crypto: drop home-grown elliptic crypto, use crypto/elliptic
As NEO uses P256 we can use standard crypto/elliptic library for almost everything, the only exception being decompression of the Y coordinate. For some reason the standard library only supports uncompressed format in its Marshal()/Unmarshal() functions. elliptic.P256() is known to have constant-time implementation, so it fixes #245 (and the decompression using big.Int operates on public key, so nobody really cares about that part being constant-time). New decompress function is inspired by https://stackoverflow.com/questions/46283760, even though the previous one really did the same thing just in a little less obvious way.
This commit is contained in:
Roman Khimov
parent
0b884b92b3
commit
f0fbe9f6c9
5 changed files with 66 additions and 348 deletions
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@ -1,256 +0,0 @@
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package crypto
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// Original work completed by @vsergeev: https://github.com/vsergeev/btckeygenie
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// Expanded and tweaked upon here under MIT license.
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import (
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"bytes"
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"encoding/binary"
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"encoding/hex"
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"errors"
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"fmt"
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"io"
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"math/big"
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"github.com/CityOfZion/neo-go/pkg/util"
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)
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type (
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// EllipticCurve represents the parameters of a short Weierstrass equation elliptic
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// curve.
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EllipticCurve struct {
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A *big.Int
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B *big.Int
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P *big.Int
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G ECPoint
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N *big.Int
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H *big.Int
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}
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// ECPoint represents a point on the EllipticCurve.
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ECPoint struct {
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X *big.Int
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Y *big.Int
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}
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)
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// NewEllipticCurve returns a ready to use EllipticCurve with preconfigured
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// fields for the NEO protocol.
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func NewEllipticCurve() EllipticCurve {
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c := EllipticCurve{}
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c.P, _ = new(big.Int).SetString(
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"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF", 16,
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)
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c.A, _ = new(big.Int).SetString(
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"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC", 16,
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)
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c.B, _ = new(big.Int).SetString(
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"5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B", 16,
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)
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c.G.X, _ = new(big.Int).SetString(
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"6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296", 16,
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)
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c.G.Y, _ = new(big.Int).SetString(
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"4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5", 16,
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)
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c.N, _ = new(big.Int).SetString(
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"FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551", 16,
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)
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c.H, _ = new(big.Int).SetString("01", 16)
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return c
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}
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// ECPointFromReader return a new point from the given reader.
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// f == 4, 6 or 7 are not implemented.
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func ECPointFromReader(r io.Reader) (point ECPoint, err error) {
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var f uint8
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if err = binary.Read(r, binary.LittleEndian, &f); err != nil {
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return
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}
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// Infinity
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if f == 0 {
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return ECPoint{
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X: new(big.Int),
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Y: new(big.Int),
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}, nil
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}
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if f == 2 || f == 3 {
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y := new(big.Int).SetBytes([]byte{f & 1})
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data := make([]byte, 32)
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if err = binary.Read(r, binary.LittleEndian, data); err != nil {
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return
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}
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data = util.ArrayReverse(data)
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data = append(data, byte(0x00))
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return ECPoint{
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X: new(big.Int).SetBytes(data),
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Y: y,
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}, nil
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}
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return
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}
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// EncodeBinary encodes the point to the given io.Writer.
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func (p ECPoint) EncodeBinary(w io.Writer) error {
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bx := p.X.Bytes()
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padded := append(
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bytes.Repeat(
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[]byte{0x00},
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32-len(bx),
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),
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bx...,
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)
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prefix := byte(0x03)
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if p.Y.Bit(0) == 0 {
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prefix = byte(0x02)
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}
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buf := make([]byte, len(padded)+1)
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buf[0] = prefix
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copy(buf[1:], padded)
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return binary.Write(w, binary.LittleEndian, buf)
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}
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// String implements the Stringer interface.
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func (p *ECPoint) String() string {
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if p.IsInfinity() {
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return "00"
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}
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bx := hex.EncodeToString(p.X.Bytes())
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by := hex.EncodeToString(p.Y.Bytes())
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return fmt.Sprintf("%s%s", bx, by)
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}
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// IsInfinity checks if point P is infinity on EllipticCurve ec.
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func (p *ECPoint) IsInfinity() bool {
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return p.X == nil && p.Y == nil
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}
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// IsInfinity checks if point P is infinity on EllipticCurve ec.
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func (c *EllipticCurve) IsInfinity(P ECPoint) bool {
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return P.X == nil && P.Y == nil
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}
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// IsOnCurve checks if point P is on EllipticCurve ec.
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func (c *EllipticCurve) IsOnCurve(P ECPoint) bool {
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if c.IsInfinity(P) {
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return false
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}
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lhs := mulMod(P.Y, P.Y, c.P)
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rhs := addMod(
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addMod(
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expMod(P.X, big.NewInt(3), c.P),
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mulMod(c.A, P.X, c.P), c.P),
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c.B, c.P)
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return lhs.Cmp(rhs) == 0
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}
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// Add computes R = P + Q on EllipticCurve ec.
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func (c *EllipticCurve) Add(P, Q ECPoint) (R ECPoint) {
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// See rules 1-5 on SEC1 pg.7 http://www.secg.org/collateral/sec1_final.pdf
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if c.IsInfinity(P) && c.IsInfinity(Q) {
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R.X = nil
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R.Y = nil
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} else if c.IsInfinity(P) {
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R.X = new(big.Int).Set(Q.X)
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R.Y = new(big.Int).Set(Q.Y)
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} else if c.IsInfinity(Q) {
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R.X = new(big.Int).Set(P.X)
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R.Y = new(big.Int).Set(P.Y)
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} else if P.X.Cmp(Q.X) == 0 && addMod(P.Y, Q.Y, c.P).Sign() == 0 {
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R.X = nil
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R.Y = nil
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} else if P.X.Cmp(Q.X) == 0 && P.Y.Cmp(Q.Y) == 0 && P.Y.Sign() != 0 {
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num := addMod(
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mulMod(big.NewInt(3),
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mulMod(P.X, P.X, c.P), c.P),
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c.A, c.P)
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den := invMod(mulMod(big.NewInt(2), P.Y, c.P), c.P)
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lambda := mulMod(num, den, c.P)
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R.X = subMod(
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mulMod(lambda, lambda, c.P),
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mulMod(big.NewInt(2), P.X, c.P),
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c.P)
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R.Y = subMod(
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mulMod(lambda, subMod(P.X, R.X, c.P), c.P),
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P.Y, c.P)
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} else if P.X.Cmp(Q.X) != 0 {
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num := subMod(Q.Y, P.Y, c.P)
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den := invMod(subMod(Q.X, P.X, c.P), c.P)
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lambda := mulMod(num, den, c.P)
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R.X = subMod(
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subMod(
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mulMod(lambda, lambda, c.P),
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P.X, c.P),
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Q.X, c.P)
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R.Y = subMod(
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mulMod(lambda,
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subMod(P.X, R.X, c.P), c.P),
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P.Y, c.P)
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} else {
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panic(fmt.Sprintf("Unsupported point addition: %v + %v", P, Q))
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}
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return R
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}
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// ScalarMult computes Q = k * P on EllipticCurve ec.
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func (c *EllipticCurve) ScalarMult(k *big.Int, P ECPoint) (Q ECPoint) {
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// Implementation based on pseudocode here:
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// https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Montgomery_ladder
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var R0 ECPoint
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var R1 ECPoint
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R0.X = nil
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R0.Y = nil
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R1.X = new(big.Int).Set(P.X)
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R1.Y = new(big.Int).Set(P.Y)
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for i := c.N.BitLen() - 1; i >= 0; i-- {
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if k.Bit(i) == 0 {
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R1 = c.Add(R0, R1)
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R0 = c.Add(R0, R0)
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} else {
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R0 = c.Add(R0, R1)
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R1 = c.Add(R1, R1)
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}
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}
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return R0
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}
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// ScalarBaseMult computes Q = k * G on EllipticCurve ec.
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func (c *EllipticCurve) ScalarBaseMult(k *big.Int) (Q ECPoint) {
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return c.ScalarMult(k, c.G)
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}
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// Decompress decompresses coordinate x and ylsb (y's least significant bit) into a ECPoint P on EllipticCurve ec.
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func (c *EllipticCurve) Decompress(x *big.Int, ylsb uint) (P ECPoint, err error) {
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/* y**2 = x**3 + a*x + b % p */
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rhs := addMod(
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addMod(
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expMod(x, big.NewInt(3), c.P),
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mulMod(c.A, x, c.P),
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c.P),
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c.B, c.P)
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y := sqrtMod(rhs, c.P)
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if y.Bit(0) != (ylsb & 0x1) {
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y = subMod(big.NewInt(0), y, c.P)
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}
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P.X = x
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P.Y = y
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if !c.IsOnCurve(P) {
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return P, errors.New("compressed (x, ylsb) not on curve")
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}
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return P, nil
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}
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@ -10,10 +10,8 @@ import (
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"encoding/hex"
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"errors"
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"fmt"
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"io"
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"math/big"
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"github.com/CityOfZion/neo-go/pkg/crypto"
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"github.com/nspcc-dev/rfc6979"
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)
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@ -24,18 +22,11 @@ type PrivateKey struct {
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// NewPrivateKey creates a new random private key.
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func NewPrivateKey() (*PrivateKey, error) {
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c := crypto.NewEllipticCurve()
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b := make([]byte, c.N.BitLen()/8+8)
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if _, err := io.ReadFull(rand.Reader, b); err != nil {
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priv, _, _, err := elliptic.GenerateKey(elliptic.P256(), rand.Reader)
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if err != nil {
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return nil, err
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}
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d := new(big.Int).SetBytes(b)
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d.Mod(d, new(big.Int).Sub(c.N, big.NewInt(1)))
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d.Add(d, big.NewInt(1))
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p := &PrivateKey{b: d.Bytes()}
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return p, nil
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return &PrivateKey{b: priv}, nil
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}
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// NewPrivateKeyFromHex returns a PrivateKey created from the
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@ -72,16 +63,16 @@ func (p *PrivateKey) PublicKey() (*PublicKey, error) {
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var (
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err error
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pk PublicKey
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c = crypto.NewEllipticCurve()
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c = elliptic.P256()
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q = new(big.Int).SetBytes(p.b)
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)
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point := c.ScalarBaseMult(q)
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if !c.IsOnCurve(point) {
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x, y := c.ScalarBaseMult(q.Bytes())
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if !c.IsOnCurve(x, y) {
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return nil, errors.New("failed to derive public key using elliptic curve")
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}
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bx := point.X.Bytes()
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bx := x.Bytes()
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padded := append(
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bytes.Repeat(
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[]byte{0x00},
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@ -91,7 +82,7 @@ func (p *PrivateKey) PublicKey() (*PublicKey, error) {
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)
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prefix := []byte{0x03}
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if point.Y.Bit(0) == 0 {
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if y.Bit(0) == 0 {
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prefix = []byte{0x02}
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}
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b := append(prefix, padded...)
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@ -7,6 +7,7 @@ import (
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"crypto/x509"
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"encoding/binary"
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"encoding/hex"
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"fmt"
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"io"
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"math/big"
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@ -35,9 +36,10 @@ func (keys PublicKeys) Less(i, j int) bool {
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}
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// PublicKey represents a public key and provides a high level
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// API around the ECPoint.
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// API around the X/Y point.
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type PublicKey struct {
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crypto.ECPoint
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X *big.Int
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Y *big.Int
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}
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// NewPublicKeyFromString return a public key created from the
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@ -58,7 +60,7 @@ func NewPublicKeyFromString(s string) (*PublicKey, error) {
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// Bytes returns the byte array representation of the public key.
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func (p *PublicKey) Bytes() []byte {
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if p.IsInfinity() {
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if p.isInfinity() {
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return []byte{0x00}
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}
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@ -89,14 +91,38 @@ func NewPublicKeyFromRawBytes(data []byte) (*PublicKey, error) {
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return nil, errors.New("given bytes aren't ECDSA public key")
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}
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key := PublicKey{
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crypto.ECPoint{
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X: pk.X,
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Y: pk.Y,
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},
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X: pk.X,
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Y: pk.Y,
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}
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return &key, nil
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}
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// decodeCompressedY performs decompression of Y coordinate for given X and Y's least significant bit
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func decodeCompressedY(x *big.Int, ylsb uint) (*big.Int, error) {
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c := elliptic.P256()
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cp := c.Params()
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three := big.NewInt(3)
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/* y**2 = x**3 + a*x + b % p */
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xCubed := new(big.Int).Exp(x, three, cp.P)
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threeX := new(big.Int).Mul(x, three)
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threeX.Mod(threeX, cp.P)
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ySquared := new(big.Int).Sub(xCubed, threeX)
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ySquared.Add(ySquared, cp.B)
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ySquared.Mod(ySquared, cp.P)
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y := new(big.Int).ModSqrt(ySquared, cp.P)
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if y == nil {
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return nil, errors.New("error computing Y for compressed point")
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}
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if y.Bit(0) != ylsb {
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y.Neg(y)
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y.Mod(y, cp.P)
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}
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if !c.IsOnCurve(x, y) {
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return nil, errors.New("compressed (x, ylsb) not on curve")
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}
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return y, nil
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}
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// DecodeBytes decodes a PublicKey from the given slice of bytes.
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func (p *PublicKey) DecodeBytes(data []byte) error {
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l := len(data)
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@ -104,19 +130,22 @@ func (p *PublicKey) DecodeBytes(data []byte) error {
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switch prefix := data[0]; prefix {
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// Infinity
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case 0x00:
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p.ECPoint = crypto.ECPoint{}
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p.X = nil
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p.Y = nil
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// Compressed public keys
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case 0x02, 0x03:
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if l < 33 {
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return errors.Errorf("bad binary size(%d)", l)
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}
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c := crypto.NewEllipticCurve()
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var err error
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p.ECPoint, err = c.Decompress(new(big.Int).SetBytes(data[1:]), uint(prefix&0x1))
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x := new(big.Int).SetBytes(data[1:])
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ylsb := uint(prefix&0x1)
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y, err := decodeCompressedY(x, ylsb)
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if err != nil {
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return err
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}
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p.X = x
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p.Y = y
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case 0x04:
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if l < 66 {
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return errors.Errorf("bad binary size(%d)", l)
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@ -141,7 +170,8 @@ func (p *PublicKey) DecodeBinary(r io.Reader) error {
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// Infinity
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switch prefix {
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case 0x00:
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p.ECPoint = crypto.ECPoint{}
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p.X = nil
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p.Y = nil
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return nil
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// Compressed public keys
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case 0x02, 0x03:
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@ -206,3 +236,18 @@ func (p *PublicKey) Verify(signature []byte, hash []byte) bool {
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sBytes := new(big.Int).SetBytes(signature[32:64])
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return ecdsa.Verify(publicKey, hash, rBytes, sBytes)
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}
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// isInfinity checks if point P is infinity on EllipticCurve ec.
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func (p *PublicKey) isInfinity() bool {
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return p.X == nil && p.Y == nil
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}
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// String implements the Stringer interface.
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func (p *PublicKey) String() string {
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if p.isInfinity() {
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return "00"
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}
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bx := hex.EncodeToString(p.X.Bytes())
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by := hex.EncodeToString(p.Y.Bytes())
|
||||
return fmt.Sprintf("%s%s", bx, by)
|
||||
}
|
||||
|
|
|
|||
|
|
@ -5,12 +5,11 @@ import (
|
|||
"encoding/hex"
|
||||
"testing"
|
||||
|
||||
"github.com/CityOfZion/neo-go/pkg/crypto"
|
||||
"github.com/stretchr/testify/assert"
|
||||
)
|
||||
|
||||
func TestEncodeDecodeInfinity(t *testing.T) {
|
||||
key := &PublicKey{crypto.ECPoint{}}
|
||||
key := &PublicKey{}
|
||||
buf := new(bytes.Buffer)
|
||||
assert.Nil(t, key.EncodeBinary(buf))
|
||||
assert.Equal(t, 1, buf.Len())
|
||||
|
|
|
|||
|
|
@ -1,61 +0,0 @@
|
|||
package crypto
|
||||
|
||||
import "math/big"
|
||||
|
||||
// addMod computes z = (x + y) % p.
|
||||
func addMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
|
||||
z = new(big.Int).Add(x, y)
|
||||
z.Mod(z, p)
|
||||
return z
|
||||
}
|
||||
|
||||
// subMod computes z = (x - y) % p.
|
||||
func subMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
|
||||
z = new(big.Int).Sub(x, y)
|
||||
z.Mod(z, p)
|
||||
return z
|
||||
}
|
||||
|
||||
// mulMod computes z = (x * y) % p.
|
||||
func mulMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
|
||||
n := new(big.Int).Set(x)
|
||||
z = big.NewInt(0)
|
||||
|
||||
for i := 0; i < y.BitLen(); i++ {
|
||||
if y.Bit(i) == 1 {
|
||||
z = addMod(z, n, p)
|
||||
}
|
||||
n = addMod(n, n, p)
|
||||
}
|
||||
|
||||
return z
|
||||
}
|
||||
|
||||
// invMod computes z = (1/x) % p.
|
||||
func invMod(x *big.Int, p *big.Int) (z *big.Int) {
|
||||
z = new(big.Int).ModInverse(x, p)
|
||||
return z
|
||||
}
|
||||
|
||||
// expMod computes z = (x^e) % p.
|
||||
func expMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
|
||||
z = new(big.Int).Exp(x, y, p)
|
||||
return z
|
||||
}
|
||||
|
||||
// sqrtMod computes z = sqrt(x) % p.
|
||||
func sqrtMod(x *big.Int, p *big.Int) (z *big.Int) {
|
||||
/* assert that p % 4 == 3 */
|
||||
if new(big.Int).Mod(p, big.NewInt(4)).Cmp(big.NewInt(3)) != 0 {
|
||||
panic("p is not equal to 3 mod 4!")
|
||||
}
|
||||
|
||||
/* z = sqrt(x) % p = x^((p+1)/4) % p */
|
||||
|
||||
/* e = (p+1)/4 */
|
||||
e := new(big.Int).Add(p, big.NewInt(1))
|
||||
e = e.Rsh(e, 2)
|
||||
|
||||
z = expMod(x, e, p)
|
||||
return z
|
||||
}
|
||||
Loading…
Reference in a new issue