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crypto, crypto/ecies, crypto/secp256k1: libsecp256k1 scalar mult

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thanks to Felix Lange (fjl) for help with design & impl
This commit is contained in:
Gustav Simonsson
2015-09-29 19:37:44 +02:00
parent 27a50c8f4b
commit c8ad64f33c
16 changed files with 321 additions and 171 deletions
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335
crypto/secp256k1/curve.go Normal file
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// 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
}

39
crypto/secp256k1/curve_test.go Normal file
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@ -0,0 +1,39 @@
// Copyright 2015 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
package secp256k1
import (
"bytes"
"encoding/hex"
"math/big"
"testing"
)
func TestReadBits(t *testing.T) {
check := func(input string) {
want, _ := hex.DecodeString(input)
int, _ := new(big.Int).SetString(input, 16)
buf := make([]byte, len(want))
readBits(buf, int)
if !bytes.Equal(buf, want) {
t.Errorf("have: %x\nwant: %x", buf, want)
}
}
check("000000000000000000000000000000000000000000000000000000FEFCF3F8F0")
check("0000000000012345000000000000000000000000000000000000FEFCF3F8F0")
check("18F8F8F1000111000110011100222004330052300000000000000000FEFCF3F8F0")
}

56
crypto/secp256k1/pubkey_scalar_mul.h Normal file
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@ -0,0 +1,56 @@
// Copyright 2015 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
/** Multiply point by scalar in constant time.
* Returns: 1: multiplication was successful
* 0: scalar was invalid (zero or overflow)
* Args: ctx: pointer to a context object (cannot be NULL)
* Out: point: the multiplied point (usually secret)
* In: point: pointer to a 64-byte bytepublic point,
encoded as two 256bit big-endian numbers.
* scalar: a 32-byte scalar with which to multiply the point
*/
int secp256k1_pubkey_scalar_mul(const secp256k1_context* ctx, unsigned char *point, const unsigned char *scalar) {
int ret = 0;
int overflow = 0;
secp256k1_fe feX, feY;
secp256k1_gej res;
secp256k1_ge ge;
secp256k1_scalar s;
ARG_CHECK(point != NULL);
ARG_CHECK(scalar != NULL);
(void)ctx;
secp256k1_fe_set_b32(&feX, point);
secp256k1_fe_set_b32(&feY, point+32);
secp256k1_ge_set_xy(&ge, &feX, &feY);
secp256k1_scalar_set_b32(&s, scalar, &overflow);
if (overflow || secp256k1_scalar_is_zero(&s)) {
ret = 0;
} else {
secp256k1_ecmult_const(&res, &ge, &s);
secp256k1_ge_set_gej(&ge, &res);
/* Note: can't use secp256k1_pubkey_save here because it is not constant time. */
secp256k1_fe_normalize(&ge.x);
secp256k1_fe_normalize(&ge.y);
secp256k1_fe_get_b32(point, &ge.x);
secp256k1_fe_get_b32(point+32, &ge.y);
ret = 1;
}
secp256k1_scalar_clear(&s);
return ret;
}

28
crypto/secp256k1/secp256.go
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@ -20,6 +20,7 @@ package secp256k1
/*
#cgo CFLAGS: -I./libsecp256k1
#cgo CFLAGS: -I./libsecp256k1/src/
#cgo darwin CFLAGS: -I/usr/local/include
#cgo freebsd CFLAGS: -I/usr/local/include
#cgo linux,arm CFLAGS: -I/usr/local/arm/include
@ -35,6 +36,7 @@ package secp256k1
#define NDEBUG
#include "./libsecp256k1/src/secp256k1.c"
#include "./libsecp256k1/src/modules/recovery/main_impl.h"
#include "pubkey_scalar_mul.h"
typedef void (*callbackFunc) (const char* msg, void* data);
extern void secp256k1GoPanicIllegal(const char* msg, void* data);
@ -44,6 +46,7 @@ import "C"
import (
"errors"
"math/big"
"unsafe"
"github.com/ethereum/go-ethereum/crypto/randentropy"
@ -56,13 +59,16 @@ import (
> store private keys in buffer and shuffle (deters persistance on swap disc)
> byte permutation (changing)
> xor with chaning random block (to deter scanning memory for 0x63) (stream cipher?)
> on disk: store keys in wallets
*/
// holds ptr to secp256k1_context_struct (see secp256k1/include/secp256k1.h)
var context *C.secp256k1_context
var (
context *C.secp256k1_context
N *big.Int
)
func init() {
N, _ = new(big.Int).SetString("fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141", 16)
// around 20 ms on a modern CPU.
context = C.secp256k1_context_create(3) // SECP256K1_START_SIGN | SECP256K1_START_VERIFY
C.secp256k1_context_set_illegal_callback(context, C.callbackFunc(C.secp256k1GoPanicIllegal), nil)
@ -78,7 +84,6 @@ var (
func GenerateKeyPair() ([]byte, []byte) {
var seckey []byte = randentropy.GetEntropyCSPRNG(32)
var seckey_ptr *C.uchar = (*C.uchar)(unsafe.Pointer(&seckey[0]))
var pubkey64 []byte = make([]byte, 64) // secp256k1_pubkey
var pubkey65 []byte = make([]byte, 65) // 65 byte uncompressed pubkey
pubkey64_ptr := (*C.secp256k1_pubkey)(unsafe.Pointer(&pubkey64[0]))
@ -96,7 +101,7 @@ func GenerateKeyPair() ([]byte, []byte) {
var output_len C.size_t
_ = C.secp256k1_ec_pubkey_serialize( // always returns 1
C.secp256k1_ec_pubkey_serialize( // always returns 1
context,
pubkey65_ptr,
&output_len,
@ -163,7 +168,7 @@ func Sign(msg []byte, seckey []byte) ([]byte, error) {
sig_serialized_ptr := (*C.uchar)(unsafe.Pointer(&sig_serialized[0]))
var recid C.int
_ = C.secp256k1_ecdsa_recoverable_signature_serialize_compact(
C.secp256k1_ecdsa_recoverable_signature_serialize_compact(
context,
sig_serialized_ptr, // 64 byte compact signature
&recid,
@ -254,3 +259,16 @@ func checkSignature(sig []byte) error {
}
return nil
}
// reads num into buf as big-endian bytes.
func readBits(buf []byte, num *big.Int) {
const wordLen = int(unsafe.Sizeof(big.Word(0)))
i := len(buf)
for _, d := range num.Bits() {
for j := 0; j < wordLen && i > 0; j++ {
i--
buf[i] = byte(d)
d >>= 8
}
}
}

2
crypto/secp256k1/secp256_test.go
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@ -24,7 +24,7 @@ import (
"github.com/ethereum/go-ethereum/crypto/randentropy"
)
const TestCount = 10000
const TestCount = 1000
func TestPrivkeyGenerate(t *testing.T) {
_, seckey := GenerateKeyPair()