// pubKeyBytes returns bytes for the serialized compressed public key associated
// with this extended key in an efficient manner including memoization as
// necessary.
//
// When the extended key is already a public key, the key is simply returned as
// is since it's already in the correct form. However, when the extended key is
// a private key, the public key will be calculated and memoized so future
// accesses can simply return the cached result.
func (k *ExtendedKey) pubKeyBytes() []byte {
// Just return the key if it's already an extended public key.
if !k.isPrivate {
return k.key
}
// This is a private extended key, so calculate and memoize the public
// key if needed.
if len(k.pubKey) == 0 {
pkx, pky := btcec.S256().ScalarBaseMult(k.key)
pubKey := btcec.PublicKey{Curve: btcec.S256(), X: pkx, Y: pky}
k.pubKey = pubKey.SerializeCompressed()
}
return k.pubKey
}
// Child returns a derived child extended key at the given index. When this
// extended key is a private extended key (as determined by the IsPrivate
// function), a private extended key will be derived. Otherwise, the derived
// extended key will be also be a public extended key.
//
// When the index is greater to or equal than the HardenedKeyStart constant, the
// derived extended key will be a hardened extended key. It is only possible to
// derive a hardended extended key from a private extended key. Consequently,
// this function will return ErrDeriveHardFromPublic if a hardened child
// extended key is requested from a public extended key.
//
// A hardened extended key is useful since, as previously mentioned, it requires
// a parent private extended key to derive. In other words, normal child
// extended public keys can be derived from a parent public extended key (no
// knowledge of the parent private key) whereas hardened extended keys may not
// be.
//
// NOTE: There is an extremely small chance (< 1 in 2^127) the specific child
// index does not derive to a usable child. The ErrInvalidChild error will be
// returned if this should occur, and the caller is expected to ignore the
// invalid child and simply increment to the next index.
func (k *ExtendedKey) Child(i uint32) (*ExtendedKey, error) {
// There are four scenarios that could happen here:
// 1) Private extended key -> Hardened child private extended key
// 2) Private extended key -> Non-hardened child private extended key
// 3) Public extended key -> Non-hardened child public extended key
// 4) Public extended key -> Hardened child public extended key (INVALID!)
// Case #4 is invalid, so error out early.
// A hardened child extended key may not be created from a public
// extended key.
isChildHardened := i >= HardenedKeyStart
if !k.isPrivate && isChildHardened {
return nil, ErrDeriveHardFromPublic
}
// The data used to derive the child key depends on whether or not the
// child is hardened per [BIP32].
//
// For hardened children:
// 0x00 || ser256(parentKey) || ser32(i)
//
// For normal children:
// serP(parentPubKey) || ser32(i)
keyLen := 33
data := make([]byte, keyLen+4)
if isChildHardened {
// Case #1.
// When the child is a hardened child, the key is known to be a
// private key due to the above early return. Pad it with a
// leading zero as required by [BIP32] for deriving the child.
copy(data[1:], k.key)
} else {
// Case #2 or #3.
// This is either a public or private extended key, but in
// either case, the data which is used to derive the child key
// starts with the secp256k1 compressed public key bytes.
copy(data, k.pubKeyBytes())
}
binary.BigEndian.PutUint32(data[keyLen:], i)
// Take the HMAC-SHA512 of the current key's chain code and the derived
// data:
// I = HMAC-SHA512(Key = chainCode, Data = data)
hmac512 := hmac.New(sha512.New, k.chainCode)
hmac512.Write(data)
ilr := hmac512.Sum(nil)
// Split "I" into two 32-byte sequences Il and Ir where:
// Il = intermediate key used to derive the child
// Ir = child chain code
il := ilr[:len(ilr)/2]
childChainCode := ilr[len(ilr)/2:]
// Both derived public or private keys rely on treating the left 32-byte
// sequence calculated above (Il) as a 256-bit integer that must be
// within the valid range for a secp256k1 private key. There is a small
// chance (< 1 in 2^127) this condition will not hold, and in that case,
// a child extended key can't be created for this index and the caller
// should simply increment to the next index.
ilNum := new(big.Int).SetBytes(il)
if ilNum.Cmp(btcec.S256().N) >= 0 || ilNum.Sign() == 0 {
return nil, ErrInvalidChild
}
// The algorithm used to derive the child key depends on whether or not
// a private or public child is being derived.
//
// For private children:
// childKey = parse256(Il) + parentKey
//
// For public children:
// childKey = serP(point(parse256(Il)) + parentKey)
var isPrivate bool
var childKey []byte
if k.isPrivate {
// Case #1 or #2.
// Add the parent private key to the intermediate private key to
// derive the final child key.
//
// childKey = parse256(Il) + parenKey
keyNum := new(big.Int).SetBytes(k.key)
ilNum.Add(ilNum, keyNum)
ilNum.Mod(ilNum, btcec.S256().N)
childKey = ilNum.Bytes()
isPrivate = true
} else {
// Case #3.
// Calculate the corresponding intermediate public key for
// intermediate private key.
ilx, ily := btcec.S256().ScalarBaseMult(il)
if ilx.Sign() == 0 || ily.Sign() == 0 {
return nil, ErrInvalidChild
}
// Convert the serialized compressed parent public key into X
// and Y coordinates so it can be added to the intermediate
// public key.
pubKey, err := btcec.ParsePubKey(k.key, btcec.S256())
if err != nil {
return nil, err
}
// Add the intermediate public key to the parent public key to
// derive the final child key.
//
// childKey = serP(point(parse256(Il)) + parentKey)
childX, childY := btcec.S256().Add(ilx, ily, pubKey.X, pubKey.Y)
pk := btcec.PublicKey{Curve: btcec.S256(), X: childX, Y: childY}
childKey = pk.SerializeCompressed()
}
// The fingerprint of the parent for the derived child is the first 4
// bytes of the RIPEMD160(SHA256(parentPubKey)).
parentFP := btcutil.Hash160(k.pubKeyBytes())[:4]
return newExtendedKey(k.version, childKey, childChainCode, parentFP,
k.depth+1, i, isPrivate), nil
}
func recoverKey(sigA, sigB *btcec.Signature, hashA, hashB []byte, pubKey *btcec.PublicKey) *btcec.PrivateKey {
// Sanity checks
if sigA.R.Cmp(sigB.R) != 0 {
log.Println("Different R!")
return nil
}
if !ecdsa.Verify(pubKey.ToECDSA(), hashA, sigA.R, sigA.S) {
log.Println("A fails to verify!")
return nil
}
if !ecdsa.Verify(pubKey.ToECDSA(), hashB, sigB.R, sigB.S) {
log.Println("B fails to verify!")
return nil
}
if !reflect.DeepEqual(pubKey.Curve, btcec.S256()) {
log.Println("What the curve?!")
return nil
}
c := btcec.S256()
N := c.Params().N
zA := hashToInt(hashA, c)
zB := hashToInt(hashB, c)
sDiffInv := new(big.Int).Sub(sigA.S, sigB.S)
sDiffInv.Mod(sDiffInv, N)
sDiffInv.ModInverse(sDiffInv, N)
zDiff := new(big.Int).Sub(zA, zB)
zDiff.Mod(zDiff, N)
k := new(big.Int).Mul(zDiff, sDiffInv)
k.Mod(k, N)
rInv := new(big.Int).ModInverse(sigA.R, N)
D := new(big.Int)
D.Mul(sigA.S, k)
D.Sub(D, zA)
D.Mul(D, rInv)
D.Mod(D, N)
x, y := c.ScalarBaseMult(D.Bytes())
if pubKey.X.Cmp(x) != 0 {
log.Println("X!")
return nil
}
if pubKey.Y.Cmp(y) != 0 {
log.Println("Y!")
return nil
}
return &btcec.PrivateKey{
PublicKey: ecdsa.PublicKey{
Curve: c,
X: x,
Y: y,
},
D: D,
}
}