1 files changed, 236 insertions, 0 deletions

diff --git a/internal/secp256k1/schnorr.go b/internal/secp256k1/schnorr.go
new file mode 100644
index 0000000..ae7fa75
--- /dev/null
+++ b/internal/secp256k1/schnorr.go
@@ -0,0 +1,236 @@
+package secp256k1
+
+import (
+        "crypto/sha256"
+        "fmt"
+        "math/big"
+)
+
+// Signature represents a Schnorr signature (r, s)
+// r is the x-coordinate of R (32 bytes)
+// s is the scalar response (32 bytes)
+type Signature struct {
+        R *big.Int // x-coordinate of the nonce point
+        S *big.Int // the response scalar
+}
+
+// TaggedHash computes SHA256(SHA256(tag) || SHA256(tag) || msg)
+// This is BIP-340's domain separation technique
+func TaggedHash(tag string, data ...[]byte) []byte {
+        tagHash := sha256.Sum256([]byte(tag))
+        h := sha256.New()
+        h.Write(tagHash[:])
+        h.Write(tagHash[:])
+        for _, d := range data {
+                h.Write(d)
+        }
+        return h.Sum(nil)
+}
+
+// LiftX recovers a point from just its x-coordinate
+// Returns the point with even y (BIP-340 convention)
+func LiftX(x *big.Int) (*Point, error) {
+        // Check x is in valid range
+        if x.Sign() < 0 || x.Cmp(P) >= 0 {
+                return nil, fmt.Errorf("x out of range")
+        }
+
+        // Compute y² = x³ + 7
+        xFe := NewFieldElement(x)
+        ySquared := xFe.Square().Mul(xFe).Add(curveB)
+
+        // Compute y = sqrt(y²) mod p
+        // For secp256k1, sqrt(a) = a^((p+1)/4) mod p
+        exp := new(big.Int).Add(P, big.NewInt(1))
+        exp.Div(exp, big.NewInt(4))
+        y := new(big.Int).Exp(ySquared.value, exp, P)
+
+        // Verify it's actually a square root
+        ySquaredCheck := new(big.Int).Mul(y, y)
+        ySquaredCheck.Mod(ySquaredCheck, P)
+        if ySquaredCheck.Cmp(ySquared.value) != 0 {
+                return nil, fmt.Errorf("x is not on the curve")
+        }
+
+        // BIP-340: use the even y
+        if y.Bit(0) == 1 {
+                y.Sub(P, y)
+        }
+
+        return &Point{
+                x:        NewFieldElement(x),
+                y:        NewFieldElement(y),
+                infinity: false,
+        }, nil
+}
+
+// hasEvenY returns true if the point's y-coordinate is even
+func hasEvenY(p *Point) bool {
+        if p.infinity {
+                return false
+        }
+        return p.y.value.Bit(0) == 0
+}
+
+// xOnlyBytes returns the 32-byte x-coordinate of a public key
+func (pub *PublicKey) XOnlyBytes() []byte {
+        result := make([]byte, 32)
+        xBytes := pub.Point.x.value.Bytes()
+        copy(result[32-len(xBytes):], xBytes)
+        return result
+}
+
+// Sign creates a Schnorr signature for a message
+// Follows BIP-340 specification
+// aux is optional auxiliary randomness (32 bytes); nil uses zeros
+func Sign(priv *PrivateKey, message []byte, aux ...[]byte) (*Signature, error) {
+        // Get the public key point
+        P := G.ScalarMul(priv.D)
+
+        // BIP-340: if P.y is odd, negate the private key
+        d := new(big.Int).Set(priv.D)
+        if !hasEvenY(P) {
+                d.Sub(N, d)
+                P = P.Negate()
+        }
+
+        // Serialize public key x-coordinate (32 bytes)
+        pBytes := make([]byte, 32)
+        pxBytes := P.x.value.Bytes()
+        copy(pBytes[32-len(pxBytes):], pxBytes)
+
+        // BIP-340 nonce generation:
+        // t = d XOR tagged_hash("BIP0340/aux", aux)
+        // k = tagged_hash("BIP0340/nonce", t || P || m)
+        // For deterministic signing, use aux = 32 zero bytes
+        dBytes := make([]byte, 32)
+        dBytesRaw := d.Bytes()
+        copy(dBytes[32-len(dBytesRaw):], dBytesRaw)
+
+        // Use provided aux or default to 32 zero bytes
+        var auxBytes []byte
+        if len(aux) > 0 && len(aux[0]) == 32 {
+                auxBytes = aux[0]
+        } else {
+                auxBytes = make([]byte, 32)
+        }
+        auxHash := TaggedHash("BIP0340/aux", auxBytes)
+
+        t := make([]byte, 32)
+        for i := 0; i < 32; i++ {
+                t[i] = dBytes[i] ^ auxHash[i]
+        }
+
+        kHash := TaggedHash("BIP0340/nonce", t, pBytes, message)
+        k := new(big.Int).SetBytes(kHash)
+        k.Mod(k, N)
+
+        // k cannot be zero (extremely unlikely)
+        if k.Sign() == 0 {
+                return nil, fmt.Errorf("nonce is zero")
+        }
+
+        // R = k * G
+        R := G.ScalarMul(k)
+
+        // BIP-340: if R.y is odd, negate k
+        if !hasEvenY(R) {
+                k.Sub(N, k)
+                R = R.Negate()
+        }
+
+        // Serialize R.x (32 bytes)
+        rBytes := make([]byte, 32)
+        rxBytes := R.x.value.Bytes()
+        copy(rBytes[32-len(rxBytes):], rxBytes)
+
+        // Compute challenge e = hash(R.x || P.x || m)
+        eHash := TaggedHash("BIP0340/challenge", rBytes, pBytes, message)
+        e := new(big.Int).SetBytes(eHash)
+        e.Mod(e, N)
+
+        // Compute s = k + e * d (mod N)
+        s := new(big.Int).Mul(e, d)
+        s.Add(s, k)
+        s.Mod(s, N)
+
+        return &Signature{
+                R: R.x.value,
+                S: s,
+        }, nil
+}
+
+// Verify checks if a Schnorr signature is valid
+// Follows BIP-340 specification
+func Verify(pub *PublicKey, message []byte, sig *Signature) bool {
+        // Check signature values are in range
+        if sig.R.Sign() < 0 || sig.R.Cmp(P) >= 0 {
+                return false
+        }
+        if sig.S.Sign() < 0 || sig.S.Cmp(N) >= 0 {
+                return false
+        }
+
+        // Lift R from x-coordinate
+        R, err := LiftX(sig.R)
+        if err != nil {
+                return false
+        }
+
+        // Get public key with even y
+        P := pub.Point
+        if !hasEvenY(P) {
+                P = P.Negate()
+        }
+
+        // Serialize for hashing
+        rBytes := make([]byte, 32)
+        rxBytes := sig.R.Bytes()
+        copy(rBytes[32-len(rxBytes):], rxBytes)
+
+        pBytes := make([]byte, 32)
+        pxBytes := P.x.value.Bytes()
+        copy(pBytes[32-len(pxBytes):], pxBytes)
+
+        // Compute challenge e = hash(R.x || P.x || m)
+        eHash := TaggedHash("BIP0340/challenge", rBytes, pBytes, message)
+        e := new(big.Int).SetBytes(eHash)
+        e.Mod(e, N)
+
+        // Verify: s*G == R + e*P
+        sG := G.ScalarMul(sig.S)
+        eP := P.ScalarMul(e)
+        expected := R.Add(eP)
+
+        return sG.Equal(expected)
+}
+
+// Bytes returns the signature as 64 bytes (r || s)
+func (sig *Signature) Bytes() []byte {
+        result := make([]byte, 64)
+
+        rBytes := sig.R.Bytes()
+        sBytes := sig.S.Bytes()
+
+        copy(result[32-len(rBytes):32], rBytes)
+        copy(result[64-len(sBytes):64], sBytes)
+
+        return result
+}
+
+// SignatureFromBytes parses a 64-byte signature
+func SignatureFromBytes(b []byte) (*Signature, error) {
+        if len(b) != 64 {
+                return nil, fmt.Errorf("signature must be 64 bytes")
+        }
+
+        r := new(big.Int).SetBytes(b[:32])
+        s := new(big.Int).SetBytes(b[32:])
+
+        return &Signature{R: r, S: s}, nil
+}
+
+// Hex returns the signature as a 128-character hex string
+func (sig *Signature) Hex() string {
+        return fmt.Sprintf("%x", sig.Bytes())
+}