// Copyright (c) 2013-2014 The btcsuite developers
// Use of this source code is governed by an ISC
// license that can be found in the LICENSE file.
package btcec
import (
"crypto/ecdsa"
"errors"
"fmt"
"math/big"
)
// These constants define the lengths of serialized public keys.
const (
PubKeyBytesLenCompressed = 33
PubKeyBytesLenUncompressed = 65
PubKeyBytesLenHybrid = 65
)
func isOdd(a *big.Int) bool {
return a.Bit(0) == 1
}
// decompressPoint decompresses a point on the given curve given the X point and
// the solution to use.
func decompressPoint(curve *KoblitzCurve, x *big.Int, ybit bool) (*big.Int, error) {
// TODO: This will probably only work for secp256k1 due to
// optimizations.
// Y = +-sqrt(x^3 + B)
x3 := new(big.Int).Mul(x, x)
x3.Mul(x3, x)
x3.Add(x3, curve.Params().B)
// now calculate sqrt mod p of x2 + B
// This code used to do a full sqrt based on tonelli/shanks,
// but this was replaced by the algorithms referenced in
// https://bitcointalk.org/index.php?topic=162805.msg1712294#msg1712294
y := new(big.Int).Exp(x3, curve.QPlus1Div4(), curve.Params().P)
if ybit != isOdd(y) {
y.Sub(curve.Params().P, y)
}
if ybit != isOdd(y) {
return nil, fmt.Errorf("ybit doesn't match oddness")
}
return y, nil
}
const (
pubkeyCompressed byte = 0x2 // y_bit + x coord
pubkeyUncompressed byte = 0x4 // x coord + y coord
pubkeyHybrid byte = 0x6 // y_bit + x coord + y coord
)
// ParsePubKey parses a public key for a koblitz curve from a bytestring into a
// ecdsa.Publickey, verifying that it is valid. It supports compressed,
// uncompressed and hybrid signature formats.
func ParsePubKey(pubKeyStr []byte, curve *KoblitzCurve) (key *PublicKey, err error) {
pubkey := PublicKey{}
pubkey.Curve = curve
if len(pubKeyStr) == 0 {
return nil, errors.New("pubkey string is empty")
}
format := pubKeyStr[0]
ybit := (format & 0x1) == 0x1
format &= ^byte(0x1)
switch len(pubKeyStr) {
case PubKeyBytesLenUncompressed:
if format != pubkeyUncompressed && format != pubkeyHybrid {
return nil, fmt.Errorf("invalid magic in pubkey str: "+
"%d", pubKeyStr[0])
}
pubkey.X = new(big.Int).SetBytes(pubKeyStr[1:33])
pubkey.Y = new(big.Int).SetBytes(pubKeyStr[33:])
// hybrid keys have extra information, make use of it.
if format == pubkeyHybrid && ybit != isOdd(pubkey.Y) {
return nil, fmt.Errorf("ybit doesn't match oddness")
}
case PubKeyBytesLenCompressed:
// format is 0x2 | solution, <X coordinate>
// solution determines which solution of the curve we use.
/// y^2 = x^3 + Curve.B
if format != pubkeyCompressed {
return nil, fmt.Errorf("invalid magic in compressed "+
"pubkey string: %d", pubKeyStr[0])
}
pubkey.X = new(big.Int).SetBytes(pubKeyStr[1:33])
pubkey.Y, err = decompressPoint(curve, pubkey.X, ybit)
if err != nil {
return nil, err
}
default: // wrong!
return nil, fmt.Errorf("invalid pub key length %d",
len(pubKeyStr))
}
if pubkey.X.Cmp(pubkey.Curve.Params().P) >= 0 {
return nil, fmt.Errorf("pubkey X parameter is >= to P")
}
if pubkey.Y.Cmp(pubkey.Curve.Params().P) >= 0 {
return nil, fmt.Errorf("pubkey Y parameter is >= to P")
}
if !pubkey.Curve.IsOnCurve(pubkey.X, pubkey.Y) {
return nil, fmt.Errorf("pubkey isn't on secp256k1 curve")
}
return &pubkey, nil
}
// PublicKey is an ecdsa.PublicKey with additional functions to
// serialize in uncompressed, compressed, and hybrid formats.
type PublicKey ecdsa.PublicKey
// ToECDSA returns the public key as a *ecdsa.PublicKey.
func (p *PublicKey) ToECDSA() *ecdsa.PublicKey {
return (*ecdsa.PublicKey)(p)
}
// SerializeUncompressed serializes a public key in a 65-byte uncompressed
// format.
func (p *PublicKey) SerializeUncompressed() []byte {
b := make([]byte, 0, PubKeyBytesLenUncompressed)
b = append(b, pubkeyUncompressed)
b = paddedAppend(32, b, p.X.Bytes())
return paddedAppend(32, b, p.Y.Bytes())
}
// SerializeCompressed serializes a public key in a 33-byte compressed format.
func (p *PublicKey) SerializeCompressed() []byte {
b := make([]byte, 0, PubKeyBytesLenCompressed)
format := pubkeyCompressed
if isOdd(p.Y) {
format |= 0x1
}
b = append(b, format)
return paddedAppend(32, b, p.X.Bytes())
}
// SerializeHybrid serializes a public key in a 65-byte hybrid format.
func (p *PublicKey) SerializeHybrid() []byte {
b := make([]byte, 0, PubKeyBytesLenHybrid)
format := pubkeyHybrid
if isOdd(p.Y) {
format |= 0x1
}
b = append(b, format)
b = paddedAppend(32, b, p.X.Bytes())
return paddedAppend(32, b, p.Y.Bytes())
}
// IsEqual compares this PublicKey instance to the one passed, returning true if
// both PublicKeys are equivalent. A PublicKey is equivalent to another, if they
// both have the same X and Y coordinate.
func (p *PublicKey) IsEqual(otherPubKey *PublicKey) bool {
return p.X.Cmp(otherPubKey.X) == 0 &&
p.Y.Cmp(otherPubKey.Y) == 0
}
// paddedAppend appends the src byte slice to dst, returning the new slice.
// If the length of the source is smaller than the passed size, leading zero
// bytes are appended to the dst slice before appending src.
func paddedAppend(size uint, dst, src []byte) []byte {
for i := 0; i < int(size)-len(src); i++ {
dst = append(dst, 0)
}
return append(dst, src...)
}
