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hash.go
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hash.go
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//
// Copyright Coinbase, Inc. All Rights Reserved.
//
// SPDX-License-Identifier: Apache-2.0
//
package core
import (
"bytes"
"crypto/elliptic"
"crypto/sha256"
"fmt"
"hash"
"math"
"math/big"
"github.com/btcsuite/btcd/btcec"
"golang.org/x/crypto/hkdf"
"github.com/coinbase/kryptology/internal"
)
type HashField struct {
// F_p^k
Order *big.Int // p^k
Characteristic *big.Int // p
ExtensionDegree *big.Int // k
}
type Params struct {
F *HashField
SecurityParameter int
Hash func() hash.Hash
L int
}
func getParams(curve elliptic.Curve) (*Params, error) {
switch curve.Params().Name {
case btcec.S256().Name, elliptic.P256().Params().Name:
return &Params{
F: &HashField{
Order: curve.Params().P,
Characteristic: curve.Params().P,
ExtensionDegree: new(big.Int).SetInt64(1),
},
SecurityParameter: 128,
Hash: sha256.New,
L: 48,
}, nil
case "Bls12381G1":
return &Params{
F: &HashField{
Order: curve.Params().P,
Characteristic: curve.Params().P,
ExtensionDegree: new(big.Int).SetInt64(1),
},
SecurityParameter: 128,
Hash: sha256.New,
L: 48,
}, nil
case "ed25519":
return &Params{
F: &HashField{
Order: curve.Params().P,
Characteristic: curve.Params().P,
ExtensionDegree: new(big.Int).SetInt64(1),
},
SecurityParameter: 128,
Hash: sha256.New,
L: 48,
}, nil
default:
return nil, fmt.Errorf("Not implemented: %s", curve.Params().Name)
}
}
func I2OSP(b, n int) []byte {
os := new(big.Int).SetInt64(int64(b)).Bytes()
if n > len(os) {
var buf bytes.Buffer
buf.Write(make([]byte, n-len(os)))
buf.Write(os)
return buf.Bytes()
}
return os[:n]
}
func OS2IP(os []byte) *big.Int {
return new(big.Int).SetBytes(os)
}
func hashThis(f func() hash.Hash, this []byte) ([]byte, error) {
h := f()
w, err := h.Write(this)
if w != len(this) {
return nil, fmt.Errorf("bytes written to hash doesn't match expected")
} else if err != nil {
return nil, err
}
v := h.Sum(nil)
return v, nil
}
func concat(xs ...[]byte) []byte {
var result []byte
for _, x := range xs {
result = append(result, x...)
}
return result
}
func xor(b1, b2 []byte) []byte {
// b1 and b2 must be same length
result := make([]byte, len(b1))
for i := range b1 {
result[i] = b1[i] ^ b2[i]
}
return result
}
func ExpandMessageXmd(f func() hash.Hash, msg, DST []byte, lenInBytes int) ([]byte, error) {
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-10#section-5.4.1
// step 1
ell := int(math.Ceil(float64(lenInBytes) / float64(f().Size())))
//step 2
if ell > 255 {
return nil, fmt.Errorf("ell > 255")
}
// step 3
dstPrime := append(DST, I2OSP(len(DST), 1)...)
// step 4
zPad := I2OSP(0, f().BlockSize())
// step 5 & 6
msgPrime := concat(zPad, msg, I2OSP(lenInBytes, 2), I2OSP(0, 1), dstPrime)
var err error
b := make([][]byte, ell+1)
// step 7
b[0], err = hashThis(f, msgPrime)
if err != nil {
return nil, err
}
// step 8
b[1], err = hashThis(f, concat(b[0], I2OSP(1, 1), dstPrime))
if err != nil {
return nil, err
}
// step 9
for i := 2; i <= ell; i++ {
// step 10
b[i], err = hashThis(f, concat(xor(b[0], b[i-1]), I2OSP(i, 1), dstPrime))
if err != nil {
return nil, err
}
}
// step 11
uniformBytes := concat(b[1:]...)
// step 12
return uniformBytes[:lenInBytes], nil
}
func hashToField(msg []byte, count int, curve elliptic.Curve) ([][]*big.Int, error) {
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-10#section-5.3
parameters, err := getParams(curve)
if err != nil {
return nil, err
}
f := parameters.Hash
DST := []byte("Coinbase_tECDSA")
m := int(parameters.F.ExtensionDegree.Int64())
L := parameters.L
// step 1
lenInBytes := count * m * L
// step 2
uniformBytes, err := ExpandMessageXmd(f, msg, DST, lenInBytes)
if err != nil {
return nil, err
}
u := make([][]*big.Int, count)
// step 3
for i := 0; i < count; i++ {
e := make([]*big.Int, m)
// step 4
for j := 0; j < m; j++ {
// step 5
elmOffset := L * (j + i*m)
// step 6
tv := uniformBytes[elmOffset : elmOffset+L]
// step 7
e[j] = new(big.Int).Mod(OS2IP(tv), parameters.F.Characteristic)
}
// step 8
u[i] = e
}
// step 9
return u, nil
}
func Hash(msg []byte, curve elliptic.Curve) (*big.Int, error) {
u, err := hashToField(msg, 1, curve)
if err != nil {
return nil, err
}
return u[0][0], nil
}
// fiatShamir computes the HKDF over many values
// iteratively such that each value is hashed separately
// and based on preceding values
//
// The first value is computed as okm_0 = KDF(f || value) where
// f is a byte slice of 32 0xFF
// salt is zero-filled byte slice with length equal to the hash output length
// info is the protocol name
// okm is the 32 byte output
//
// The each subsequent iteration is computed by as okm_i = KDF(f_i || value || okm_{i-1})
// where f_i = 2^b - 1 - i such that there are 0xFF bytes prior to the value.
// f_1 changes the first byte to 0xFE, f_2 to 0xFD. The previous okm is appended to the value
// to provide cryptographic domain separation.
// See https://signal.org/docs/specifications/x3dh/#cryptographic-notation
// and https://signal.org/docs/specifications/xeddsa/#hash-functions
// for more details.
// This uses the KDF function similar to X3DH for each `value`
// But changes the key just like XEdDSA where the prefix bytes change by a single bit
func FiatShamir(values ...*big.Int) ([]byte, error) {
// Don't accept any nil arguments
if AnyNil(values...) {
return nil, internal.ErrNilArguments
}
info := []byte("Coinbase tECDSA 1.0")
salt := make([]byte, 32)
okm := make([]byte, 32)
f := bytes.Repeat([]byte{0xFF}, 32)
for _, b := range values {
ikm := append(f, b.Bytes()...)
ikm = append(ikm, okm...)
kdf := hkdf.New(sha256.New, ikm, salt, info)
n, err := kdf.Read(okm)
if err != nil {
return nil, err
}
if n != len(okm) {
return nil, fmt.Errorf("unable to read expected number of bytes want=%v got=%v", len(okm), n)
}
internal.ByteSub(f)
}
return okm, nil
}