crypto, crypto/ecies, crypto/secp256k1: libsecp256k1 scalar mult
thanks to Felix Lange (fjl) for help with design & impl
This commit is contained in:
Gustav Simonsson
335
crypto/secp256k1/curve.go
Normal file
335
crypto/secp256k1/curve.go
Normal file
@ -0,0 +1,335 @@
|
||||
// Copyright 2010 The Go Authors. All rights reserved.
|
||||
// Copyright 2011 ThePiachu. All rights reserved.
|
||||
//
|
||||
// Redistribution and use in source and binary forms, with or without
|
||||
// modification, are permitted provided that the following conditions are
|
||||
// met:
|
||||
//
|
||||
// * Redistributions of source code must retain the above copyright
|
||||
// notice, this list of conditions and the following disclaimer.
|
||||
// * Redistributions in binary form must reproduce the above
|
||||
// copyright notice, this list of conditions and the following disclaimer
|
||||
// in the documentation and/or other materials provided with the
|
||||
// distribution.
|
||||
// * Neither the name of Google Inc. nor the names of its
|
||||
// contributors may be used to endorse or promote products derived from
|
||||
// this software without specific prior written permission.
|
||||
// * The name of ThePiachu may not be used to endorse or promote products
|
||||
// derived from this software without specific prior written permission.
|
||||
//
|
||||
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
// "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 THE COPYRIGHT
|
||||
// OWNER OR CONTRIBUTORS 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.
|
||||
|
||||
package secp256k1
|
||||
|
||||
import (
|
||||
"crypto/elliptic"
|
||||
"io"
|
||||
"math/big"
|
||||
"sync"
|
||||
"unsafe"
|
||||
)
|
||||
|
||||
/*
|
||||
#include "libsecp256k1/include/secp256k1.h"
|
||||
extern int secp256k1_pubkey_scalar_mul(const secp256k1_context* ctx, const unsigned char *point, const unsigned char *scalar);
|
||||
*/
|
||||
import "C"
|
||||
|
||||
// This code is from https://github.com/ThePiachu/GoBit and implements
|
||||
// several Koblitz elliptic curves over prime fields.
|
||||
//
|
||||
// The curve methods, internally, on Jacobian coordinates. For a given
|
||||
// (x, y) position on the curve, the Jacobian coordinates are (x1, y1,
|
||||
// z1) where x = x1/z1² and y = y1/z1³. The greatest speedups come
|
||||
// when the whole calculation can be performed within the transform
|
||||
// (as in ScalarMult and ScalarBaseMult). But even for Add and Double,
|
||||
// it's faster to apply and reverse the transform than to operate in
|
||||
// affine coordinates.
|
||||
|
||||
// A BitCurve represents a Koblitz Curve with a=0.
|
||||
// See http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html
|
||||
type BitCurve struct {
|
||||
P *big.Int // the order of the underlying field
|
||||
N *big.Int // the order of the base point
|
||||
B *big.Int // the constant of the BitCurve equation
|
||||
Gx, Gy *big.Int // (x,y) of the base point
|
||||
BitSize int // the size of the underlying field
|
||||
}
|
||||
|
||||
func (BitCurve *BitCurve) Params() *elliptic.CurveParams {
|
||||
return &elliptic.CurveParams{
|
||||
P: BitCurve.P,
|
||||
N: BitCurve.N,
|
||||
B: BitCurve.B,
|
||||
Gx: BitCurve.Gx,
|
||||
Gy: BitCurve.Gy,
|
||||
BitSize: BitCurve.BitSize,
|
||||
}
|
||||
}
|
||||
|
||||
// IsOnBitCurve returns true if the given (x,y) lies on the BitCurve.
|
||||
func (BitCurve *BitCurve) IsOnCurve(x, y *big.Int) bool {
|
||||
// y² = x³ + b
|
||||
y2 := new(big.Int).Mul(y, y) //y²
|
||||
y2.Mod(y2, BitCurve.P) //y²%P
|
||||
|
||||
x3 := new(big.Int).Mul(x, x) //x²
|
||||
x3.Mul(x3, x) //x³
|
||||
|
||||
x3.Add(x3, BitCurve.B) //x³+B
|
||||
x3.Mod(x3, BitCurve.P) //(x³+B)%P
|
||||
|
||||
return x3.Cmp(y2) == 0
|
||||
}
|
||||
|
||||
//TODO: double check if the function is okay
|
||||
// affineFromJacobian reverses the Jacobian transform. See the comment at the
|
||||
// top of the file.
|
||||
func (BitCurve *BitCurve) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) {
|
||||
zinv := new(big.Int).ModInverse(z, BitCurve.P)
|
||||
zinvsq := new(big.Int).Mul(zinv, zinv)
|
||||
|
||||
xOut = new(big.Int).Mul(x, zinvsq)
|
||||
xOut.Mod(xOut, BitCurve.P)
|
||||
zinvsq.Mul(zinvsq, zinv)
|
||||
yOut = new(big.Int).Mul(y, zinvsq)
|
||||
yOut.Mod(yOut, BitCurve.P)
|
||||
return
|
||||
}
|
||||
|
||||
// Add returns the sum of (x1,y1) and (x2,y2)
|
||||
func (BitCurve *BitCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
|
||||
z := new(big.Int).SetInt64(1)
|
||||
return BitCurve.affineFromJacobian(BitCurve.addJacobian(x1, y1, z, x2, y2, z))
|
||||
}
|
||||
|
||||
// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and
|
||||
// (x2, y2, z2) and returns their sum, also in Jacobian form.
|
||||
func (BitCurve *BitCurve) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) {
|
||||
// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl
|
||||
z1z1 := new(big.Int).Mul(z1, z1)
|
||||
z1z1.Mod(z1z1, BitCurve.P)
|
||||
z2z2 := new(big.Int).Mul(z2, z2)
|
||||
z2z2.Mod(z2z2, BitCurve.P)
|
||||
|
||||
u1 := new(big.Int).Mul(x1, z2z2)
|
||||
u1.Mod(u1, BitCurve.P)
|
||||
u2 := new(big.Int).Mul(x2, z1z1)
|
||||
u2.Mod(u2, BitCurve.P)
|
||||
h := new(big.Int).Sub(u2, u1)
|
||||
if h.Sign() == -1 {
|
||||
h.Add(h, BitCurve.P)
|
||||
}
|
||||
i := new(big.Int).Lsh(h, 1)
|
||||
i.Mul(i, i)
|
||||
j := new(big.Int).Mul(h, i)
|
||||
|
||||
s1 := new(big.Int).Mul(y1, z2)
|
||||
s1.Mul(s1, z2z2)
|
||||
s1.Mod(s1, BitCurve.P)
|
||||
s2 := new(big.Int).Mul(y2, z1)
|
||||
s2.Mul(s2, z1z1)
|
||||
s2.Mod(s2, BitCurve.P)
|
||||
r := new(big.Int).Sub(s2, s1)
|
||||
if r.Sign() == -1 {
|
||||
r.Add(r, BitCurve.P)
|
||||
}
|
||||
r.Lsh(r, 1)
|
||||
v := new(big.Int).Mul(u1, i)
|
||||
|
||||
x3 := new(big.Int).Set(r)
|
||||
x3.Mul(x3, x3)
|
||||
x3.Sub(x3, j)
|
||||
x3.Sub(x3, v)
|
||||
x3.Sub(x3, v)
|
||||
x3.Mod(x3, BitCurve.P)
|
||||
|
||||
y3 := new(big.Int).Set(r)
|
||||
v.Sub(v, x3)
|
||||
y3.Mul(y3, v)
|
||||
s1.Mul(s1, j)
|
||||
s1.Lsh(s1, 1)
|
||||
y3.Sub(y3, s1)
|
||||
y3.Mod(y3, BitCurve.P)
|
||||
|
||||
z3 := new(big.Int).Add(z1, z2)
|
||||
z3.Mul(z3, z3)
|
||||
z3.Sub(z3, z1z1)
|
||||
if z3.Sign() == -1 {
|
||||
z3.Add(z3, BitCurve.P)
|
||||
}
|
||||
z3.Sub(z3, z2z2)
|
||||
if z3.Sign() == -1 {
|
||||
z3.Add(z3, BitCurve.P)
|
||||
}
|
||||
z3.Mul(z3, h)
|
||||
z3.Mod(z3, BitCurve.P)
|
||||
|
||||
return x3, y3, z3
|
||||
}
|
||||
|
||||
// Double returns 2*(x,y)
|
||||
func (BitCurve *BitCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
|
||||
z1 := new(big.Int).SetInt64(1)
|
||||
return BitCurve.affineFromJacobian(BitCurve.doubleJacobian(x1, y1, z1))
|
||||
}
|
||||
|
||||
// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and
|
||||
// returns its double, also in Jacobian form.
|
||||
func (BitCurve *BitCurve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
|
||||
// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
|
||||
|
||||
a := new(big.Int).Mul(x, x) //X1²
|
||||
b := new(big.Int).Mul(y, y) //Y1²
|
||||
c := new(big.Int).Mul(b, b) //B²
|
||||
|
||||
d := new(big.Int).Add(x, b) //X1+B
|
||||
d.Mul(d, d) //(X1+B)²
|
||||
d.Sub(d, a) //(X1+B)²-A
|
||||
d.Sub(d, c) //(X1+B)²-A-C
|
||||
d.Mul(d, big.NewInt(2)) //2*((X1+B)²-A-C)
|
||||
|
||||
e := new(big.Int).Mul(big.NewInt(3), a) //3*A
|
||||
f := new(big.Int).Mul(e, e) //E²
|
||||
|
||||
x3 := new(big.Int).Mul(big.NewInt(2), d) //2*D
|
||||
x3.Sub(f, x3) //F-2*D
|
||||
x3.Mod(x3, BitCurve.P)
|
||||
|
||||
y3 := new(big.Int).Sub(d, x3) //D-X3
|
||||
y3.Mul(e, y3) //E*(D-X3)
|
||||
y3.Sub(y3, new(big.Int).Mul(big.NewInt(8), c)) //E*(D-X3)-8*C
|
||||
y3.Mod(y3, BitCurve.P)
|
||||
|
||||
z3 := new(big.Int).Mul(y, z) //Y1*Z1
|
||||
z3.Mul(big.NewInt(2), z3) //3*Y1*Z1
|
||||
z3.Mod(z3, BitCurve.P)
|
||||
|
||||
return x3, y3, z3
|
||||
}
|
||||
|
||||
func (BitCurve *BitCurve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int) {
|
||||
// Ensure scalar is exactly 32 bytes. We pad always, even if
|
||||
// scalar is 32 bytes long, to avoid a timing side channel.
|
||||
if len(scalar) > 32 {
|
||||
panic("can't handle scalars > 256 bits")
|
||||
}
|
||||
padded := make([]byte, 32)
|
||||
copy(padded[32-len(scalar):], scalar)
|
||||
scalar = padded
|
||||
|
||||
// Do the multiplication in C, updating point.
|
||||
point := make([]byte, 64)
|
||||
readBits(point[:32], Bx)
|
||||
readBits(point[32:], By)
|
||||
pointPtr := (*C.uchar)(unsafe.Pointer(&point[0]))
|
||||
scalarPtr := (*C.uchar)(unsafe.Pointer(&scalar[0]))
|
||||
res := C.secp256k1_pubkey_scalar_mul(context, pointPtr, scalarPtr)
|
||||
|
||||
// Unpack the result and clear temporaries.
|
||||
x := new(big.Int).SetBytes(point[:32])
|
||||
y := new(big.Int).SetBytes(point[32:])
|
||||
for i := range point {
|
||||
point[i] = 0
|
||||
}
|
||||
for i := range padded {
|
||||
scalar[i] = 0
|
||||
}
|
||||
if res != 1 {
|
||||
return nil, nil
|
||||
}
|
||||
return x, y
|
||||
}
|
||||
|
||||
// ScalarBaseMult returns k*G, where G is the base point of the group and k is
|
||||
// an integer in big-endian form.
|
||||
func (BitCurve *BitCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
|
||||
return BitCurve.ScalarMult(BitCurve.Gx, BitCurve.Gy, k)
|
||||
}
|
||||
|
||||
var mask = []byte{0xff, 0x1, 0x3, 0x7, 0xf, 0x1f, 0x3f, 0x7f}
|
||||
|
||||
//TODO: double check if it is okay
|
||||
// GenerateKey returns a public/private key pair. The private key is generated
|
||||
// using the given reader, which must return random data.
|
||||
func (BitCurve *BitCurve) GenerateKey(rand io.Reader) (priv []byte, x, y *big.Int, err error) {
|
||||
byteLen := (BitCurve.BitSize + 7) >> 3
|
||||
priv = make([]byte, byteLen)
|
||||
|
||||
for x == nil {
|
||||
_, err = io.ReadFull(rand, priv)
|
||||
if err != nil {
|
||||
return
|
||||
}
|
||||
// We have to mask off any excess bits in the case that the size of the
|
||||
// underlying field is not a whole number of bytes.
|
||||
priv[0] &= mask[BitCurve.BitSize%8]
|
||||
// This is because, in tests, rand will return all zeros and we don't
|
||||
// want to get the point at infinity and loop forever.
|
||||
priv[1] ^= 0x42
|
||||
x, y = BitCurve.ScalarBaseMult(priv)
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Marshal converts a point into the form specified in section 4.3.6 of ANSI
|
||||
// X9.62.
|
||||
func (BitCurve *BitCurve) Marshal(x, y *big.Int) []byte {
|
||||
byteLen := (BitCurve.BitSize + 7) >> 3
|
||||
|
||||
ret := make([]byte, 1+2*byteLen)
|
||||
ret[0] = 4 // uncompressed point
|
||||
|
||||
xBytes := x.Bytes()
|
||||
copy(ret[1+byteLen-len(xBytes):], xBytes)
|
||||
yBytes := y.Bytes()
|
||||
copy(ret[1+2*byteLen-len(yBytes):], yBytes)
|
||||
return ret
|
||||
}
|
||||
|
||||
// Unmarshal converts a point, serialised by Marshal, into an x, y pair. On
|
||||
// error, x = nil.
|
||||
func (BitCurve *BitCurve) Unmarshal(data []byte) (x, y *big.Int) {
|
||||
byteLen := (BitCurve.BitSize + 7) >> 3
|
||||
if len(data) != 1+2*byteLen {
|
||||
return
|
||||
}
|
||||
if data[0] != 4 { // uncompressed form
|
||||
return
|
||||
}
|
||||
x = new(big.Int).SetBytes(data[1 : 1+byteLen])
|
||||
y = new(big.Int).SetBytes(data[1+byteLen:])
|
||||
return
|
||||
}
|
||||
|
||||
var (
|
||||
initonce sync.Once
|
||||
theCurve *BitCurve
|
||||
)
|
||||
|
||||
// S256 returns a BitCurve which implements secp256k1 (see SEC 2 section 2.7.1)
|
||||
func S256() *BitCurve {
|
||||
initonce.Do(func() {
|
||||
// See SEC 2 section 2.7.1
|
||||
// curve parameters taken from:
|
||||
// http://www.secg.org/collateral/sec2_final.pdf
|
||||
theCurve = new(BitCurve)
|
||||
theCurve.P, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", 16)
|
||||
theCurve.N, _ = new(big.Int).SetString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 16)
|
||||
theCurve.B, _ = new(big.Int).SetString("0000000000000000000000000000000000000000000000000000000000000007", 16)
|
||||
theCurve.Gx, _ = new(big.Int).SetString("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", 16)
|
||||
theCurve.Gy, _ = new(big.Int).SetString("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", 16)
|
||||
theCurve.BitSize = 256
|
||||
})
|
||||
return theCurve
|
||||
}
|
||||
Reference in New Issue
Block a user