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239 changes: 3 additions & 236 deletions crypto/secp256k1/curve.go
Original file line number Diff line number Diff line change
Expand Up @@ -39,10 +39,9 @@ package secp256k1
import "C"

import (
"crypto/elliptic"
"math/big"

"github.com/kaiachain/kaia/common"
"github.com/erigontech/secp256k1"
)

const (
Expand All @@ -66,241 +65,9 @@ func readBits(bigint *big.Int, buf []byte) {
}
}

// 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,
}
}

// IsOnCurve 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) {
if z.Sign() == 0 {
return new(big.Int), new(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) {
// If one point is at infinity, return the other point.
// Adding the point at infinity to any point will preserve the other point.
if x1.Sign() == 0 && y1.Sign() == 0 {
return x2, y2
}
if x2.Sign() == 0 && y2.Sign() == 0 {
return x1, y1
}
z := new(big.Int).SetInt64(1)
if x1.Cmp(x2) == 0 && y1.Cmp(y2) == 0 {
return BitCurve.affineFromJacobian(BitCurve.doubleJacobian(x1, y1, z))
}
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, common.Big2) // 2*((X1+B)²-A-C)

e := new(big.Int).Mul(common.Big3, a) // 3*A
f := new(big.Int).Mul(e, e) // E²

x3 := new(big.Int).Mul(common.Big2, 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(common.Big2, z3) // 3*Y1*Z1
z3.Mod(z3, BitCurve.P)

return x3, y3, z3
}

// 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)
}

// 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 flag
readBits(x, ret[1:1+byteLen])
readBits(y, ret[1+byteLen:])
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 theCurve = new(BitCurve)

func init() {
// See SEC 2 section 2.7.1
// curve parameters taken from:
// http://www.secg.org/sec2-v2.pdf
theCurve.P, _ = new(big.Int).SetString("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", 0)
theCurve.N, _ = new(big.Int).SetString("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 0)
theCurve.B, _ = new(big.Int).SetString("0x0000000000000000000000000000000000000000000000000000000000000007", 0)
theCurve.Gx, _ = new(big.Int).SetString("0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", 0)
theCurve.Gy, _ = new(big.Int).SetString("0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", 0)
theCurve.BitSize = 256
}
type BitCurve = secp256k1.BitCurve

// S256 returns a BitCurve which implements secp256k1.
func S256() *BitCurve {
return theCurve
return secp256k1.S256()
}
16 changes: 4 additions & 12 deletions crypto/secp256k1/doc.go
Original file line number Diff line number Diff line change
Expand Up @@ -19,18 +19,10 @@
// Modified and improved for the klaytn development.

/*
Package secp256k1 wraps the bitcoin secp256k1 C library.
Package secp256k1 wraps the github.com/erigontech/secp256k1 library.

secp256k1 refers to the parameters of the elliptic curve used in Bitcoin's public-key cryptography and is defined in Standards for Efficient Cryptography (SEC)(Certicom Research, http://www.secg.org/sec2-v2.pdf).

Package secp256k1 provides wrapper functions to utilize the library functions in Go.

# Source Files

Each source file has the following contents
- secp256.go : Provides wrapper functions to utilize the secp256k1 library written in C
- curve.go : Implements Koblitz elliptic curves
- panic_cb.go : Provides callbacks for converting libsecp256k1 internal faults into recoverable Go panics
- schnorr.go : Implements Schnorr signature algorithm. It is planned to be used in Kaia
A CGO implementation used to be in this directory. But was deleted and replaced by a simple wrapper to erigontech/secp256k1 package.
When we imported the erigontech/erigon-lib, the kaiachain/kaia/crypto/secp256k1 and erigontech/secp256k1 caused CGO symbol collision.
The resolution was using erigontech/secp256k1 only.
*/
package secp256k1
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