in[2]) << 16
- r |= int64(in[3]) << 24
- return r
+ // This function is outlined to make the allocations inline in the caller
+ // rather than happen on the heap.
+ var encoded [32]byte
+ return s.bytes(&encoded)
}
-// Input:
-//
-// a[0]+256*a[1]+...+256^31*a[31] = a
-// b[0]+256*b[1]+...+256^31*b[31] = b
-// c[0]+256*c[1]+...+256^31*c[31] = c
-//
-// Output:
-//
-// s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
-// where l = 2^252 + 27742317777372353535851937790883648493.
-func scMulAdd(s, a, b, c *[32]byte) {
- a0 := 2097151 & load3(a[:])
- a1 := 2097151 & (load4(a[2:]) >> 5)
- a2 := 2097151 & (load3(a[5:]) >> 2)
- a3 := 2097151 & (load4(a[7:]) >> 7)
- a4 := 2097151 & (load4(a[10:]) >> 4)
- a5 := 2097151 & (load3(a[13:]) >> 1)
- a6 := 2097151 & (load4(a[15:]) >> 6)
- a7 := 2097151 & (load3(a[18:]) >> 3)
- a8 := 2097151 & load3(a[21:])
- a9 := 2097151 & (load4(a[23:]) >> 5)
- a10 := 2097151 & (load3(a[26:]) >> 2)
- a11 := (load4(a[28:]) >> 7)
- b0 := 2097151 & load3(b[:])
- b1 := 2097151 & (load4(b[2:]) >> 5)
- b2 := 2097151 & (load3(b[5:]) >> 2)
- b3 := 2097151 & (load4(b[7:]) >> 7)
- b4 := 2097151 & (load4(b[10:]) >> 4)
- b5 := 2097151 & (load3(b[13:]) >> 1)
- b6 := 2097151 & (load4(b[15:]) >> 6)
- b7 := 2097151 & (load3(b[18:]) >> 3)
- b8 := 2097151 & load3(b[21:])
- b9 := 2097151 & (load4(b[23:]) >> 5)
- b10 := 2097151 & (load3(b[26:]) >> 2)
- b11 := (load4(b[28:]) >> 7)
- c0 := 2097151 & load3(c[:])
- c1 := 2097151 & (load4(c[2:]) >> 5)
- c2 := 2097151 & (load3(c[5:]) >> 2)
- c3 := 2097151 & (load4(c[7:]) >> 7)
- c4 := 2097151 & (load4(c[10:]) >> 4)
- c5 := 2097151 & (load3(c[13:]) >> 1)
- c6 := 2097151 & (load4(c[15:]) >> 6)
- c7 := 2097151 & (load3(c[18:]) >> 3)
- c8 := 2097151 & load3(c[21:])
- c9 := 2097151 & (load4(c[23:]) >> 5)
- c10 := 2097151 & (load3(c[26:]) >> 2)
- c11 := (load4(c[28:]) >> 7)
- var carry [23]int64
-
- s0 := c0 + a0*b0
- s1 := c1 + a0*b1 + a1*b0
- s2 := c2 + a0*b2 + a1*b1 + a2*b0
- s3 := c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0
- s4 := c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0
- s5 := c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0
- s6 := c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0
- s7 := c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0
- s8 := c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0
- s9 := c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0
- s10 := c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0
- s11 := c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0
- s12 := a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1
- s13 := a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2
- s14 := a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3
- s15 := a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4
- s16 := a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5
- s17 := a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6
- s18 := a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7
- s19 := a8*b11 + a9*b10 + a10*b9 + a11*b8
- s20 := a9*b11 + a10*b10 + a11*b9
- s21 := a10*b11 + a11*b10
- s22 := a11 * b11
- s23 := int64(0)
-
- carry[0] = (s0 + (1 << 20)) >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[2] = (s2 + (1 << 20)) >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[4] = (s4 + (1 << 20)) >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[12] = (s12 + (1 << 20)) >> 21
- s13 += carry[12]
- s12 -= carry[12] << 21
- carry[14] = (s14 + (1 << 20)) >> 21
- s15 += carry[14]
- s14 -= carry[14] << 21
- carry[16] = (s16 + (1 << 20)) >> 21
- s17 += carry[16]
- s16 -= carry[16] << 21
- carry[18] = (s18 + (1 << 20)) >> 21
- s19 += carry[18]
- s18 -= carry[18] << 21
- carry[20] = (s20 + (1 << 20)) >> 21
- s21 += carry[20]
- s20 -= carry[20] << 21
- carry[22] = (s22 + (1 << 20)) >> 21
- s23 += carry[22]
- s22 -= carry[22] << 21
-
- carry[1] = (s1 + (1 << 20)) >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[3] = (s3 + (1 << 20)) >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[5] = (s5 + (1 << 20)) >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
- carry[13] = (s13 + (1 << 20)) >> 21
- s14 += carry[13]
- s13 -= carry[13] << 21
- carry[15] = (s15 + (1 << 20)) >> 21
- s16 += carry[15]
- s15 -= carry[15] << 21
- carry[17] = (s17 + (1 << 20)) >> 21
- s18 += carry[17]
- s17 -= carry[17] << 21
- carry[19] = (s19 + (1 << 20)) >> 21
- s20 += carry[19]
- s19 -= carry[19] << 21
- carry[21] = (s21 + (1 << 20)) >> 21
- s22 += carry[21]
- s21 -= carry[21] << 21
-
- s11 += s23 * 666643
- s12 += s23 * 470296
- s13 += s23 * 654183
- s14 -= s23 * 997805
- s15 += s23 * 136657
- s16 -= s23 * 683901
- s23 = 0
-
- s10 += s22 * 666643
- s11 += s22 * 470296
- s12 += s22 * 654183
- s13 -= s22 * 997805
- s14 += s22 * 136657
- s15 -= s22 * 683901
- s22 = 0
-
- s9 += s21 * 666643
- s10 += s21 * 470296
- s11 += s21 * 654183
- s12 -= s21 * 997805
- s13 += s21 * 136657
- s14 -= s21 * 683901
- s21 = 0
-
- s8 += s20 * 666643
- s9 += s20 * 470296
- s10 += s20 * 654183
- s11 -= s20 * 997805
- s12 += s20 * 136657
- s13 -= s20 * 683901
- s20 = 0
-
- s7 += s19 * 666643
- s8 += s19 * 470296
- s9 += s19 * 654183
- s10 -= s19 * 997805
- s11 += s19 * 136657
- s12 -= s19 * 683901
- s19 = 0
-
- s6 += s18 * 666643
- s7 += s18 * 470296
- s8 += s18 * 654183
- s9 -= s18 * 997805
- s10 += s18 * 136657
- s11 -= s18 * 683901
- s18 = 0
-
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[12] = (s12 + (1 << 20)) >> 21
- s13 += carry[12]
- s12 -= carry[12] << 21
- carry[14] = (s14 + (1 << 20)) >> 21
- s15 += carry[14]
- s14 -= carry[14] << 21
- carry[16] = (s16 + (1 << 20)) >> 21
- s17 += carry[16]
- s16 -= carry[16] << 21
-
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
- carry[13] = (s13 + (1 << 20)) >> 21
- s14 += carry[13]
- s13 -= carry[13] << 21
- carry[15] = (s15 + (1 << 20)) >> 21
- s16 += carry[15]
- s15 -= carry[15] << 21
-
- s5 += s17 * 666643
- s6 += s17 * 470296
- s7 += s17 * 654183
- s8 -= s17 * 997805
- s9 += s17 * 136657
- s10 -= s17 * 683901
- s17 = 0
-
- s4 += s16 * 666643
- s5 += s16 * 470296
- s6 += s16 * 654183
- s7 -= s16 * 997805
- s8 += s16 * 136657
- s9 -= s16 * 683901
- s16 = 0
-
- s3 += s15 * 666643
- s4 += s15 * 470296
- s5 += s15 * 654183
- s6 -= s15 * 997805
- s7 += s15 * 136657
- s8 -= s15 * 683901
- s15 = 0
-
- s2 += s14 * 666643
- s3 += s14 * 470296
- s4 += s14 * 654183
- s5 -= s14 * 997805
- s6 += s14 * 136657
- s7 -= s14 * 683901
- s14 = 0
-
- s1 += s13 * 666643
- s2 += s13 * 470296
- s3 += s13 * 654183
- s4 -= s13 * 997805
- s5 += s13 * 136657
- s6 -= s13 * 683901
- s13 = 0
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = (s0 + (1 << 20)) >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[2] = (s2 + (1 << 20)) >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[4] = (s4 + (1 << 20)) >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
-
- carry[1] = (s1 + (1 << 20)) >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[3] = (s3 + (1 << 20)) >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[5] = (s5 + (1 << 20)) >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = s0 >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[1] = s1 >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[2] = s2 >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[3] = s3 >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[4] = s4 >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[5] = s5 >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[6] = s6 >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[7] = s7 >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[8] = s8 >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[9] = s9 >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[10] = s10 >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[11] = s11 >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = s0 >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[1] = s1 >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[2] = s2 >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[3] = s3 >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[4] = s4 >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[5] = s5 >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[6] = s6 >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[7] = s7 >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[8] = s8 >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[9] = s9 >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[10] = s10 >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
-
- s[0] = byte(s0 >> 0)
- s[1] = byte(s0 >> 8)
- s[2] = byte((s0 >> 16) | (s1 << 5))
- s[3] = byte(s1 >> 3)
- s[4] = byte(s1 >> 11)
- s[5] = byte((s1 >> 19) | (s2 << 2))
- s[6] = byte(s2 >> 6)
- s[7] = byte((s2 >> 14) | (s3 << 7))
- s[8] = byte(s3 >> 1)
- s[9] = byte(s3 >> 9)
- s[10] = byte((s3 >> 17) | (s4 << 4))
- s[11] = byte(s4 >> 4)
- s[12] = byte(s4 >> 12)
- s[13] = byte((s4 >> 20) | (s5 << 1))
- s[14] = byte(s5 >> 7)
- s[15] = byte((s5 >> 15) | (s6 << 6))
- s[16] = byte(s6 >> 2)
- s[17] = byte(s6 >> 10)
- s[18] = byte((s6 >> 18) | (s7 << 3))
- s[19] = byte(s7 >> 5)
- s[20] = byte(s7 >> 13)
- s[21] = byte(s8 >> 0)
- s[22] = byte(s8 >> 8)
- s[23] = byte((s8 >> 16) | (s9 << 5))
- s[24] = byte(s9 >> 3)
- s[25] = byte(s9 >> 11)
- s[26] = byte((s9 >> 19) | (s10 << 2))
- s[27] = byte(s10 >> 6)
- s[28] = byte((s10 >> 14) | (s11 << 7))
- s[29] = byte(s11 >> 1)
- s[30] = byte(s11 >> 9)
- s[31] = byte(s11 >> 17)
+func (s *Scalar) bytes(out *[32]byte) []byte {
+ var ss fiatScalarNonMontgomeryDomainFieldElement
+ fiatScalarFromMontgomery(&ss, &s.s)
+ fiatScalarToBytes(out, (*[4]uint64)(&ss))
+ return out[:]
}
-// Input:
-//
-// s[0]+256*s[1]+...+256^63*s[63] = s
-//
-// Output:
-//
-// s[0]+256*s[1]+...+256^31*s[31] = s mod l
-// where l = 2^252 + 27742317777372353535851937790883648493.
-func scReduce(out *[32]byte, s *[64]byte) {
- s0 := 2097151 & load3(s[:])
- s1 := 2097151 & (load4(s[2:]) >> 5)
- s2 := 2097151 & (load3(s[5:]) >> 2)
- s3 := 2097151 & (load4(s[7:]) >> 7)
- s4 := 2097151 & (load4(s[10:]) >> 4)
- s5 := 2097151 & (load3(s[13:]) >> 1)
- s6 := 2097151 & (load4(s[15:]) >> 6)
- s7 := 2097151 & (load3(s[18:]) >> 3)
- s8 := 2097151 & load3(s[21:])
- s9 := 2097151 & (load4(s[23:]) >> 5)
- s10 := 2097151 & (load3(s[26:]) >> 2)
- s11 := 2097151 & (load4(s[28:]) >> 7)
- s12 := 2097151 & (load4(s[31:]) >> 4)
- s13 := 2097151 & (load3(s[34:]) >> 1)
- s14 := 2097151 & (load4(s[36:]) >> 6)
- s15 := 2097151 & (load3(s[39:]) >> 3)
- s16 := 2097151 & load3(s[42:])
- s17 := 2097151 & (load4(s[44:]) >> 5)
- s18 := 2097151 & (load3(s[47:]) >> 2)
- s19 := 2097151 & (load4(s[49:]) >> 7)
- s20 := 2097151 & (load4(s[52:]) >> 4)
- s21 := 2097151 & (load3(s[55:]) >> 1)
- s22 := 2097151 & (load4(s[57:]) >> 6)
- s23 := (load4(s[60:]) >> 3)
-
- s11 += s23 * 666643
- s12 += s23 * 470296
- s13 += s23 * 654183
- s14 -= s23 * 997805
- s15 += s23 * 136657
- s16 -= s23 * 683901
- s23 = 0
-
- s10 += s22 * 666643
- s11 += s22 * 470296
- s12 += s22 * 654183
- s13 -= s22 * 997805
- s14 += s22 * 136657
- s15 -= s22 * 683901
- s22 = 0
-
- s9 += s21 * 666643
- s10 += s21 * 470296
- s11 += s21 * 654183
- s12 -= s21 * 997805
- s13 += s21 * 136657
- s14 -= s21 * 683901
- s21 = 0
-
- s8 += s20 * 666643
- s9 += s20 * 470296
- s10 += s20 * 654183
- s11 -= s20 * 997805
- s12 += s20 * 136657
- s13 -= s20 * 683901
- s20 = 0
-
- s7 += s19 * 666643
- s8 += s19 * 470296
- s9 += s19 * 654183
- s10 -= s19 * 997805
- s11 += s19 * 136657
- s12 -= s19 * 683901
- s19 = 0
-
- s6 += s18 * 666643
- s7 += s18 * 470296
- s8 += s18 * 654183
- s9 -= s18 * 997805
- s10 += s18 * 136657
- s11 -= s18 * 683901
- s18 = 0
-
- var carry [17]int64
-
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[12] = (s12 + (1 << 20)) >> 21
- s13 += carry[12]
- s12 -= carry[12] << 21
- carry[14] = (s14 + (1 << 20)) >> 21
- s15 += carry[14]
- s14 -= carry[14] << 21
- carry[16] = (s16 + (1 << 20)) >> 21
- s17 += carry[16]
- s16 -= carry[16] << 21
-
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
- carry[13] = (s13 + (1 << 20)) >> 21
- s14 += carry[13]
- s13 -= carry[13] << 21
- carry[15] = (s15 + (1 << 20)) >> 21
- s16 += carry[15]
- s15 -= carry[15] << 21
-
- s5 += s17 * 666643
- s6 += s17 * 470296
- s7 += s17 * 654183
- s8 -= s17 * 997805
- s9 += s17 * 136657
- s10 -= s17 * 683901
- s17 = 0
-
- s4 += s16 * 666643
- s5 += s16 * 470296
- s6 += s16 * 654183
- s7 -= s16 * 997805
- s8 += s16 * 136657
- s9 -= s16 * 683901
- s16 = 0
-
- s3 += s15 * 666643
- s4 += s15 * 470296
- s5 += s15 * 654183
- s6 -= s15 * 997805
- s7 += s15 * 136657
- s8 -= s15 * 683901
- s15 = 0
-
- s2 += s14 * 666643
- s3 += s14 * 470296
- s4 += s14 * 654183
- s5 -= s14 * 997805
- s6 += s14 * 136657
- s7 -= s14 * 683901
- s14 = 0
-
- s1 += s13 * 666643
- s2 += s13 * 470296
- s3 += s13 * 654183
- s4 -= s13 * 997805
- s5 += s13 * 136657
- s6 -= s13 * 683901
- s13 = 0
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = (s0 + (1 << 20)) >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[2] = (s2 + (1 << 20)) >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[4] = (s4 + (1 << 20)) >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[6] = (s6 + (1 << 20)) >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[8] = (s8 + (1 << 20)) >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[10] = (s10 + (1 << 20)) >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
-
- carry[1] = (s1 + (1 << 20)) >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[3] = (s3 + (1 << 20)) >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[5] = (s5 + (1 << 20)) >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[7] = (s7 + (1 << 20)) >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[9] = (s9 + (1 << 20)) >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[11] = (s11 + (1 << 20)) >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = s0 >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[1] = s1 >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[2] = s2 >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[3] = s3 >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[4] = s4 >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[5] = s5 >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[6] = s6 >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[7] = s7 >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[8] = s8 >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[9] = s9 >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[10] = s10 >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
- carry[11] = s11 >> 21
- s12 += carry[11]
- s11 -= carry[11] << 21
-
- s0 += s12 * 666643
- s1 += s12 * 470296
- s2 += s12 * 654183
- s3 -= s12 * 997805
- s4 += s12 * 136657
- s5 -= s12 * 683901
- s12 = 0
-
- carry[0] = s0 >> 21
- s1 += carry[0]
- s0 -= carry[0] << 21
- carry[1] = s1 >> 21
- s2 += carry[1]
- s1 -= carry[1] << 21
- carry[2] = s2 >> 21
- s3 += carry[2]
- s2 -= carry[2] << 21
- carry[3] = s3 >> 21
- s4 += carry[3]
- s3 -= carry[3] << 21
- carry[4] = s4 >> 21
- s5 += carry[4]
- s4 -= carry[4] << 21
- carry[5] = s5 >> 21
- s6 += carry[5]
- s5 -= carry[5] << 21
- carry[6] = s6 >> 21
- s7 += carry[6]
- s6 -= carry[6] << 21
- carry[7] = s7 >> 21
- s8 += carry[7]
- s7 -= carry[7] << 21
- carry[8] = s8 >> 21
- s9 += carry[8]
- s8 -= carry[8] << 21
- carry[9] = s9 >> 21
- s10 += carry[9]
- s9 -= carry[9] << 21
- carry[10] = s10 >> 21
- s11 += carry[10]
- s10 -= carry[10] << 21
-
- out[0] = byte(s0 >> 0)
- out[1] = byte(s0 >> 8)
- out[2] = byte((s0 >> 16) | (s1 << 5))
- out[3] = byte(s1 >> 3)
- out[4] = byte(s1 >> 11)
- out[5] = byte((s1 >> 19) | (s2 << 2))
- out[6] = byte(s2 >> 6)
- out[7] = byte((s2 >> 14) | (s3 << 7))
- out[8] = byte(s3 >> 1)
- out[9] = byte(s3 >> 9)
- out[10] = byte((s3 >> 17) | (s4 << 4))
- out[11] = byte(s4 >> 4)
- out[12] = byte(s4 >> 12)
- out[13] = byte((s4 >> 20) | (s5 << 1))
- out[14] = byte(s5 >> 7)
- out[15] = byte((s5 >> 15) | (s6 << 6))
- out[16] = byte(s6 >> 2)
- out[17] = byte(s6 >> 10)
- out[18] = byte((s6 >> 18) | (s7 << 3))
- out[19] = byte(s7 >> 5)
- out[20] = byte(s7 >> 13)
- out[21] = byte(s8 >> 0)
- out[22] = byte(s8 >> 8)
- out[23] = byte((s8 >> 16) | (s9 << 5))
- out[24] = byte(s9 >> 3)
- out[25] = byte(s9 >> 11)
- out[26] = byte((s9 >> 19) | (s10 << 2))
- out[27] = byte(s10 >> 6)
- out[28] = byte((s10 >> 14) | (s11 << 7))
- out[29] = byte(s11 >> 1)
- out[30] = byte(s11 >> 9)
- out[31] = byte(s11 >> 17)
+// Equal returns 1 if s and t are equal, and 0 otherwise.
+func (s *Scalar) Equal(t *Scalar) int {
+ var diff fiatScalarMontgomeryDomainFieldElement
+ fiatScalarSub(&diff, &s.s, &t.s)
+ var nonzero uint64
+ fiatScalarNonzero(&nonzero, (*[4]uint64)(&diff))
+ nonzero |= nonzero >> 32
+ nonzero |= nonzero >> 16
+ nonzero |= nonzero >> 8
+ nonzero |= nonzero >> 4
+ nonzero |= nonzero >> 2
+ nonzero |= nonzero >> 1
+ return int(^nonzero) & 1
}
// nonAdjacentForm computes a width-w non-adjacent form for this scalar.
// This implementation is adapted from the one
// in curve25519-dalek and is documented there:
// https://github.com/dalek-cryptography/curve25519-dalek/blob/f630041af28e9a405255f98a8a93adca18e4315b/src/scalar.rs#L800-L871
- if s.s[31] > 127 {
+ b := s.Bytes()
+ if b[31] > 127 {
panic("scalar has high bit set illegally")
}
if w < 2 {
var digits [5]uint64
for i := 0; i < 4; i++ {
- digits[i] = binary.LittleEndian.Uint64(s.s[i*8:])
+ digits[i] = binary.LittleEndian.Uint64(b[i*8:])
}
width := uint64(1 << w)
}
func (s *Scalar) signedRadix16() [64]int8 {
- if s.s[31] > 127 {
+ b := s.Bytes()
+ if b[31] > 127 {
panic("scalar has high bit set illegally")
}
// Compute unsigned radix-16 digits:
for i := 0; i < 32; i++ {
- digits[2*i] = int8(s.s[i] & 15)
- digits[2*i+1] = int8((s.s[i] >> 4) & 15)
+ digits[2*i] = int8(b[i] & 15)
+ digits[2*i+1] = int8((b[i] >> 4) & 15)
}
// Recenter coefficients:
x1, v1 := x, x
// Calculate a reference f(x) without aliasing.
- if out := f(&v, &x); out != &v || !isReduced(out) {
+ if out := f(&v, &x); out != &v || !isReduced(out.Bytes()) {
return false
}
// Test aliasing the argument and the receiver.
- if out := f(&v1, &v1); out != &v1 || v1 != v || !isReduced(out) {
+ if out := f(&v1, &v1); out != &v1 || v1 != v || !isReduced(out.Bytes()) {
return false
}
x1, y1, v1 := x, y, Scalar{}
// Calculate a reference f(x, y) without aliasing.
- if out := f(&v, &x, &y); out != &v || !isReduced(out) {
+ if out := f(&v, &x, &y); out != &v || !isReduced(out.Bytes()) {
return false
}
// Test aliasing the first argument and the receiver.
v1 = x
- if out := f(&v1, &v1, &y); out != &v1 || v1 != v || !isReduced(out) {
+ if out := f(&v1, &v1, &y); out != &v1 || v1 != v || !isReduced(out.Bytes()) {
return false
}
// Test aliasing the second argument and the receiver.
v1 = y
- if out := f(&v1, &x, &v1); out != &v1 || v1 != v || !isReduced(out) {
+ if out := f(&v1, &x, &v1); out != &v1 || v1 != v || !isReduced(out.Bytes()) {
return false
}
// Calculate a reference f(x, x) without aliasing.
- if out := f(&v, &x, &x); out != &v || !isReduced(out) {
+ if out := f(&v, &x, &x); out != &v || !isReduced(out.Bytes()) {
return false
}
// Test aliasing the first argument and the receiver.
v1 = x
- if out := f(&v1, &v1, &x); out != &v1 || v1 != v || !isReduced(out) {
+ if out := f(&v1, &v1, &x); out != &v1 || v1 != v || !isReduced(out.Bytes()) {
return false
}
// Test aliasing the second argument and the receiver.
v1 = x
- if out := f(&v1, &x, &v1); out != &v1 || v1 != v || !isReduced(out) {
+ if out := f(&v1, &x, &v1); out != &v1 || v1 != v || !isReduced(out.Bytes()) {
return false
}
// Test aliasing both arguments and the receiver.
v1 = x
- if out := f(&v1, &v1, &v1); out != &v1 || v1 != v || !isReduced(out) {
+ if out := f(&v1, &v1, &v1); out != &v1 || v1 != v || !isReduced(out.Bytes()) {
return false
}
return x == x1 && y == y1
}
- for name, f := range map[string]any{
+ for name, f := range map[string]interface{}{
"Negate": func(v, x Scalar) bool {
return checkAliasingOneArg((*Scalar).Negate, v, x)
},
"Subtract": func(v, x, y Scalar) bool {
return checkAliasingTwoArgs((*Scalar).Subtract, v, x, y)
},
+ "MultiplyAdd1": func(v, x, y, fixed Scalar) bool {
+ return checkAliasingTwoArgs(func(v, x, y *Scalar) *Scalar {
+ return v.MultiplyAdd(&fixed, x, y)
+ }, v, x, y)
+ },
+ "MultiplyAdd2": func(v, x, y, fixed Scalar) bool {
+ return checkAliasingTwoArgs(func(v, x, y *Scalar) *Scalar {
+ return v.MultiplyAdd(x, &fixed, y)
+ }, v, x, y)
+ },
+ "MultiplyAdd3": func(v, x, y, fixed Scalar) bool {
+ return checkAliasingTwoArgs(func(v, x, y *Scalar) *Scalar {
+ return v.MultiplyAdd(x, y, &fixed)
+ }, v, x, y)
+ },
} {
err := quick.Check(f, &quick.Config{MaxCountScale: 1 << 5})
if err != nil {
--- /dev/null
+// Code generated by Fiat Cryptography. DO NOT EDIT.
+//
+// Autogenerated: word_by_word_montgomery --lang Go --cmovznz-by-mul --relax-primitive-carry-to-bitwidth 32,64 --public-function-case camelCase --public-type-case camelCase --private-function-case camelCase --private-type-case camelCase --doc-text-before-function-name '' --doc-newline-before-package-declaration --doc-prepend-header 'Code generated by Fiat Cryptography. DO NOT EDIT.' --package-name edwards25519 Scalar 64 '2^252 + 27742317777372353535851937790883648493' mul add sub opp nonzero from_montgomery to_montgomery to_bytes from_bytes
+//
+// curve description: Scalar
+//
+// machine_wordsize = 64 (from "64")
+//
+// requested operations: mul, add, sub, opp, nonzero, from_montgomery, to_montgomery, to_bytes, from_bytes
+//
+// m = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed (from "2^252 + 27742317777372353535851937790883648493")
+//
+//
+//
+// NOTE: In addition to the bounds specified above each function, all
+//
+// functions synthesized for this Montgomery arithmetic require the
+//
+// input to be strictly less than the prime modulus (m), and also
+//
+// require the input to be in the unique saturated representation.
+//
+// All functions also ensure that these two properties are true of
+//
+// return values.
+//
+//
+//
+// Computed values:
+//
+// eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192)
+//
+// bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248)
+//
+// twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in
+//
+// if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256
+
+package edwards25519
+
+import "math/bits"
+
+type fiatScalarUint1 uint64 // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927
+type fiatScalarInt1 int64 // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927
+
+// The type fiatScalarMontgomeryDomainFieldElement is a field element in the Montgomery domain.
+//
+// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+type fiatScalarMontgomeryDomainFieldElement [4]uint64
+
+// The type fiatScalarNonMontgomeryDomainFieldElement is a field element NOT in the Montgomery domain.
+//
+// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+type fiatScalarNonMontgomeryDomainFieldElement [4]uint64
+
+// fiatScalarCmovznzU64 is a single-word conditional move.
+//
+// Postconditions:
+//
+// out1 = (if arg1 = 0 then arg2 else arg3)
+//
+// Input Bounds:
+//
+// arg1: [0x0 ~> 0x1]
+// arg2: [0x0 ~> 0xffffffffffffffff]
+// arg3: [0x0 ~> 0xffffffffffffffff]
+//
+// Output Bounds:
+//
+// out1: [0x0 ~> 0xffffffffffffffff]
+func fiatScalarCmovznzU64(out1 *uint64, arg1 fiatScalarUint1, arg2 uint64, arg3 uint64) {
+ x1 := (uint64(arg1) * 0xffffffffffffffff)
+ x2 := ((x1 & arg3) | ((^x1) & arg2))
+ *out1 = x2
+}
+
+// fiatScalarMul multiplies two field elements in the Montgomery domain.
+//
+// Preconditions:
+//
+// 0 ≤ eval arg1 < m
+// 0 ≤ eval arg2 < m
+//
+// Postconditions:
+//
+// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m
+// 0 ≤ eval out1 < m
+func fiatScalarMul(out1 *fiatScalarMontgomeryDomainFieldElement, arg1 *fiatScalarMontgomeryDomainFieldElement, arg2 *fiatScalarMontgomeryDomainFieldElement) {
+ x1 := arg1[1]
+ x2 := arg1[2]
+ x3 := arg1[3]
+ x4 := arg1[0]
+ var x5 uint64
+ var x6 uint64
+ x6, x5 = bits.Mul64(x4, arg2[3])
+ var x7 uint64
+ var x8 uint64
+ x8, x7 = bits.Mul64(x4, arg2[2])
+ var x9 uint64
+ var x10 uint64
+ x10, x9 = bits.Mul64(x4, arg2[1])
+ var x11 uint64
+ var x12 uint64
+ x12, x11 = bits.Mul64(x4, arg2[0])
+ var x13 uint64
+ var x14 uint64
+ x13, x14 = bits.Add64(x12, x9, uint64(0x0))
+ var x15 uint64
+ var x16 uint64
+ x15, x16 = bits.Add64(x10, x7, uint64(fiatScalarUint1(x14)))
+ var x17 uint64
+ var x18 uint64
+ x17, x18 = bits.Add64(x8, x5, uint64(fiatScalarUint1(x16)))
+ x19 := (uint64(fiatScalarUint1(x18)) + x6)
+ var x20 uint64
+ _, x20 = bits.Mul64(x11, 0xd2b51da312547e1b)
+ var x22 uint64
+ var x23 uint64
+ x23, x22 = bits.Mul64(x20, 0x1000000000000000)
+ var x24 uint64
+ var x25 uint64
+ x25, x24 = bits.Mul64(x20, 0x14def9dea2f79cd6)
+ var x26 uint64
+ var x27 uint64
+ x27, x26 = bits.Mul64(x20, 0x5812631a5cf5d3ed)
+ var x28 uint64
+ var x29 uint64
+ x28, x29 = bits.Add64(x27, x24, uint64(0x0))
+ x30 := (uint64(fiatScalarUint1(x29)) + x25)
+ var x32 uint64
+ _, x32 = bits.Add64(x11, x26, uint64(0x0))
+ var x33 uint64
+ var x34 uint64
+ x33, x34 = bits.Add64(x13, x28, uint64(fiatScalarUint1(x32)))
+ var x35 uint64
+ var x36 uint64
+ x35, x36 = bits.Add64(x15, x30, uint64(fiatScalarUint1(x34)))
+ var x37 uint64
+ var x38 uint64
+ x37, x38 = bits.Add64(x17, x22, uint64(fiatScalarUint1(x36)))
+ var x39 uint64
+ var x40 uint64
+ x39, x40 = bits.Add64(x19, x23, uint64(fiatScalarUint1(x38)))
+ var x41 uint64
+ var x42 uint64
+ x42, x41 = bits.Mul64(x1, arg2[3])
+ var x43 uint64
+ var x44 uint64
+ x44, x43 = bits.Mul64(x1, arg2[2])
+ var x45 uint64
+ var x46 uint64
+ x46, x45 = bits.Mul64(x1, arg2[1])
+ var x47 uint64
+ var x48 uint64
+ x48, x47 = bits.Mul64(x1, arg2[0])
+ var x49 uint64
+ var x50 uint64
+ x49, x50 = bits.Add64(x48, x45, uint64(0x0))
+ var x51 uint64
+ var x52 uint64
+ x51, x52 = bits.Add64(x46, x43, uint64(fiatScalarUint1(x50)))
+ var x53 uint64
+ var x54 uint64
+ x53, x54 = bits.Add64(x44, x41, uint64(fiatScalarUint1(x52)))
+ x55 := (uint64(fiatScalarUint1(x54)) + x42)
+ var x56 uint64
+ var x57 uint64
+ x56, x57 = bits.Add64(x33, x47, uint64(0x0))
+ var x58 uint64
+ var x59 uint64
+ x58, x59 = bits.Add64(x35, x49, uint64(fiatScalarUint1(x57)))
+ var x60 uint64
+ var x61 uint64
+ x60, x61 = bits.Add64(x37, x51, uint64(fiatScalarUint1(x59)))
+ var x62 uint64
+ var x63 uint64
+ x62, x63 = bits.Add64(x39, x53, uint64(fiatScalarUint1(x61)))
+ var x64 uint64
+ var x65 uint64
+ x64, x65 = bits.Add64(uint64(fiatScalarUint1(x40)), x55, uint64(fiatScalarUint1(x63)))
+ var x66 uint64
+ _, x66 = bits.Mul64(x56, 0xd2b51da312547e1b)
+ var x68 uint64
+ var x69 uint64
+ x69, x68 = bits.Mul64(x66, 0x1000000000000000)
+ var x70 uint64
+ var x71 uint64
+ x71, x70 = bits.Mul64(x66, 0x14def9dea2f79cd6)
+ var x72 uint64
+ var x73 uint64
+ x73, x72 = bits.Mul64(x66, 0x5812631a5cf5d3ed)
+ var x74 uint64
+ var x75 uint64
+ x74, x75 = bits.Add64(x73, x70, uint64(0x0))
+ x76 := (uint64(fiatScalarUint1(x75)) + x71)
+ var x78 uint64
+ _, x78 = bits.Add64(x56, x72, uint64(0x0))
+ var x79 uint64
+ var x80 uint64
+ x79, x80 = bits.Add64(x58, x74, uint64(fiatScalarUint1(x78)))
+ var x81 uint64
+ var x82 uint64
+ x81, x82 = bits.Add64(x60, x76, uint64(fiatScalarUint1(x80)))
+ var x83 uint64
+ var x84 uint64
+ x83, x84 = bits.Add64(x62, x68, uint64(fiatScalarUint1(x82)))
+ var x85 uint64
+ var x86 uint64
+ x85, x86 = bits.Add64(x64, x69, uint64(fiatScalarUint1(x84)))
+ x87 := (uint64(fiatScalarUint1(x86)) + uint64(fiatScalarUint1(x65)))
+ var x88 uint64
+ var x89 uint64
+ x89, x88 = bits.Mul64(x2, arg2[3])
+ var x90 uint64
+ var x91 uint64
+ x91, x90 = bits.Mul64(x2, arg2[2])
+ var x92 uint64
+ var x93 uint64
+ x93, x92 = bits.Mul64(x2, arg2[1])
+ var x94 uint64
+ var x95 uint64
+ x95, x94 = bits.Mul64(x2, arg2[0])
+ var x96 uint64
+ var x97 uint64
+ x96, x97 = bits.Add64(x95, x92, uint64(0x0))
+ var x98 uint64
+ var x99 uint64
+ x98, x99 = bits.Add64(x93, x90, uint64(fiatScalarUint1(x97)))
+ var x100 uint64
+ var x101 uint64
+ x100, x101 = bits.Add64(x91, x88, uint64(fiatScalarUint1(x99)))
+ x102 := (uint64(fiatScalarUint1(x101)) + x89)
+ var x103 uint64
+ var x104 uint64
+ x103, x104 = bits.Add64(x79, x94, uint64(0x0))
+ var x105 uint64
+ var x106 uint64
+ x105, x106 = bits.Add64(x81, x96, uint64(fiatScalarUint1(x104)))
+ var x107 uint64
+ var x108 uint64
+ x107, x108 = bits.Add64(x83, x98, uint64(fiatScalarUint1(x106)))
+ var x109 uint64
+ var x110 uint64
+ x109, x110 = bits.Add64(x85, x100, uint64(fiatScalarUint1(x108)))
+ var x111 uint64
+ var x112 uint64
+ x111, x112 = bits.Add64(x87, x102, uint64(fiatScalarUint1(x110)))
+ var x113 uint64
+ _, x113 = bits.Mul64(x103, 0xd2b51da312547e1b)
+ var x115 uint64
+ var x116 uint64
+ x116, x115 = bits.Mul64(x113, 0x1000000000000000)
+ var x117 uint64
+ var x118 uint64
+ x118, x117 = bits.Mul64(x113, 0x14def9dea2f79cd6)
+ var x119 uint64
+ var x120 uint64
+ x120, x119 = bits.Mul64(x113, 0x5812631a5cf5d3ed)
+ var x121 uint64
+ var x122 uint64
+ x121, x122 = bits.Add64(x120, x117, uint64(0x0))
+ x123 := (uint64(fiatScalarUint1(x122)) + x118)
+ var x125 uint64
+ _, x125 = bits.Add64(x103, x119, uint64(0x0))
+ var x126 uint64
+ var x127 uint64
+ x126, x127 = bits.Add64(x105, x121, uint64(fiatScalarUint1(x125)))
+ var x128 uint64
+ var x129 uint64
+ x128, x129 = bits.Add64(x107, x123, uint64(fiatScalarUint1(x127)))
+ var x130 uint64
+ var x131 uint64
+ x130, x131 = bits.Add64(x109, x115, uint64(fiatScalarUint1(x129)))
+ var x132 uint64
+ var x133 uint64
+ x132, x133 = bits.Add64(x111, x116, uint64(fiatScalarUint1(x131)))
+ x134 := (uint64(fiatScalarUint1(x133)) + uint64(fiatScalarUint1(x112)))
+ var x135 uint64
+ var x136 uint64
+ x136, x135 = bits.Mul64(x3, arg2[3])
+ var x137 uint64
+ var x138 uint64
+ x138, x137 = bits.Mul64(x3, arg2[2])
+ var x139 uint64
+ var x140 uint64
+ x140, x139 = bits.Mul64(x3, arg2[1])
+ var x141 uint64
+ var x142 uint64
+ x142, x141 = bits.Mul64(x3, arg2[0])
+ var x143 uint64
+ var x144 uint64
+ x143, x144 = bits.Add64(x142, x139, uint64(0x0))
+ var x145 uint64
+ var x146 uint64
+ x145, x146 = bits.Add64(x140, x137, uint64(fiatScalarUint1(x144)))
+ var x147 uint64
+ var x148 uint64
+ x147, x148 = bits.Add64(x138, x135, uint64(fiatScalarUint1(x146)))
+ x149 := (uint64(fiatScalarUint1(x148)) + x136)
+ var x150 uint64
+ var x151 uint64
+ x150, x151 = bits.Add64(x126, x141, uint64(0x0))
+ var x152 uint64
+ var x153 uint64
+ x152, x153 = bits.Add64(x128, x143, uint64(fiatScalarUint1(x151)))
+ var x154 uint64
+ var x155 uint64
+ x154, x155 = bits.Add64(x130, x145, uint64(fiatScalarUint1(x153)))
+ var x156 uint64
+ var x157 uint64
+ x156, x157 = bits.Add64(x132, x147, uint64(fiatScalarUint1(x155)))
+ var x158 uint64
+ var x159 uint64
+ x158, x159 = bits.Add64(x134, x149, uint64(fiatScalarUint1(x157)))
+ var x160 uint64
+ _, x160 = bits.Mul64(x150, 0xd2b51da312547e1b)
+ var x162 uint64
+ var x163 uint64
+ x163, x162 = bits.Mul64(x160, 0x1000000000000000)
+ var x164 uint64
+ var x165 uint64
+ x165, x164 = bits.Mul64(x160, 0x14def9dea2f79cd6)
+ var x166 uint64
+ var x167 uint64
+ x167, x166 = bits.Mul64(x160, 0x5812631a5cf5d3ed)
+ var x168 uint64
+ var x169 uint64
+ x168, x169 = bits.Add64(x167, x164, uint64(0x0))
+ x170 := (uint64(fiatScalarUint1(x169)) + x165)
+ var x172 uint64
+ _, x172 = bits.Add64(x150, x166, uint64(0x0))
+ var x173 uint64
+ var x174 uint64
+ x173, x174 = bits.Add64(x152, x168, uint64(fiatScalarUint1(x172)))
+ var x175 uint64
+ var x176 uint64
+ x175, x176 = bits.Add64(x154, x170, uint64(fiatScalarUint1(x174)))
+ var x177 uint64
+ var x178 uint64
+ x177, x178 = bits.Add64(x156, x162, uint64(fiatScalarUint1(x176)))
+ var x179 uint64
+ var x180 uint64
+ x179, x180 = bits.Add64(x158, x163, uint64(fiatScalarUint1(x178)))
+ x181 := (uint64(fiatScalarUint1(x180)) + uint64(fiatScalarUint1(x159)))
+ var x182 uint64
+ var x183 uint64
+ x182, x183 = bits.Sub64(x173, 0x5812631a5cf5d3ed, uint64(0x0))
+ var x184 uint64
+ var x185 uint64
+ x184, x185 = bits.Sub64(x175, 0x14def9dea2f79cd6, uint64(fiatScalarUint1(x183)))
+ var x186 uint64
+ var x187 uint64
+ x186, x187 = bits.Sub64(x177, uint64(0x0), uint64(fiatScalarUint1(x185)))
+ var x188 uint64
+ var x189 uint64
+ x188, x189 = bits.Sub64(x179, 0x1000000000000000, uint64(fiatScalarUint1(x187)))
+ var x191 uint64
+ _, x191 = bits.Sub64(x181, uint64(0x0), uint64(fiatScalarUint1(x189)))
+ var x192 uint64
+ fiatScalarCmovznzU64(&x192, fiatScalarUint1(x191), x182, x173)
+ var x193 uint64
+ fiatScalarCmovznzU64(&x193, fiatScalarUint1(x191), x184, x175)
+ var x194 uint64
+ fiatScalarCmovznzU64(&x194, fiatScalarUint1(x191), x186, x177)
+ var x195 uint64
+ fiatScalarCmovznzU64(&x195, fiatScalarUint1(x191), x188, x179)
+ out1[0] = x192
+ out1[1] = x193
+ out1[2] = x194
+ out1[3] = x195
+}
+
+// fiatScalarAdd adds two field elements in the Montgomery domain.
+//
+// Preconditions:
+//
+// 0 ≤ eval arg1 < m
+// 0 ≤ eval arg2 < m
+//
+// Postconditions:
+//
+// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m
+// 0 ≤ eval out1 < m
+func fiatScalarAdd(out1 *fiatScalarMontgomeryDomainFieldElement, arg1 *fiatScalarMontgomeryDomainFieldElement, arg2 *fiatScalarMontgomeryDomainFieldElement) {
+ var x1 uint64
+ var x2 uint64
+ x1, x2 = bits.Add64(arg1[0], arg2[0], uint64(0x0))
+ var x3 uint64
+ var x4 uint64
+ x3, x4 = bits.Add64(arg1[1], arg2[1], uint64(fiatScalarUint1(x2)))
+ var x5 uint64
+ var x6 uint64
+ x5, x6 = bits.Add64(arg1[2], arg2[2], uint64(fiatScalarUint1(x4)))
+ var x7 uint64
+ var x8 uint64
+ x7, x8 = bits.Add64(arg1[3], arg2[3], uint64(fiatScalarUint1(x6)))
+ var x9 uint64
+ var x10 uint64
+ x9, x10 = bits.Sub64(x1, 0x5812631a5cf5d3ed, uint64(0x0))
+ var x11 uint64
+ var x12 uint64
+ x11, x12 = bits.Sub64(x3, 0x14def9dea2f79cd6, uint64(fiatScalarUint1(x10)))
+ var x13 uint64
+ var x14 uint64
+ x13, x14 = bits.Sub64(x5, uint64(0x0), uint64(fiatScalarUint1(x12)))
+ var x15 uint64
+ var x16 uint64
+ x15, x16 = bits.Sub64(x7, 0x1000000000000000, uint64(fiatScalarUint1(x14)))
+ var x18 uint64
+ _, x18 = bits.Sub64(uint64(fiatScalarUint1(x8)), uint64(0x0), uint64(fiatScalarUint1(x16)))
+ var x19 uint64
+ fiatScalarCmovznzU64(&x19, fiatScalarUint1(x18), x9, x1)
+ var x20 uint64
+ fiatScalarCmovznzU64(&x20, fiatScalarUint1(x18), x11, x3)
+ var x21 uint64
+ fiatScalarCmovznzU64(&x21, fiatScalarUint1(x18), x13, x5)
+ var x22 uint64
+ fiatScalarCmovznzU64(&x22, fiatScalarUint1(x18), x15, x7)
+ out1[0] = x19
+ out1[1] = x20
+ out1[2] = x21
+ out1[3] = x22
+}
+
+// fiatScalarSub subtracts two field elements in the Montgomery domain.
+//
+// Preconditions:
+//
+// 0 ≤ eval arg1 < m
+// 0 ≤ eval arg2 < m
+//
+// Postconditions:
+//
+// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m
+// 0 ≤ eval out1 < m
+func fiatScalarSub(out1 *fiatScalarMontgomeryDomainFieldElement, arg1 *fiatScalarMontgomeryDomainFieldElement, arg2 *fiatScalarMontgomeryDomainFieldElement) {
+ var x1 uint64
+ var x2 uint64
+ x1, x2 = bits.Sub64(arg1[0], arg2[0], uint64(0x0))
+ var x3 uint64
+ var x4 uint64
+ x3, x4 = bits.Sub64(arg1[1], arg2[1], uint64(fiatScalarUint1(x2)))
+ var x5 uint64
+ var x6 uint64
+ x5, x6 = bits.Sub64(arg1[2], arg2[2], uint64(fiatScalarUint1(x4)))
+ var x7 uint64
+ var x8 uint64
+ x7, x8 = bits.Sub64(arg1[3], arg2[3], uint64(fiatScalarUint1(x6)))
+ var x9 uint64
+ fiatScalarCmovznzU64(&x9, fiatScalarUint1(x8), uint64(0x0), 0xffffffffffffffff)
+ var x10 uint64
+ var x11 uint64
+ x10, x11 = bits.Add64(x1, (x9 & 0x5812631a5cf5d3ed), uint64(0x0))
+ var x12 uint64
+ var x13 uint64
+ x12, x13 = bits.Add64(x3, (x9 & 0x14def9dea2f79cd6), uint64(fiatScalarUint1(x11)))
+ var x14 uint64
+ var x15 uint64
+ x14, x15 = bits.Add64(x5, uint64(0x0), uint64(fiatScalarUint1(x13)))
+ var x16 uint64
+ x16, _ = bits.Add64(x7, (x9 & 0x1000000000000000), uint64(fiatScalarUint1(x15)))
+ out1[0] = x10
+ out1[1] = x12
+ out1[2] = x14
+ out1[3] = x16
+}
+
+// fiatScalarOpp negates a field element in the Montgomery domain.
+//
+// Preconditions:
+//
+// 0 ≤ eval arg1 < m
+//
+// Postconditions:
+//
+// eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m
+// 0 ≤ eval out1 < m
+func fiatScalarOpp(out1 *fiatScalarMontgomeryDomainFieldElement, arg1 *fiatScalarMontgomeryDomainFieldElement) {
+ var x1 uint64
+ var x2 uint64
+ x1, x2 = bits.Sub64(uint64(0x0), arg1[0], uint64(0x0))
+ var x3 uint64
+ var x4 uint64
+ x3, x4 = bits.Sub64(uint64(0x0), arg1[1], uint64(fiatScalarUint1(x2)))
+ var x5 uint64
+ var x6 uint64
+ x5, x6 = bits.Sub64(uint64(0x0), arg1[2], uint64(fiatScalarUint1(x4)))
+ var x7 uint64
+ var x8 uint64
+ x7, x8 = bits.Sub64(uint64(0x0), arg1[3], uint64(fiatScalarUint1(x6)))
+ var x9 uint64
+ fiatScalarCmovznzU64(&x9, fiatScalarUint1(x8), uint64(0x0), 0xffffffffffffffff)
+ var x10 uint64
+ var x11 uint64
+ x10, x11 = bits.Add64(x1, (x9 & 0x5812631a5cf5d3ed), uint64(0x0))
+ var x12 uint64
+ var x13 uint64
+ x12, x13 = bits.Add64(x3, (x9 & 0x14def9dea2f79cd6), uint64(fiatScalarUint1(x11)))
+ var x14 uint64
+ var x15 uint64
+ x14, x15 = bits.Add64(x5, uint64(0x0), uint64(fiatScalarUint1(x13)))
+ var x16 uint64
+ x16, _ = bits.Add64(x7, (x9 & 0x1000000000000000), uint64(fiatScalarUint1(x15)))
+ out1[0] = x10
+ out1[1] = x12
+ out1[2] = x14
+ out1[3] = x16
+}
+
+// fiatScalarNonzero outputs a single non-zero word if the input is non-zero and zero otherwise.
+//
+// Preconditions:
+//
+// 0 ≤ eval arg1 < m
+//
+// Postconditions:
+//
+// out1 = 0 ↔ eval (from_montgomery arg1) mod m = 0
+//
+// Input Bounds:
+//
+// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+//
+// Output Bounds:
+//
+// out1: [0x0 ~> 0xffffffffffffffff]
+func fiatScalarNonzero(out1 *uint64, arg1 *[4]uint64) {
+ x1 := (arg1[0] | (arg1[1] | (arg1[2] | arg1[3])))
+ *out1 = x1
+}
+
+// fiatScalarFromMontgomery translates a field element out of the Montgomery domain.
+//
+// Preconditions:
+//
+// 0 ≤ eval arg1 < m
+//
+// Postconditions:
+//
+// eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m
+// 0 ≤ eval out1 < m
+func fiatScalarFromMontgomery(out1 *fiatScalarNonMontgomeryDomainFieldElement, arg1 *fiatScalarMontgomeryDomainFieldElement) {
+ x1 := arg1[0]
+ var x2 uint64
+ _, x2 = bits.Mul64(x1, 0xd2b51da312547e1b)
+ var x4 uint64
+ var x5 uint64
+ x5, x4 = bits.Mul64(x2, 0x1000000000000000)
+ var x6 uint64
+ var x7 uint64
+ x7, x6 = bits.Mul64(x2, 0x14def9dea2f79cd6)
+ var x8 uint64
+ var x9 uint64
+ x9, x8 = bits.Mul64(x2, 0x5812631a5cf5d3ed)
+ var x10 uint64
+ var x11 uint64
+ x10, x11 = bits.Add64(x9, x6, uint64(0x0))
+ var x13 uint64
+ _, x13 = bits.Add64(x1, x8, uint64(0x0))
+ var x14 uint64
+ var x15 uint64
+ x14, x15 = bits.Add64(uint64(0x0), x10, uint64(fiatScalarUint1(x13)))
+ var x16 uint64
+ var x17 uint64
+ x16, x17 = bits.Add64(x14, arg1[1], uint64(0x0))
+ var x18 uint64
+ _, x18 = bits.Mul64(x16, 0xd2b51da312547e1b)
+ var x20 uint64
+ var x21 uint64
+ x21, x20 = bits.Mul64(x18, 0x1000000000000000)
+ var x22 uint64
+ var x23 uint64
+ x23, x22 = bits.Mul64(x18, 0x14def9dea2f79cd6)
+ var x24 uint64
+ var x25 uint64
+ x25, x24 = bits.Mul64(x18, 0x5812631a5cf5d3ed)
+ var x26 uint64
+ var x27 uint64
+ x26, x27 = bits.Add64(x25, x22, uint64(0x0))
+ var x29 uint64
+ _, x29 = bits.Add64(x16, x24, uint64(0x0))
+ var x30 uint64
+ var x31 uint64
+ x30, x31 = bits.Add64((uint64(fiatScalarUint1(x17)) + (uint64(fiatScalarUint1(x15)) + (uint64(fiatScalarUint1(x11)) + x7))), x26, uint64(fiatScalarUint1(x29)))
+ var x32 uint64
+ var x33 uint64
+ x32, x33 = bits.Add64(x4, (uint64(fiatScalarUint1(x27)) + x23), uint64(fiatScalarUint1(x31)))
+ var x34 uint64
+ var x35 uint64
+ x34, x35 = bits.Add64(x5, x20, uint64(fiatScalarUint1(x33)))
+ var x36 uint64
+ var x37 uint64
+ x36, x37 = bits.Add64(x30, arg1[2], uint64(0x0))
+ var x38 uint64
+ var x39 uint64
+ x38, x39 = bits.Add64(x32, uint64(0x0), uint64(fiatScalarUint1(x37)))
+ var x40 uint64
+ var x41 uint64
+ x40, x41 = bits.Add64(x34, uint64(0x0), uint64(fiatScalarUint1(x39)))
+ var x42 uint64
+ _, x42 = bits.Mul64(x36, 0xd2b51da312547e1b)
+ var x44 uint64
+ var x45 uint64
+ x45, x44 = bits.Mul64(x42, 0x1000000000000000)
+ var x46 uint64
+ var x47 uint64
+ x47, x46 = bits.Mul64(x42, 0x14def9dea2f79cd6)
+ var x48 uint64
+ var x49 uint64
+ x49, x48 = bits.Mul64(x42, 0x5812631a5cf5d3ed)
+ var x50 uint64
+ var x51 uint64
+ x50, x51 = bits.Add64(x49, x46, uint64(0x0))
+ var x53 uint64
+ _, x53 = bits.Add64(x36, x48, uint64(0x0))
+ var x54 uint64
+ var x55 uint64
+ x54, x55 = bits.Add64(x38, x50, uint64(fiatScalarUint1(x53)))
+ var x56 uint64
+ var x57 uint64
+ x56, x57 = bits.Add64(x40, (uint64(fiatScalarUint1(x51)) + x47), uint64(fiatScalarUint1(x55)))
+ var x58 uint64
+ var x59 uint64
+ x58, x59 = bits.Add64((uint64(fiatScalarUint1(x41)) + (uint64(fiatScalarUint1(x35)) + x21)), x44, uint64(fiatScalarUint1(x57)))
+ var x60 uint64
+ var x61 uint64
+ x60, x61 = bits.Add64(x54, arg1[3], uint64(0x0))
+ var x62 uint64
+ var x63 uint64
+ x62, x63 = bits.Add64(x56, uint64(0x0), uint64(fiatScalarUint1(x61)))
+ var x64 uint64
+ var x65 uint64
+ x64, x65 = bits.Add64(x58, uint64(0x0), uint64(fiatScalarUint1(x63)))
+ var x66 uint64
+ _, x66 = bits.Mul64(x60, 0xd2b51da312547e1b)
+ var x68 uint64
+ var x69 uint64
+ x69, x68 = bits.Mul64(x66, 0x1000000000000000)
+ var x70 uint64
+ var x71 uint64
+ x71, x70 = bits.Mul64(x66, 0x14def9dea2f79cd6)
+ var x72 uint64
+ var x73 uint64
+ x73, x72 = bits.Mul64(x66, 0x5812631a5cf5d3ed)
+ var x74 uint64
+ var x75 uint64
+ x74, x75 = bits.Add64(x73, x70, uint64(0x0))
+ var x77 uint64
+ _, x77 = bits.Add64(x60, x72, uint64(0x0))
+ var x78 uint64
+ var x79 uint64
+ x78, x79 = bits.Add64(x62, x74, uint64(fiatScalarUint1(x77)))
+ var x80 uint64
+ var x81 uint64
+ x80, x81 = bits.Add64(x64, (uint64(fiatScalarUint1(x75)) + x71), uint64(fiatScalarUint1(x79)))
+ var x82 uint64
+ var x83 uint64
+ x82, x83 = bits.Add64((uint64(fiatScalarUint1(x65)) + (uint64(fiatScalarUint1(x59)) + x45)), x68, uint64(fiatScalarUint1(x81)))
+ x84 := (uint64(fiatScalarUint1(x83)) + x69)
+ var x85 uint64
+ var x86 uint64
+ x85, x86 = bits.Sub64(x78, 0x5812631a5cf5d3ed, uint64(0x0))
+ var x87 uint64
+ var x88 uint64
+ x87, x88 = bits.Sub64(x80, 0x14def9dea2f79cd6, uint64(fiatScalarUint1(x86)))
+ var x89 uint64
+ var x90 uint64
+ x89, x90 = bits.Sub64(x82, uint64(0x0), uint64(fiatScalarUint1(x88)))
+ var x91 uint64
+ var x92 uint64
+ x91, x92 = bits.Sub64(x84, 0x1000000000000000, uint64(fiatScalarUint1(x90)))
+ var x94 uint64
+ _, x94 = bits.Sub64(uint64(0x0), uint64(0x0), uint64(fiatScalarUint1(x92)))
+ var x95 uint64
+ fiatScalarCmovznzU64(&x95, fiatScalarUint1(x94), x85, x78)
+ var x96 uint64
+ fiatScalarCmovznzU64(&x96, fiatScalarUint1(x94), x87, x80)
+ var x97 uint64
+ fiatScalarCmovznzU64(&x97, fiatScalarUint1(x94), x89, x82)
+ var x98 uint64
+ fiatScalarCmovznzU64(&x98, fiatScalarUint1(x94), x91, x84)
+ out1[0] = x95
+ out1[1] = x96
+ out1[2] = x97
+ out1[3] = x98
+}
+
+// fiatScalarToMontgomery translates a field element into the Montgomery domain.
+//
+// Preconditions:
+//
+// 0 ≤ eval arg1 < m
+//
+// Postconditions:
+//
+// eval (from_montgomery out1) mod m = eval arg1 mod m
+// 0 ≤ eval out1 < m
+func fiatScalarToMontgomery(out1 *fiatScalarMontgomeryDomainFieldElement, arg1 *fiatScalarNonMontgomeryDomainFieldElement) {
+ x1 := arg1[1]
+ x2 := arg1[2]
+ x3 := arg1[3]
+ x4 := arg1[0]
+ var x5 uint64
+ var x6 uint64
+ x6, x5 = bits.Mul64(x4, 0x399411b7c309a3d)
+ var x7 uint64
+ var x8 uint64
+ x8, x7 = bits.Mul64(x4, 0xceec73d217f5be65)
+ var x9 uint64
+ var x10 uint64
+ x10, x9 = bits.Mul64(x4, 0xd00e1ba768859347)
+ var x11 uint64
+ var x12 uint64
+ x12, x11 = bits.Mul64(x4, 0xa40611e3449c0f01)
+ var x13 uint64
+ var x14 uint64
+ x13, x14 = bits.Add64(x12, x9, uint64(0x0))
+ var x15 uint64
+ var x16 uint64
+ x15, x16 = bits.Add64(x10, x7, uint64(fiatScalarUint1(x14)))
+ var x17 uint64
+ var x18 uint64
+ x17, x18 = bits.Add64(x8, x5, uint64(fiatScalarUint1(x16)))
+ var x19 uint64
+ _, x19 = bits.Mul64(x11, 0xd2b51da312547e1b)
+ var x21 uint64
+ var x22 uint64
+ x22, x21 = bits.Mul64(x19, 0x1000000000000000)
+ var x23 uint64
+ var x24 uint64
+ x24, x23 = bits.Mul64(x19, 0x14def9dea2f79cd6)
+ var x25 uint64
+ var x26 uint64
+ x26, x25 = bits.Mul64(x19, 0x5812631a5cf5d3ed)
+ var x27 uint64
+ var x28 uint64
+ x27, x28 = bits.Add64(x26, x23, uint64(0x0))
+ var x30 uint64
+ _, x30 = bits.Add64(x11, x25, uint64(0x0))
+ var x31 uint64
+ var x32 uint64
+ x31, x32 = bits.Add64(x13, x27, uint64(fiatScalarUint1(x30)))
+ var x33 uint64
+ var x34 uint64
+ x33, x34 = bits.Add64(x15, (uint64(fiatScalarUint1(x28)) + x24), uint64(fiatScalarUint1(x32)))
+ var x35 uint64
+ var x36 uint64
+ x35, x36 = bits.Add64(x17, x21, uint64(fiatScalarUint1(x34)))
+ var x37 uint64
+ var x38 uint64
+ x38, x37 = bits.Mul64(x1, 0x399411b7c309a3d)
+ var x39 uint64
+ var x40 uint64
+ x40, x39 = bits.Mul64(x1, 0xceec73d217f5be65)
+ var x41 uint64
+ var x42 uint64
+ x42, x41 = bits.Mul64(x1, 0xd00e1ba768859347)
+ var x43 uint64
+ var x44 uint64
+ x44, x43 = bits.Mul64(x1, 0xa40611e3449c0f01)
+ var x45 uint64
+ var x46 uint64
+ x45, x46 = bits.Add64(x44, x41, uint64(0x0))
+ var x47 uint64
+ var x48 uint64
+ x47, x48 = bits.Add64(x42, x39, uint64(fiatScalarUint1(x46)))
+ var x49 uint64
+ var x50 uint64
+ x49, x50 = bits.Add64(x40, x37, uint64(fiatScalarUint1(x48)))
+ var x51 uint64
+ var x52 uint64
+ x51, x52 = bits.Add64(x31, x43, uint64(0x0))
+ var x53 uint64
+ var x54 uint64
+ x53, x54 = bits.Add64(x33, x45, uint64(fiatScalarUint1(x52)))
+ var x55 uint64
+ var x56 uint64
+ x55, x56 = bits.Add64(x35, x47, uint64(fiatScalarUint1(x54)))
+ var x57 uint64
+ var x58 uint64
+ x57, x58 = bits.Add64(((uint64(fiatScalarUint1(x36)) + (uint64(fiatScalarUint1(x18)) + x6)) + x22), x49, uint64(fiatScalarUint1(x56)))
+ var x59 uint64
+ _, x59 = bits.Mul64(x51, 0xd2b51da312547e1b)
+ var x61 uint64
+ var x62 uint64
+ x62, x61 = bits.Mul64(x59, 0x1000000000000000)
+ var x63 uint64
+ var x64 uint64
+ x64, x63 = bits.Mul64(x59, 0x14def9dea2f79cd6)
+ var x65 uint64
+ var x66 uint64
+ x66, x65 = bits.Mul64(x59, 0x5812631a5cf5d3ed)
+ var x67 uint64
+ var x68 uint64
+ x67, x68 = bits.Add64(x66, x63, uint64(0x0))
+ var x70 uint64
+ _, x70 = bits.Add64(x51, x65, uint64(0x0))
+ var x71 uint64
+ var x72 uint64
+ x71, x72 = bits.Add64(x53, x67, uint64(fiatScalarUint1(x70)))
+ var x73 uint64
+ var x74 uint64
+ x73, x74 = bits.Add64(x55, (uint64(fiatScalarUint1(x68)) + x64), uint64(fiatScalarUint1(x72)))
+ var x75 uint64
+ var x76 uint64
+ x75, x76 = bits.Add64(x57, x61, uint64(fiatScalarUint1(x74)))
+ var x77 uint64
+ var x78 uint64
+ x78, x77 = bits.Mul64(x2, 0x399411b7c309a3d)
+ var x79 uint64
+ var x80 uint64
+ x80, x79 = bits.Mul64(x2, 0xceec73d217f5be65)
+ var x81 uint64
+ var x82 uint64
+ x82, x81 = bits.Mul64(x2, 0xd00e1ba768859347)
+ var x83 uint64
+ var x84 uint64
+ x84, x83 = bits.Mul64(x2, 0xa40611e3449c0f01)
+ var x85 uint64
+ var x86 uint64
+ x85, x86 = bits.Add64(x84, x81, uint64(0x0))
+ var x87 uint64
+ var x88 uint64
+ x87, x88 = bits.Add64(x82, x79, uint64(fiatScalarUint1(x86)))
+ var x89 uint64
+ var x90 uint64
+ x89, x90 = bits.Add64(x80, x77, uint64(fiatScalarUint1(x88)))
+ var x91 uint64
+ var x92 uint64
+ x91, x92 = bits.Add64(x71, x83, uint64(0x0))
+ var x93 uint64
+ var x94 uint64
+ x93, x94 = bits.Add64(x73, x85, uint64(fiatScalarUint1(x92)))
+ var x95 uint64
+ var x96 uint64
+ x95, x96 = bits.Add64(x75, x87, uint64(fiatScalarUint1(x94)))
+ var x97 uint64
+ var x98 uint64
+ x97, x98 = bits.Add64(((uint64(fiatScalarUint1(x76)) + (uint64(fiatScalarUint1(x58)) + (uint64(fiatScalarUint1(x50)) + x38))) + x62), x89, uint64(fiatScalarUint1(x96)))
+ var x99 uint64
+ _, x99 = bits.Mul64(x91, 0xd2b51da312547e1b)
+ var x101 uint64
+ var x102 uint64
+ x102, x101 = bits.Mul64(x99, 0x1000000000000000)
+ var x103 uint64
+ var x104 uint64
+ x104, x103 = bits.Mul64(x99, 0x14def9dea2f79cd6)
+ var x105 uint64
+ var x106 uint64
+ x106, x105 = bits.Mul64(x99, 0x5812631a5cf5d3ed)
+ var x107 uint64
+ var x108 uint64
+ x107, x108 = bits.Add64(x106, x103, uint64(0x0))
+ var x110 uint64
+ _, x110 = bits.Add64(x91, x105, uint64(0x0))
+ var x111 uint64
+ var x112 uint64
+ x111, x112 = bits.Add64(x93, x107, uint64(fiatScalarUint1(x110)))
+ var x113 uint64
+ var x114 uint64
+ x113, x114 = bits.Add64(x95, (uint64(fiatScalarUint1(x108)) + x104), uint64(fiatScalarUint1(x112)))
+ var x115 uint64
+ var x116 uint64
+ x115, x116 = bits.Add64(x97, x101, uint64(fiatScalarUint1(x114)))
+ var x117 uint64
+ var x118 uint64
+ x118, x117 = bits.Mul64(x3, 0x399411b7c309a3d)
+ var x119 uint64
+ var x120 uint64
+ x120, x119 = bits.Mul64(x3, 0xceec73d217f5be65)
+ var x121 uint64
+ var x122 uint64
+ x122, x121 = bits.Mul64(x3, 0xd00e1ba768859347)
+ var x123 uint64
+ var x124 uint64
+ x124, x123 = bits.Mul64(x3, 0xa40611e3449c0f01)
+ var x125 uint64
+ var x126 uint64
+ x125, x126 = bits.Add64(x124, x121, uint64(0x0))
+ var x127 uint64
+ var x128 uint64
+ x127, x128 = bits.Add64(x122, x119, uint64(fiatScalarUint1(x126)))
+ var x129 uint64
+ var x130 uint64
+ x129, x130 = bits.Add64(x120, x117, uint64(fiatScalarUint1(x128)))
+ var x131 uint64
+ var x132 uint64
+ x131, x132 = bits.Add64(x111, x123, uint64(0x0))
+ var x133 uint64
+ var x134 uint64
+ x133, x134 = bits.Add64(x113, x125, uint64(fiatScalarUint1(x132)))
+ var x135 uint64
+ var x136 uint64
+ x135, x136 = bits.Add64(x115, x127, uint64(fiatScalarUint1(x134)))
+ var x137 uint64
+ var x138 uint64
+ x137, x138 = bits.Add64(((uint64(fiatScalarUint1(x116)) + (uint64(fiatScalarUint1(x98)) + (uint64(fiatScalarUint1(x90)) + x78))) + x102), x129, uint64(fiatScalarUint1(x136)))
+ var x139 uint64
+ _, x139 = bits.Mul64(x131, 0xd2b51da312547e1b)
+ var x141 uint64
+ var x142 uint64
+ x142, x141 = bits.Mul64(x139, 0x1000000000000000)
+ var x143 uint64
+ var x144 uint64
+ x144, x143 = bits.Mul64(x139, 0x14def9dea2f79cd6)
+ var x145 uint64
+ var x146 uint64
+ x146, x145 = bits.Mul64(x139, 0x5812631a5cf5d3ed)
+ var x147 uint64
+ var x148 uint64
+ x147, x148 = bits.Add64(x146, x143, uint64(0x0))
+ var x150 uint64
+ _, x150 = bits.Add64(x131, x145, uint64(0x0))
+ var x151 uint64
+ var x152 uint64
+ x151, x152 = bits.Add64(x133, x147, uint64(fiatScalarUint1(x150)))
+ var x153 uint64
+ var x154 uint64
+ x153, x154 = bits.Add64(x135, (uint64(fiatScalarUint1(x148)) + x144), uint64(fiatScalarUint1(x152)))
+ var x155 uint64
+ var x156 uint64
+ x155, x156 = bits.Add64(x137, x141, uint64(fiatScalarUint1(x154)))
+ x157 := ((uint64(fiatScalarUint1(x156)) + (uint64(fiatScalarUint1(x138)) + (uint64(fiatScalarUint1(x130)) + x118))) + x142)
+ var x158 uint64
+ var x159 uint64
+ x158, x159 = bits.Sub64(x151, 0x5812631a5cf5d3ed, uint64(0x0))
+ var x160 uint64
+ var x161 uint64
+ x160, x161 = bits.Sub64(x153, 0x14def9dea2f79cd6, uint64(fiatScalarUint1(x159)))
+ var x162 uint64
+ var x163 uint64
+ x162, x163 = bits.Sub64(x155, uint64(0x0), uint64(fiatScalarUint1(x161)))
+ var x164 uint64
+ var x165 uint64
+ x164, x165 = bits.Sub64(x157, 0x1000000000000000, uint64(fiatScalarUint1(x163)))
+ var x167 uint64
+ _, x167 = bits.Sub64(uint64(0x0), uint64(0x0), uint64(fiatScalarUint1(x165)))
+ var x168 uint64
+ fiatScalarCmovznzU64(&x168, fiatScalarUint1(x167), x158, x151)
+ var x169 uint64
+ fiatScalarCmovznzU64(&x169, fiatScalarUint1(x167), x160, x153)
+ var x170 uint64
+ fiatScalarCmovznzU64(&x170, fiatScalarUint1(x167), x162, x155)
+ var x171 uint64
+ fiatScalarCmovznzU64(&x171, fiatScalarUint1(x167), x164, x157)
+ out1[0] = x168
+ out1[1] = x169
+ out1[2] = x170
+ out1[3] = x171
+}
+
+// fiatScalarToBytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order.
+//
+// Preconditions:
+//
+// 0 ≤ eval arg1 < m
+//
+// Postconditions:
+//
+// out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31]
+//
+// Input Bounds:
+//
+// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0x1fffffffffffffff]]
+//
+// Output Bounds:
+//
+// out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x1f]]
+func fiatScalarToBytes(out1 *[32]uint8, arg1 *[4]uint64) {
+ x1 := arg1[3]
+ x2 := arg1[2]
+ x3 := arg1[1]
+ x4 := arg1[0]
+ x5 := (uint8(x4) & 0xff)
+ x6 := (x4 >> 8)
+ x7 := (uint8(x6) & 0xff)
+ x8 := (x6 >> 8)
+ x9 := (uint8(x8) & 0xff)
+ x10 := (x8 >> 8)
+ x11 := (uint8(x10) & 0xff)
+ x12 := (x10 >> 8)
+ x13 := (uint8(x12) & 0xff)
+ x14 := (x12 >> 8)
+ x15 := (uint8(x14) & 0xff)
+ x16 := (x14 >> 8)
+ x17 := (uint8(x16) & 0xff)
+ x18 := uint8((x16 >> 8))
+ x19 := (uint8(x3) & 0xff)
+ x20 := (x3 >> 8)
+ x21 := (uint8(x20) & 0xff)
+ x22 := (x20 >> 8)
+ x23 := (uint8(x22) & 0xff)
+ x24 := (x22 >> 8)
+ x25 := (uint8(x24) & 0xff)
+ x26 := (x24 >> 8)
+ x27 := (uint8(x26) & 0xff)
+ x28 := (x26 >> 8)
+ x29 := (uint8(x28) & 0xff)
+ x30 := (x28 >> 8)
+ x31 := (uint8(x30) & 0xff)
+ x32 := uint8((x30 >> 8))
+ x33 := (uint8(x2) & 0xff)
+ x34 := (x2 >> 8)
+ x35 := (uint8(x34) & 0xff)
+ x36 := (x34 >> 8)
+ x37 := (uint8(x36) & 0xff)
+ x38 := (x36 >> 8)
+ x39 := (uint8(x38) & 0xff)
+ x40 := (x38 >> 8)
+ x41 := (uint8(x40) & 0xff)
+ x42 := (x40 >> 8)
+ x43 := (uint8(x42) & 0xff)
+ x44 := (x42 >> 8)
+ x45 := (uint8(x44) & 0xff)
+ x46 := uint8((x44 >> 8))
+ x47 := (uint8(x1) & 0xff)
+ x48 := (x1 >> 8)
+ x49 := (uint8(x48) & 0xff)
+ x50 := (x48 >> 8)
+ x51 := (uint8(x50) & 0xff)
+ x52 := (x50 >> 8)
+ x53 := (uint8(x52) & 0xff)
+ x54 := (x52 >> 8)
+ x55 := (uint8(x54) & 0xff)
+ x56 := (x54 >> 8)
+ x57 := (uint8(x56) & 0xff)
+ x58 := (x56 >> 8)
+ x59 := (uint8(x58) & 0xff)
+ x60 := uint8((x58 >> 8))
+ out1[0] = x5
+ out1[1] = x7
+ out1[2] = x9
+ out1[3] = x11
+ out1[4] = x13
+ out1[5] = x15
+ out1[6] = x17
+ out1[7] = x18
+ out1[8] = x19
+ out1[9] = x21
+ out1[10] = x23
+ out1[11] = x25
+ out1[12] = x27
+ out1[13] = x29
+ out1[14] = x31
+ out1[15] = x32
+ out1[16] = x33
+ out1[17] = x35
+ out1[18] = x37
+ out1[19] = x39
+ out1[20] = x41
+ out1[21] = x43
+ out1[22] = x45
+ out1[23] = x46
+ out1[24] = x47
+ out1[25] = x49
+ out1[26] = x51
+ out1[27] = x53
+ out1[28] = x55
+ out1[29] = x57
+ out1[30] = x59
+ out1[31] = x60
+}
+
+// fiatScalarFromBytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order.
+//
+// Preconditions:
+//
+// 0 ≤ bytes_eval arg1 < m
+//
+// Postconditions:
+//
+// eval out1 mod m = bytes_eval arg1 mod m
+// 0 ≤ eval out1 < m
+//
+// Input Bounds:
+//
+// arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x1f]]
+//
+// Output Bounds:
+//
+// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0x1fffffffffffffff]]
+func fiatScalarFromBytes(out1 *[4]uint64, arg1 *[32]uint8) {
+ x1 := (uint64(arg1[31]) << 56)
+ x2 := (uint64(arg1[30]) << 48)
+ x3 := (uint64(arg1[29]) << 40)
+ x4 := (uint64(arg1[28]) << 32)
+ x5 := (uint64(arg1[27]) << 24)
+ x6 := (uint64(arg1[26]) << 16)
+ x7 := (uint64(arg1[25]) << 8)
+ x8 := arg1[24]
+ x9 := (uint64(arg1[23]) << 56)
+ x10 := (uint64(arg1[22]) << 48)
+ x11 := (uint64(arg1[21]) << 40)
+ x12 := (uint64(arg1[20]) << 32)
+ x13 := (uint64(arg1[19]) << 24)
+ x14 := (uint64(arg1[18]) << 16)
+ x15 := (uint64(arg1[17]) << 8)
+ x16 := arg1[16]
+ x17 := (uint64(arg1[15]) << 56)
+ x18 := (uint64(arg1[14]) << 48)
+ x19 := (uint64(arg1[13]) << 40)
+ x20 := (uint64(arg1[12]) << 32)
+ x21 := (uint64(arg1[11]) << 24)
+ x22 := (uint64(arg1[10]) << 16)
+ x23 := (uint64(arg1[9]) << 8)
+ x24 := arg1[8]
+ x25 := (uint64(arg1[7]) << 56)
+ x26 := (uint64(arg1[6]) << 48)
+ x27 := (uint64(arg1[5]) << 40)
+ x28 := (uint64(arg1[4]) << 32)
+ x29 := (uint64(arg1[3]) << 24)
+ x30 := (uint64(arg1[2]) << 16)
+ x31 := (uint64(arg1[1]) << 8)
+ x32 := arg1[0]
+ x33 := (x31 + uint64(x32))
+ x34 := (x30 + x33)
+ x35 := (x29 + x34)
+ x36 := (x28 + x35)
+ x37 := (x27 + x36)
+ x38 := (x26 + x37)
+ x39 := (x25 + x38)
+ x40 := (x23 + uint64(x24))
+ x41 := (x22 + x40)
+ x42 := (x21 + x41)
+ x43 := (x20 + x42)
+ x44 := (x19 + x43)
+ x45 := (x18 + x44)
+ x46 := (x17 + x45)
+ x47 := (x15 + uint64(x16))
+ x48 := (x14 + x47)
+ x49 := (x13 + x48)
+ x50 := (x12 + x49)
+ x51 := (x11 + x50)
+ x52 := (x10 + x51)
+ x53 := (x9 + x52)
+ x54 := (x7 + uint64(x8))
+ x55 := (x6 + x54)
+ x56 := (x5 + x55)
+ x57 := (x4 + x56)
+ x58 := (x3 + x57)
+ x59 := (x2 + x58)
+ x60 := (x1 + x59)
+ out1[0] = x39
+ out1[1] = x46
+ out1[2] = x53
+ out1[3] = x60
+}
"testing/quick"
)
+var scOneBytes = [32]byte{1}
+var scOne, _ = new(Scalar).SetCanonicalBytes(scOneBytes[:])
+var scMinusOne, _ = new(Scalar).SetCanonicalBytes(scalarMinusOneBytes[:])
+
// Generate returns a valid (reduced modulo l) Scalar with a distribution
// weighted towards high, low, and edge values.
func (Scalar) Generate(rand *mathrand.Rand, size int) reflect.Value {
- s := scZero
+ var s [32]byte
diceRoll := rand.Intn(100)
switch {
case diceRoll == 0:
case diceRoll == 1:
- s = scOne
+ s = scOneBytes
case diceRoll == 2:
- s = scMinusOne
+ s = scalarMinusOneBytes
case diceRoll < 5:
// Generate a low scalar in [0, 2^125).
- rand.Read(s.s[:16])
- s.s[15] &= (1 << 5) - 1
+ rand.Read(s[:16])
+ s[15] &= (1 << 5) - 1
case diceRoll < 10:
// Generate a high scalar in [2^252, 2^252 + 2^124).
- s.s[31] = 1 << 4
- rand.Read(s.s[:16])
- s.s[15] &= (1 << 4) - 1
+ s[31] = 1 << 4
+ rand.Read(s[:16])
+ s[15] &= (1 << 4) - 1
default:
// Generate a valid scalar in [0, l) by returning [0, 2^252) which has a
// negligibly different distribution (the former has a 2^-127.6 chance
// of being out of the latter range).
- rand.Read(s.s[:])
- s.s[31] &= (1 << 4) - 1
+ rand.Read(s[:])
+ s[31] &= (1 << 4) - 1
}
- return reflect.ValueOf(s)
+
+ val := Scalar{}
+ fiatScalarFromBytes((*[4]uint64)(&val.s), &s)
+ fiatScalarToMontgomery(&val.s, (*fiatScalarNonMontgomeryDomainFieldElement)(&val.s))
+
+ return reflect.ValueOf(val)
}
// quickCheckConfig1024 will make each quickcheck test run (1024 * -quickchecks)
func TestScalarGenerate(t *testing.T) {
f := func(sc Scalar) bool {
- return isReduced(&sc)
+ return isReduced(sc.Bytes())
}
if err := quick.Check(f, quickCheckConfig1024); err != nil {
t.Errorf("generated unreduced scalar: %v", err)
if _, err := sc.SetCanonicalBytes(in[:]); err != nil {
return false
}
- return bytes.Equal(in[:], sc.Bytes()) && isReduced(&sc)
+ repr := sc.Bytes()
+ return bytes.Equal(in[:], repr) && isReduced(repr)
}
if err := quick.Check(f1, quickCheckConfig1024); err != nil {
t.Errorf("failed bytes->scalar->bytes round-trip: %v", err)
t.Errorf("failed scalar->bytes->scalar round-trip: %v", err)
}
- b := scMinusOne.s
+ b := scalarMinusOneBytes
b[31] += 1
s := scOne
if out, err := s.SetCanonicalBytes(b[:]); err == nil {
mod.Add(mod, new(big.Int).Lsh(big.NewInt(1), 252))
f := func(in [64]byte, sc Scalar) bool {
sc.SetUniformBytes(in[:])
- if !isReduced(&sc) {
+ repr := sc.Bytes()
+ if !isReduced(repr) {
return false
}
- scBig := bigIntFromLittleEndianBytes(sc.s[:])
+ scBig := bigIntFromLittleEndianBytes(repr[:])
inBig := bigIntFromLittleEndianBytes(in[:])
return inBig.Mod(inBig, mod).Cmp(scBig) == 0
}
t3.Multiply(&y, &z)
t2.Add(&t2, &t3)
- return t1 == t2 && isReduced(&t1) && isReduced(&t3)
+ reprT1, reprT2 := t1.Bytes(), t2.Bytes()
+
+ return t1 == t2 && isReduced(reprT1) && isReduced(reprT2)
}
if err := quick.Check(multiplyDistributesOverAdd, quickCheckConfig1024); err != nil {
t2.Negate(&y)
t2.Add(&t2, &x)
- return t1 == t2 && isReduced(&t1)
+ return t1 == t2 && isReduced(t1.Bytes())
}
if err := quick.Check(addLikeSubNeg, quickCheckConfig1024); err != nil {
}
func TestScalarNonAdjacentForm(t *testing.T) {
- s := Scalar{[32]byte{
+ s, _ := (&Scalar{}).SetCanonicalBytes([]byte{
0x1a, 0x0e, 0x97, 0x8a, 0x90, 0xf6, 0x62, 0x2d,
0x37, 0x47, 0x02, 0x3f, 0x8a, 0xd8, 0x26, 0x4d,
0xa7, 0x58, 0xaa, 0x1b, 0x88, 0xe0, 0x40, 0xd1,
0x58, 0x9e, 0x7b, 0x7f, 0x23, 0x76, 0xef, 0x09,
- }}
+ })
+
expectedNaf := [256]int8{
0, 13, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, -11, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1,
0, 0, 0, 0, 9, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 11, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0,
func (notZeroScalar) Generate(rand *mathrand.Rand, size int) reflect.Value {
var s Scalar
- for s == scZero {
+ var isNonZero uint64
+ for isNonZero == 0 {
s = Scalar{}.Generate(rand, size).Interface().(Scalar)
+ fiatScalarNonzero(&isNonZero, (*[4]uint64)(&s.s))
}
return reflect.ValueOf(notZeroScalar(s))
}
func TestScalarEqual(t *testing.T) {
- if scOne.Equal(&scMinusOne) == 1 {
+ if scOne.Equal(scMinusOne) == 1 {
t.Errorf("scOne.Equal(&scMinusOne) is true")
}
- if scMinusOne.Equal(&scMinusOne) == 0 {
+ if scMinusOne.Equal(scMinusOne) == 0 {
t.Errorf("scMinusOne.Equal(&scMinusOne) is false")
}
}
quickCheckConfig32 = &quick.Config{MaxCountScale: 1 << 5}
// a random scalar generated using dalek.
- dalekScalar = Scalar{[32]byte{219, 106, 114, 9, 174, 249, 155, 89, 69, 203, 201, 93, 92, 116, 234, 187, 78, 115, 103, 172, 182, 98, 62, 103, 187, 136, 13, 100, 248, 110, 12, 4}}
+ dalekScalar, _ = (&Scalar{}).SetCanonicalBytes([]byte{219, 106, 114, 9, 174, 249, 155, 89, 69, 203, 201, 93, 92, 116, 234, 187, 78, 115, 103, 172, 182, 98, 62, 103, 187, 136, 13, 100, 248, 110, 12, 4})
// the above, times the edwards25519 basepoint.
dalekScalarBasepoint, _ = new(Point).SetBytes([]byte{0xf4, 0xef, 0x7c, 0xa, 0x34, 0x55, 0x7b, 0x9f, 0x72, 0x3b, 0xb6, 0x1e, 0xf9, 0x46, 0x9, 0x91, 0x1c, 0xb9, 0xc0, 0x6c, 0x17, 0x28, 0x2d, 0x8b, 0x43, 0x2b, 0x5, 0x18, 0x6a, 0x54, 0x3e, 0x48})
)
}
checkOnCurve(t, &p)
- z = Scalar{[32]byte{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}
- p.ScalarMult(&z, B)
+ scEight, _ := (&Scalar{}).SetCanonicalBytes([]byte{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
+ p.ScalarMult(scEight, B)
if B.Equal(&p) != 1 {
t.Error("1*B != 1")
}
func TestScalarMultVsDalek(t *testing.T) {
var p Point
- p.ScalarMult(&dalekScalar, B)
+ p.ScalarMult(dalekScalar, B)
if dalekScalarBasepoint.Equal(&p) != 1 {
t.Error("Scalar mul does not match dalek")
}
func TestBaseMultVsDalek(t *testing.T) {
var p Point
- p.ScalarBaseMult(&dalekScalar)
+ p.ScalarBaseMult(dalekScalar)
if dalekScalarBasepoint.Equal(&p) != 1 {
t.Error("Scalar mul does not match dalek")
}
func TestVarTimeDoubleBaseMultVsDalek(t *testing.T) {
var p Point
var z Scalar
- p.VarTimeDoubleScalarBaseMult(&dalekScalar, B, &z)
+ p.VarTimeDoubleScalarBaseMult(dalekScalar, B, &z)
if dalekScalarBasepoint.Equal(&p) != 1 {
t.Error("VarTimeDoubleScalarBaseMult fails with b=0")
}
checkOnCurve(t, &p)
- p.VarTimeDoubleScalarBaseMult(&z, B, &dalekScalar)
+ p.VarTimeDoubleScalarBaseMult(&z, B, dalekScalar)
if dalekScalarBasepoint.Equal(&p) != 1 {
t.Error("VarTimeDoubleScalarBaseMult fails with a=0")
}
var p Point
for i := 0; i < b.N; i++ {
- p.ScalarBaseMult(&dalekScalar)
+ p.ScalarBaseMult(dalekScalar)
}
}
var p Point
for i := 0; i < b.N; i++ {
- p.ScalarMult(&dalekScalar, B)
+ p.ScalarMult(dalekScalar, B)
}
}
var p Point
for i := 0; i < b.N; i++ {
- p.VarTimeDoubleScalarBaseMult(&dalekScalar, B, &dalekScalar)
+ p.VarTimeDoubleScalarBaseMult(dalekScalar, B, dalekScalar)
}
}