MuSig explained SimplyMuSig explained Simply

MuSig is a protocol for aggregating public keys and Schnorr signatures.
It allows multiple participants (A and B) to jointly sign a transaction as if it came from a single key.

If we want to spend funds locked in P_AB,
we sign the transaction by aggregating S_A and S_B:
S_AB = S_A + S_B

✅ Pros

• Saves block space
• Improves privacy
• Faster verification

❌ Cons

• Requires multiple rounds of interaction between signers

Let’s dive deeper into the issue of interactivity

Creating a MuSig signature S_AB requires 3 rounds of communication between A and B:

Before explaining the 3 rounds of communicationBefore explaining the 3 rounds of communication

let me first show you the Schnorr signature equation.

where:

• x = private key
• k = nonce (you pick it randomly)
• h = H(R || P || m)

Each signer computes:
s_i = k_i + H(X, R, m) * x_i

🧩 After aggregation🧩 After aggregation

Now the aggregated signature becomes:

s = (k1 + k2) + H(X, R, m)(x1 + x2)

To create the aggregated signature S_AB,
each participant needs the nonce k from the other participants.

🔄 Round 1🔄 Round 1

Exchange nonce commitment

🔄 Round 2🔄 Round 2

Exchange nonces

🔄 Round 3🔄 Round 3

Exchange partial signatures

After this, each participant can compute the final Schnorr signature:

🧠 MuSig2 Fixes This🧠 MuSig2 Fixes This

It requires only two rounds of communication 🎯

We’ll take a deep dive into MuSig2 in the next post.

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