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Bitcoin BIP 327 Standard
Two-Round Nonce Aggregation
BIP 340 Taproot On-Chain Parity
BIP 327 MuSig2 Multi-Signatures Studio
Simulate Bitcoin BIP 327 two-round Schnorr multisignatures. Inspect rogue-key resistant KeyAgg coefficients, dual-nonce aggregation (R_1 + b · R_2), partial signature shares, and on-chain indistinguishable 64-byte Taproot synthesis.
1. Cosigners & KeyAgg Configuration
2. Transaction Message & Round Execution
Ready (Round 1)
SECURE
Aggregate Public Key
0279be66...
P = ∑ c_i · X_i
On-Chain Signature Size
64 Bytes
Single BIP 340 Taproot Sig
Block Space Saved
68.2%
vs legacy P2WSH multisig
On-Chain Privacy
100.0%
Zero cosigner trace
Taproot Verification
VALID
s · G == R + c · P
3. Two-Round MuSig2 Cryptographic Protocol Flow
Phase 1: Key Aggregation (Offline)
Public Keys: [X_1, X_2].
Key list digest: L = H(X_1 || X_2).
Coefficients: c_1 = H(L, X_1), c_2 = H(L, X_2).
Aggregate Key: P = c_1 · X_1 + c_2 · X_2.
Key list digest: L = H(X_1 || X_2).
Coefficients: c_1 = H(L, X_1), c_2 = H(L, X_2).
Aggregate Key: P = c_1 · X_1 + c_2 · X_2.
Phase 2: Round 1 Nonce Exchange
Signers generate pairs: (r_{i,1}, r_{i,2}) → (R_{i,1}, R_{i,2}).
Aggregated nonces: R_1 = ∑ R_{i,1}, R_2 = ∑ R_{i,2}.
Scaling factor: b = H_Nonce(P, R_1, R_2, m).
Group Nonce: R = R_1 + b · R_2.
Aggregated nonces: R_1 = ∑ R_{i,1}, R_2 = ∑ R_{i,2}.
Scaling factor: b = H_Nonce(P, R_1, R_2, m).
Group Nonce: R = R_1 + b · R_2.
Phase 3: Round 2 Partial Sigs & Sum
Challenge: c = H_BIP340(R, P, m).
Partial signature: s_i = r_{i,1} + b · r_{i,2} + c · c_i · x_i.
Final Signature: s = ∑ s_i mod p.
Output: σ = (R, s) [64 Bytes].
Partial signature: s_i = r_{i,1} + b · r_{i,2} + c · c_i · x_i.
Final Signature: s = ∑ s_i mod p.
Output: σ = (R, s) [64 Bytes].
Aggregated 64-byte Taproot Signature (R || s):
79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f817983b8a1c9e4210d7a82b4c5e6f7a8b9c0d1e2f3a4b5c6d7e8f9a0b1c2d3e4f5a6b
4. BIP 327 Python Reference Implementation
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