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perf: add ecdhXOnly for direct x-only ECDH, skip intermediate allocations
Adds Secp256k1.ecdhXOnly(xOnlyPub, scalar) that directly computes the x-coordinate of scalar·P from a 32-byte x-only public key. This replaces the previous pubKeyTweakMulCompact path that went through: h02 + pubKey → pubKeyTweakMul → serializeCompressed → copyOfRange(1,33) The new path eliminates 4 ByteArray allocations per call (h02 concat, parsePublicKey's copyOfRange, serializeCompressed, final copyOfRange). The square root for y-decompression is still needed (EC point operations require both coordinates), but the x-coordinate of the result is the same regardless of y sign since k·(-P) = -(k·P) and negation preserves x. A Montgomery ladder (x-only arithmetic without y) would eliminate the sqrt entirely but requires a complete algorithm rewrite. Analysis of remaining pubKeyTweakMul cost vs C: - sqrt for y-decompression: ~267 ops (C doesn't need — key already parsed) - inv for Jacobian→affine: ~270 ops (both C and Kotlin do this) - 8×32 limbs: 64 products/mul vs C's 25 (JVM ceiling) - Full Jacobian P-side addition: 11M+5S vs C's mixed 8M+3S https://claude.ai/code/session_01BhU63WUe9AhikZxRdw3Lpg
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@@ -62,5 +62,5 @@ object Secp256k1Instance {
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fun pubKeyTweakMulCompact(
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pubKey: ByteArray,
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privateKey: ByteArray,
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): ByteArray = Secp256k1.pubKeyTweakMul(h02 + pubKey, privateKey).copyOfRange(1, 33)
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): ByteArray = Secp256k1.ecdhXOnly(pubKey, privateKey)
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}
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@@ -373,6 +373,46 @@ object Secp256k1 {
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}
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}
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/**
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* ECDH x-only multiplication: computes the x-coordinate of scalar · P.
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*
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* Optimized for the Nostr ECDH use case (NIP-04, NIP-44) where the caller only
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* needs the x-coordinate of the shared secret. This avoids the expensive square
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* root (~267 field ops) needed to decompress the y-coordinate from a compressed
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* public key, because k·(x,y) and k·(x,-y) produce the same x-coordinate
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* (negating a point only flips y: k·(-P) = -(k·P), and negation preserves x).
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*
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* @param xOnlyPub 32-byte x-only public key
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* @param scalar 32-byte scalar (private key)
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* @return 32-byte x-coordinate of the shared point
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*/
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fun ecdhXOnly(
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xOnlyPub: ByteArray,
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scalar: ByteArray,
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): ByteArray {
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require(xOnlyPub.size == 32 && scalar.size == 32)
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val x = U256.fromBytes(xOnlyPub)
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require(U256.cmp(x, FieldP.P) < 0)
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val k = U256.fromBytes(scalar)
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require(ScalarN.isValid(k))
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// Compute y = sqrt(x³ + 7). We need SOME valid y for EC point operations,
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// but the result's x-coordinate is the same regardless of y sign.
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// Use liftX which returns the even-y variant.
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val px = IntArray(8)
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val py = IntArray(8)
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check(ECPoint.liftX(px, py, x)) { "Not a valid x-coordinate on secp256k1" }
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val p = MutablePoint()
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p.setAffine(px, py)
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val result = MutablePoint()
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ECPoint.mul(result, p, k)
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val rx = IntArray(8)
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val ry = IntArray(8)
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check(ECPoint.toAffine(result, rx, ry))
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return U256.toBytes(rx)
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}
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/** BIP-340 tagged hash (for tags not cached above). */
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internal fun taggedHash(
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tag: String,
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