Add code to produce and verify compact signatures.

The format used is identical to that used in bitcoind.

btcec.go

@@ -38,6 +38,7 @@ var (
 type KoblitzCurve struct {
 	*elliptic.CurveParams
 	q *big.Int
+	H int // cofactor of the curve.
 }
 
 // Params returns the parameters for the curve.
@@ -652,6 +653,7 @@ func initS256() {
 	secp256k1.Gx, _ = new(big.Int).SetString("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", 16)
 	secp256k1.Gy, _ = new(big.Int).SetString("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", 16)
 	secp256k1.BitSize = 256
+	secp256k1.H = 1
 	secp256k1.q = new(big.Int).Div(new(big.Int).Add(secp256k1.P,
 		big.NewInt(1)), big.NewInt(4))
 }

pubkey.go

@@ -14,6 +14,32 @@ 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(oga) This will probably only work for secp256k1 due to
+	// optimisations.
+
+	// 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
@@ -53,25 +79,10 @@ func ParsePubKey(pubKeyStr []byte, curve *KoblitzCurve) (key *ecdsa.PublicKey, e
 				"pubkey string: %d", pubKeyStr[0])
 		}
 		pubkey.X = new(big.Int).SetBytes(pubKeyStr[1:33])
-		// Y = +-sqrt(x^3 + B)
-		x3 := new(big.Int).Mul(pubkey.X, pubkey.X)
-		x3.Mul(x3, pubkey.X)
-		x3.Add(x3, pubkey.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(), pubkey.Curve.Params().P)
-
-		if ybit != isOdd(y) {
-			y.Sub(pubkey.Curve.Params().P, y)
+		pubkey.Y, err = decompressPoint(curve, pubkey.X, ybit)
+		if err != nil {
+			return nil, err
 		}
-		if ybit != isOdd(y) {
-			return nil, fmt.Errorf("ybit doesn't match oddness")
-		}
-
-		pubkey.Y = y
 	default: // wrong!
 		return nil, fmt.Errorf("invalid pub key length %d",
 			len(pubKeyStr))

signature.go

@@ -5,7 +5,9 @@
 package btcec
 
 import (
+	"crypto/ecdsa"
 	"crypto/elliptic"
+	"crypto/rand"
 	"errors"
 	"fmt"
 	"math/big"
@@ -213,3 +215,169 @@ func canonicalPadding(b []byte) error {
 		return nil
 	}
 }
+
+// hashToInt converts a hash value to an integer. There is some disagreement
+// about how this is done. [NSA] suggests that this is done in the obvious
+// manner, but [SECG] truncates the hash to the bit-length of the curve order
+// first. We follow [SECG] because that's what OpenSSL does. Additionally,
+// OpenSSL right shifts excess bits from the number if the hash is too large
+// and we mirror that too.
+// This is borrowed from crypto/ecdsa.
+func hashToInt(hash []byte, c elliptic.Curve) *big.Int {
+	orderBits := c.Params().N.BitLen()
+	orderBytes := (orderBits + 7) / 8
+	if len(hash) > orderBytes {
+		hash = hash[:orderBytes]
+	}
+
+	ret := new(big.Int).SetBytes(hash)
+	excess := len(hash)*8 - orderBits
+	if excess > 0 {
+		ret.Rsh(ret, uint(excess))
+	}
+	return ret
+}
+
+// recoverKeyFromSignature recoves a public key from the signature "sig" on the
+// given message hash "msg". Based on the algorithm found in section 5.1.5 of
+// SEC 1 Ver 2.0, page 47-48 (53 and 54 in the pdf). This performs the details
+// in the inner loop in Step 1. The counter provided is actually the j parameter
+// of the loop * 2 - on the first iteration of j we do the R case, else the -R
+// case in step 1.6. This counter is used in the bitcoin compressed signature
+// format and thus we match bitcoind's behaviour here.
+func recoverKeyFromSignature(curve *KoblitzCurve, sig *Signature, msg []byte,
+	iter int, doChecks bool) (*ecdsa.PublicKey, error) {
+	// 1.1 x = (n * i) + r
+	Rx := new(big.Int).Mul(curve.Params().N,
+		new(big.Int).SetInt64(int64(iter/2)))
+	Rx.Add(Rx, sig.R)
+	if Rx.Cmp(curve.Params().P) != -1 {
+		return nil, errors.New("calculated Rx is larger than curve P")
+	}
+
+	// convert 02<Rx> to point R. (step 1.2 and 1.3). If we are on an odd
+	// iteration then 1.6 will be done with -R, so we calculate the other
+	// term when uncompressing the point.
+	Ry, err := decompressPoint(curve, Rx, iter%2 == 1)
+	if err != nil {
+		return nil, err
+	}
+
+	// 1.4 Check n*R is point at infinity
+	if doChecks {
+		nRx, nRy := curve.ScalarMult(Rx, Ry, curve.Params().N.Bytes())
+		if nRx.Sign() != 0 || nRy.Sign() != 0 {
+			return nil, errors.New("R*n does not equal the point at infinity")
+		}
+	}
+
+	// 1.5 calculate e from message using the same algorithm as ecdsa
+	// signature calculation.
+	e := hashToInt(msg, curve)
+
+	// Step 1.6.1:
+	// We calculate the two terms sR and eG separately multiplied by the
+	// inverse of r (from the signature). We then add them to calculate
+	// Q = r^-1(sR-eG)
+	invr := new(big.Int).ModInverse(sig.R, curve.Params().N)
+
+	// first term.
+	invrS := new(big.Int).Mul(invr, sig.S)
+	invrS.Mod(invrS, curve.Params().N)
+	sRx, sRy := curve.ScalarMult(Rx, Ry, invrS.Bytes())
+
+	// second term.
+	e.Neg(e)
+	e.Mod(e, curve.Params().N)
+	e.Mul(e, invr)
+	e.Mod(e, curve.Params().N)
+	minuseGx, minuseGy := curve.ScalarBaseMult(e.Bytes())
+
+	// TODO(oga) this would be faster if we did a mult and add in one
+	// step to prevent the jacobian conversion back and forth.
+	Qx, Qy := curve.Add(sRx, sRy, minuseGx, minuseGy)
+
+	return &ecdsa.PublicKey{
+		Curve: curve,
+		X:     Qx,
+		Y:     Qy,
+	}, nil
+}
+
+// SignCompact produces a compact signature of the data in hash with the given
+// private key on the given koblitz curve. The isCompressed  parameter should
+// be used to detail if the given signature should reference a compressed
+// public key or not. If successful the bytes of the compact signature will be
+// returned in the format:
+// <(byte of 27+public key solution)+4 if compressed >< padded bytes for signature R><padded bytes for signature S>
+// where the R and S parameters are padde up to the bitlengh of the curve.
+func SignCompact(curve *KoblitzCurve, key *ecdsa.PrivateKey,
+	hash []byte, isCompressedKey bool) ([]byte, error) {
+	r, s, err := ecdsa.Sign(rand.Reader, key, hash)
+	if err != nil {
+		return nil, err
+	}
+
+	sig := &Signature{R: r, S: s}
+	// bitcoind checks the bit length of R and S here. The ecdsa signature
+	// algorithm returns R and S mod N therefore they will be the bitsize of
+	// the curve, and thus correctly sized.
+	for i := 0; i < (curve.H+1)*2; i++ {
+		pk, err := recoverKeyFromSignature(curve, sig, hash, i, true)
+		if err == nil && pk.X.Cmp(key.X) == 0 && pk.Y.Cmp(key.Y) == 0 {
+			result := make([]byte, 1, 2*(curve.BitSize/8)+1)
+			result[0] = 27 + byte(i)
+			if isCompressedKey {
+				result[0] += 4
+			}
+			// Not sure this needs rounding but safer to do so.
+			curvelen := (curve.BitSize + 7) / 8
+
+			// Pad R and S to curvelen if needed.
+			bytelen := (sig.R.BitLen() + 7) / 8
+			if bytelen < curvelen {
+				result = append(result,
+					make([]byte, curvelen-bytelen)...)
+			}
+			result = append(result, sig.R.Bytes()...)
+
+			bytelen = (sig.S.BitLen() + 7) / 8
+			if bytelen < curvelen {
+				result = append(result,
+					make([]byte, curvelen-bytelen)...)
+			}
+			result = append(result, sig.S.Bytes()...)
+
+			return result, nil
+		}
+	}
+
+	return nil, errors.New("no valid solution for pubkey found")
+}
+
+// RecoverCompact verifies the compact signature "signature" of "hash" for the
+// Koblitz curve in "curve". If the signature matches then the recovered public
+// key will be returned as well as a boolen if the original key was compressed
+// or not, else an error will be returned.
+func RecoverCompact(curve *KoblitzCurve, signature,
+	hash []byte) (*ecdsa.PublicKey, bool, error) {
+	bitlen := (curve.BitSize + 7) / 8
+	if len(signature) != 1+bitlen*2 {
+		return nil, false, errors.New("invalid compact signature size")
+	}
+
+	iteration := int((signature[0] - 27) & ^byte(4))
+
+	// format is <header byte><bitlen R><bitlen S>
+	sig := &Signature{
+		R: new(big.Int).SetBytes(signature[1 : bitlen+1]),
+		S: new(big.Int).SetBytes(signature[bitlen+1:]),
+	}
+	// The iteration used here was encoded
+	key, err := recoverKeyFromSignature(curve, sig, hash, iteration, false)
+	if err != nil {
+		return nil, false, err
+	}
+
+	return key, ((signature[0] - 27) & 4) == 4, nil
+}

signature_test.go

@@ -6,6 +6,9 @@ package btcec_test
 
 import (
 	"bytes"
+	"crypto/ecdsa"
+	"crypto/rand"
+	"fmt"
 	"github.com/conformal/btcec"
 	"math/big"
 	"testing"
@@ -420,3 +423,70 @@ func TestSignatureSerialize(t *testing.T) {
 		}
 	}
 }
+
+func testSignCompact(t *testing.T, tag string, curve *btcec.KoblitzCurve,
+	data []byte, isCompressed bool) {
+	priv, _ := ecdsa.GenerateKey(curve, rand.Reader)
+
+	hashed := []byte("testing")
+	sig, err := btcec.SignCompact(curve, priv, hashed, isCompressed)
+	if err != nil {
+		t.Errorf("%s: error signing: %s", tag, err)
+		return
+	}
+
+	pk, wasCompressed, err := btcec.RecoverCompact(curve, sig, hashed)
+	if err != nil {
+		t.Errorf("%s: error recovering: %s", tag,  err)
+		return
+	}
+	if pk.X.Cmp(priv.X) != 0 || pk.Y.Cmp(priv.Y) != 0 {
+		t.Errorf("%s: recovered pubkey doesn't match original "+
+			"(%v,%v) vs (%v,%v) ", tag, pk.X, pk.Y, priv.X, priv.Y)
+		return
+	}
+	if wasCompressed != isCompressed {
+		t.Errorf("%s: recovered pubkey doesn't match compressed state "+
+			"(%v vs %v)", tag, isCompressed, wasCompressed)
+		return
+	}
+
+	// If we change the compressed bit we should get the same key back,
+	// but the compressed flag should be reversed.
+	if isCompressed {
+		sig[0] -= 4
+	} else {
+		sig[0] += 4
+	}
+
+	pk, wasCompressed, err = btcec.RecoverCompact(curve, sig, hashed)
+	if err != nil {
+		t.Errorf("%s: error recovering (2): %s", tag, err)
+		return
+	}
+	if pk.X.Cmp(priv.X) != 0 || pk.Y.Cmp(priv.Y) != 0 {
+		t.Errorf("%s: recovered pubkey (2) doesn't match original "+
+			"(%v,%v) vs (%v,%v) ", tag, pk.X, pk.Y, priv.X, priv.Y)
+		return
+	}
+	if wasCompressed == isCompressed {
+		t.Errorf("%s: recovered pubkey doesn't match reversed "+
+			"compressed state (%v vs %v)", tag, isCompressed,
+			wasCompressed)
+		return
+	}
+}
+
+func TestSignCompact(t *testing.T) {
+	for i := 0; i < 256; i++ {
+		name := fmt.Sprintf("test %d", i)
+		data := make([]byte, 32)
+		_, err := rand.Read(data)
+		if err != nil {
+			t.Errorf("failed to read random data for %s", name)
+			continue
+		}
+		compressed := i%2 != 0
+		testSignCompact(t, name, btcec.S256(), data, compressed)
+	}
+}

test_coverage.txt

@@ -10,50 +10,55 @@ github.com/conformal/btcec/field.go	 fieldVal.PutBytes			 100.00% (32/32)
 github.com/conformal/btcec/btcec.go	 KoblitzCurve.addZ1EqualsZ2		 100.00% (30/30)
 github.com/conformal/btcec/btcec.go	 KoblitzCurve.addZ1AndZ2EqualsOne	 100.00% (29/29)
 github.com/conformal/btcec/btcec.go	 KoblitzCurve.addJacobian		 100.00% (22/22)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.doubleZ1EqualsOne		 100.00% (18/18)
 github.com/conformal/btcec/btcec.go	 KoblitzCurve.doubleGeneric		 100.00% (18/18)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.doubleZ1EqualsOne		 100.00% (18/18)
 github.com/conformal/btcec/signature.go	 Signature.Serialize			 100.00% (13/13)
 github.com/conformal/btcec/btcec.go	 KoblitzCurve.fieldJacobianToBigAffine	 100.00% (12/12)
 github.com/conformal/btcec/field.go	 fieldVal.MulInt			 100.00% (12/12)
-github.com/conformal/btcec/field.go	 fieldVal.Add2				 100.00% (11/11)
 github.com/conformal/btcec/field.go	 fieldVal.Add				 100.00% (11/11)
-github.com/conformal/btcec/field.go	 fieldVal.NegateVal			 100.00% (11/11)
+github.com/conformal/btcec/field.go	 fieldVal.Add2				 100.00% (11/11)
 github.com/conformal/btcec/field.go	 fieldVal.SetBytes			 100.00% (11/11)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.ScalarMult		 100.00% (10/10)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.Add			 100.00% (10/10)
+github.com/conformal/btcec/field.go	 fieldVal.NegateVal			 100.00% (11/11)
 github.com/conformal/btcec/field.go	 fieldVal.Zero				 100.00% (10/10)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.Add			 100.00% (10/10)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.ScalarMult		 100.00% (10/10)
 github.com/conformal/btcec/btcec.go	 KoblitzCurve.doubleJacobian		 100.00% (9/9)
-github.com/conformal/btcec/signature.go	 canonicalizeInt			 100.00% (8/8)
+github.com/conformal/btcec/btcec.go	 initS256				 100.00% (9/9)
 github.com/conformal/btcec/pubkey.go	 PublicKey.SerializeHybrid		 100.00% (8/8)
-github.com/conformal/btcec/btcec.go	 initS256				 100.00% (8/8)
+github.com/conformal/btcec/signature.go	 canonicalizeInt			 100.00% (8/8)
 github.com/conformal/btcec/pubkey.go	 PublicKey.SerializeCompressed		 100.00% (7/7)
 github.com/conformal/btcec/btcec.go	 KoblitzCurve.Double			 100.00% (7/7)
-github.com/conformal/btcec/field.go	 fieldVal.SetByteSlice			 100.00% (5/5)
 github.com/conformal/btcec/pubkey.go	 PublicKey.SerializeUncompressed	 100.00% (5/5)
+github.com/conformal/btcec/field.go	 fieldVal.SetByteSlice			 100.00% (5/5)
 github.com/conformal/btcec/pubkey.go	 pad					 100.00% (5/5)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.bigAffineToField		 100.00% (4/4)
 github.com/conformal/btcec/field.go	 fieldVal.SetHex			 100.00% (4/4)
 github.com/conformal/btcec/signature.go	 canonicalPadding			 100.00% (4/4)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.bigAffineToField		 100.00% (4/4)
 github.com/conformal/btcec/btcec.go	 KoblitzCurve.IsOnCurve			 100.00% (4/4)
 github.com/conformal/btcec/field.go	 fieldVal.SetInt			 100.00% (3/3)
 github.com/conformal/btcec/field.go	 fieldVal.Bytes				 100.00% (3/3)
+github.com/conformal/btcec/field.go	 fieldVal.IsZero			 100.00% (2/2)
+github.com/conformal/btcec/field.go	 fieldVal.AddInt			 100.00% (2/2)
+github.com/conformal/btcec/field.go	 fieldVal.Equals			 100.00% (2/2)
+github.com/conformal/btcec/field.go	 fieldVal.Set				 100.00% (2/2)
 github.com/conformal/btcec/field.go	 fieldVal.String			 100.00% (2/2)
 github.com/conformal/btcec/btcec.go	 S256					 100.00% (2/2)
-github.com/conformal/btcec/field.go	 fieldVal.IsZero			 100.00% (2/2)
-github.com/conformal/btcec/field.go	 fieldVal.Equals			 100.00% (2/2)
-github.com/conformal/btcec/field.go	 fieldVal.AddInt			 100.00% (2/2)
-github.com/conformal/btcec/field.go	 fieldVal.Set				 100.00% (2/2)
 github.com/conformal/btcec/pubkey.go	 isOdd					 100.00% (1/1)
-github.com/conformal/btcec/field.go	 fieldVal.Mul				 100.00% (1/1)
-github.com/conformal/btcec/field.go	 fieldVal.Square			 100.00% (1/1)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.Params			 100.00% (1/1)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.ScalarBaseMult		 100.00% (1/1)
-github.com/conformal/btcec/btcec.go	 KoblitzCurve.QPlus1Div4		 100.00% (1/1)
-github.com/conformal/btcec/btcec.go	 initAll				 100.00% (1/1)
-github.com/conformal/btcec/field.go	 fieldVal.Negate			 100.00% (1/1)
-github.com/conformal/btcec/signature.go	 ParseSignature				 100.00% (1/1)
 github.com/conformal/btcec/signature.go	 ParseDERSignature			 100.00% (1/1)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.ScalarBaseMult		 100.00% (1/1)
+github.com/conformal/btcec/field.go	 fieldVal.Mul				 100.00% (1/1)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.Params			 100.00% (1/1)
+github.com/conformal/btcec/field.go	 fieldVal.Square			 100.00% (1/1)
+github.com/conformal/btcec/field.go	 fieldVal.Negate			 100.00% (1/1)
 github.com/conformal/btcec/field.go	 fieldVal.IsOdd				 100.00% (1/1)
-github.com/conformal/btcec/pubkey.go	 ParsePubKey				 96.88% (31/32)
-github.com/conformal/btcec		 -------------------------------------	 99.88% (846/847)
+github.com/conformal/btcec/btcec.go	 initAll				 100.00% (1/1)
+github.com/conformal/btcec/btcec.go	 KoblitzCurve.QPlus1Div4		 100.00% (1/1)
+github.com/conformal/btcec/signature.go	 ParseSignature				 100.00% (1/1)
+github.com/conformal/btcec/pubkey.go	 ParsePubKey				 96.15% (25/26)
+github.com/conformal/btcec/signature.go	 SignCompact				 90.91% (20/22)
+github.com/conformal/btcec/pubkey.go	 decompressPoint			 88.89% (8/9)
+github.com/conformal/btcec/signature.go	 recoverKeyFromSignature		 86.96% (20/23)
+github.com/conformal/btcec/signature.go	 RecoverCompact				 77.78% (7/9)
+github.com/conformal/btcec/signature.go	 hashToInt				 77.78% (7/9)
+github.com/conformal/btcec		 -------------------------------------	 98.80% (903/914)