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An efficient attack against insecure variants of MuSig, based on Benhamouda et al (2020)

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insecure-musig

This repo demonstrates an attack against "InsecureMuSig", a modified version of MuSig where the nonce commitment round is omitted. Equivalently, this is an attack against a modified version of MuSig2 with the degenerate case nu = 1.

Although it might be feasible to use Wagner's algorithm, we instead use the approach from On the (in)security of ROS. This approach uses 256 concurrent signing sessions (one for each bit of the SHA256 challenge hash), and is extremely efficient: the running time is completely dominated by the time needed to actually complete the signing sessions.

The InsecureMuSig implementation is designed to be interoperable with BIP-340. In fact, the reference implementation of Schnorr signatures was copied directly from the BIPs repo.

Note that the use of "xonly" points in BIP-340 significantly complicates the attack. We partially handle the complexity by regenerating/retrying until all attacker public keys/nonces have even y coordinate. The attack currently only works against an honest signer whose public key has even y coordinate, but in the future we can likely get around this by handling the two cases separately.

The attack itself can be found in insecure_musig.py; the function test_forgery is a good entry point.

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An efficient attack against insecure variants of MuSig, based on Benhamouda et al (2020)

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