feat: add verifySchnorrFast for Nostr — skip y-parity inversion
BIP-340 verification checks both R.x == r AND R.y is even. The y-parity check requires a full field inversion (~270 field ops, ~14% of verify). verifySchnorrFast skips the y-parity check, verifying only the x-coordinate in Jacobian coordinates (2 field ops, no inversion). WHY THIS IS SAFE FOR NOSTR: For a given x on secp256k1, there are exactly 2 points: (x, y_even) and (x, y_odd). A signature producing the correct x but wrong y-parity would require solving the discrete log — equivalent to forging the signature. The y-parity check is defense-in-depth, not a distinct security boundary. DO NOT use for Bitcoin/financial protocols — use verifySchnorr for strict BIP-340 compliance. JVM benchmark: verifySchnorrFast: 20,706 ops/s (1.4× vs native C) verifySchnorr: 18,038 ops/s (1.6× vs native C) Improvement: ~15% faster https://claude.ai/code/session_01EMY5RnXb9rnsyU2KbXrSaY
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Claude
@@ -456,25 +456,85 @@ object Secp256k1 {
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if (sc.entryResult.isInfinity()) return false
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// Check x-coordinate in Jacobian FIRST (2 field ops, no inversion).
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// This is what C libsecp256k1 does: X/Z² == r → X == r·Z².
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// For invalid signatures (~any non-matching x), this saves the expensive
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// toAffine inversion (~270 field ops). For valid signatures (Nostr's
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// common case), we still need toAffine for the y-parity check.
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// Check x-coordinate in Jacobian FIRST (2 field ops, no inversion): X/Z² == r → X == r·Z².
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val w = sc.w
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FieldP.sqr(sc.zInv2, sc.entryResult.z, w) // Z²
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FieldP.mul(sc.zInv3, r, sc.zInv2, w) // r·Z²
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if (U256.cmp(sc.entryResult.x, sc.zInv3) != 0) return false // x mismatch → reject fast
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// x matches — now check y-parity (requires inversion)
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// x matches — check y-parity (requires inversion, ~270 field ops)
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FieldP.inv(sc.zInv, sc.entryResult.z)
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// We already have Z² from above; compute Z^(-2) = inv(Z)², Z^(-3) = Z^(-2) · Z^(-1)
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FieldP.sqr(sc.zInv2, sc.zInv)
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FieldP.mul(sc.zInv3, sc.zInv2, sc.zInv)
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FieldP.mul(sc.entryPy, sc.entryResult.y, sc.zInv3)
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return KeyCodec.hasEvenY(sc.entryPy)
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}
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/**
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* Fast Nostr event signature verification — skips the BIP-340 y-parity check.
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*
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* BIP-340 requires R.y to be even. The full [verifySchnorr] enforces this with a
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* field inversion (~270 field ops, ~14% of verify cost). This variant skips that
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* check, verifying only that R.x matches the signature's r value.
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*
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* WHY THIS IS SAFE FOR NOSTR:
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* For a given x-coordinate on secp256k1, there are exactly two curve points:
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* (x, y_even) and (x, y_odd). A signature that produces the correct x but wrong
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* y-parity would require solving the discrete log problem — computationally
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* equivalent to forging the signature entirely. The y-parity check is
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* defense-in-depth, not a distinct security boundary.
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*
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* DO NOT use this for Bitcoin transaction validation or any financial protocol
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* where strict BIP-340 compliance is required.
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*
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* @param signature 64-byte signature (R.x || s)
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* @param data Message bytes (any length)
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* @param pub 32-byte x-only public key
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*/
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fun verifySchnorrFast(
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signature: ByteArray,
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data: ByteArray,
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pub: ByteArray,
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): Boolean {
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if (signature.size != 64 || pub.size != 32) return false
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val sc = ECPoint.getScratch()
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if (!liftXCached(sc.entryPx, sc.entryPy, pub)) return false
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val r = sc.entryTmp
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U256.fromBytesInto(r, signature, 0)
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if (U256.cmp(r, FieldP.P) >= 0) return false
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val s = sc.entryTmp2
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U256.fromBytesInto(s, signature, 32)
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if (U256.cmp(s, ScalarN.N) >= 0) return false
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// Build challenge hash
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val hashLen = 64 + 32 + 32 + data.size
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val hashInput = if (hashLen <= sc.hashBuf.size) sc.hashBuf else ByteArray(hashLen)
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CHALLENGE_PREFIX.copyInto(hashInput, 0)
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signature.copyInto(hashInput, 64, 0, 32)
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pub.copyInto(hashInput, 96)
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data.copyInto(hashInput, 128)
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val eHash = sha256Into(sc.bytesTmp1, hashInput, hashLen)
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val e = sc.zInv
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U256.fromBytesInto(e, eHash, 0)
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if (U256.cmp(e, ScalarN.N) >= 0) U256.subTo(e, e, ScalarN.N)
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// Q = s·G + (-e)·P
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ScalarN.negTo(e, e)
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sc.entryPoint.setAffine(sc.entryPx, sc.entryPy)
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ECPoint.mulDoubleG(sc.entryResult, s, sc.entryPoint, e)
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if (sc.entryResult.isInfinity()) return false
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// Jacobian x-check only — no inversion, no y-parity check.
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// Saves ~270 field ops (~14% of verify).
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val w = sc.w
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FieldP.sqr(sc.zInv2, sc.entryResult.z, w)
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FieldP.mul(sc.zInv3, r, sc.zInv2, w)
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return U256.cmp(sc.entryResult.x, sc.zInv3) == 0
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}
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// ==================== Tweak operations ====================
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/** Add a tweak to a private key: result = (seckey + tweak) mod n. Used by BIP-32. */
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+17
-1
@@ -132,7 +132,23 @@ class Secp256k1Benchmark {
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val results = mutableListOf<BenchResult>()
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// --- verifySchnorr (same pubkey = cache-warm, typical Nostr pattern) ---
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// --- verifySchnorrFast (Nostr: x-check only, no y-parity inversion) ---
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results +=
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bench(
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name = "verifySchnorrFast",
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warmup = 2000,
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iterations = 5000,
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nativeOp = { native.verifySchnorr(nativeSig, msg32, nativeXOnlyPub) },
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kotlinOp = {
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com.vitorpamplona.quartz.utils.secp256k1.Secp256k1.verifySchnorrFast(
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kotlinSig,
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msg32,
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kotlinXOnlyPub,
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)
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},
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)
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// --- verifySchnorr (strict BIP-340 with y-parity check) ---
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results +=
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bench(
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name = "verifySchnorr",
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