js-musig2-bip327-nonce-coefficient-partial-sig-verification-exactness
Done. The verified solution is written to ~/SOLUTION.md (self-contained: root-cause analysis, full implementation, full test harness, and verification evidence), with the runnable project at ~/musig2/.
Diagnosis (root causes of exactness/security failures):
- Parity bookkeeping — BIP-340/BIP-327 are x-only, so nonces (k_i when R is odd), key parity (g when Q is odd), and tweak parity must all be folded in; skipping any yields plausible-but-invalid signatures.
- Transcript exactness — the coefficient b = H("MuSig/noncecoef", aggnonce‖xonly(Q)‖msg) and the key coefficient a_i = H("KeyAgg coefficient", L‖pk_i) must use the exact tags and concatenation order.
- Aggregation rules — the "second unique key has coefficient 1" rule, 33-zero-byte infinity encoding, and gacc/tacc tweak accumulation.
- Nonce reuse — sign must burn the secret nonce before use.
- Rogue key — coefficients bound to the full key list turn key-cancellation into a hash fixed-point problem.
Fix: a 1:1 JS port of bip-0327/reference.py (src/musig2.js) using @noble/curves only for secp256k1 arithmetic/serialization/BIP-340 verify.
Verification (all green):
ok key_sort / key_agg / nonce_gen / nonce_agg / sign_verify / tweak / det_sign / sig_agg
ok end_to_end(random)
ok nonce_reuse_rejected
ok rogue_key_delayed_pubkey
ALL PASS (130 assertions)
Q ≠ target, the forged signature fails under Q, dropping the honest partial fails, and the honest 2-of-2 still verifies.reference.py passes the same vectors).# Evidence - Problem class: js-musig2-bip327-nonce-coefficient-partial-sig-verification-exactness - Model: openrouter/deepseek/deepseek-v4.1-flash - Solved: 2026-10-01T04:07:39.811Z - Verification: solution produced by pi in sandbox; see signatures.json
{"description": "Implement BIP-327 MuSig2 two-round Schnorr multi-signature aggregation on secp256k1 with x-only tweaked keys: every signer commits to two nonces in round one, the aggregator derives the nonce coefficient b from the aggregate nonce and the message, and round two yields partial signatures whose sum is the final 64-byte BIP-340 signature. Verify the implementation byte-for-byte against the BIP-327 vectors (plain, tweaked-key and sigagg scenarios), reject a signer that reuses a nonce pair for a different message, and prove that a rogue signer who delays publishing their public key until after seeing the aggregate nonce still cannot forge an aggregate signature.", "environment": "node20", "language": "js", "model": "openrouter/deepseek/deepseek-v4.1-flash", "problem_class": "js-musig2-bip327-nonce-coefficient-partial-sig-verification-exactness", "provider": "openrouter", "solved_at": "2026-10-01T04:07:39.811Z", "version": "20"}