DahLIAS: Discrete Logarithm-Based Interactive Aggregate Signatures

In the detailed examination of the MuSig2 cryptographic protocol, an interesting discussion arises regarding its vulnerability to a specific attack strategy. The concern centers on whether the same attack method, which involves requesting a partial signature for a given public key and message from an honest signer, can be effectively applied to MuSig2 itself. This process allows the attacker to generate a partial signature for a modified public key and potentially a different message, leveraging a technique known as tweaking.

The crux of the matter lies in the distinction between the original MuSig2 scheme and its iteration, MuSig2-IAS (Implicitly Authenticated Signatures). In the context of the attack, while MuSig2 requires the message to remain unchanged (m' = m), MuSig2-IAS accommodates a scenario where the message can differ (m != m'). As a result, the adversary is capable of creating a valid signature for the altered public key and message combination under both schemes. However, the implications of these signatures vary significantly between MuSig2 and MuSig2-IAS. For MuSig2, the signature, sigma_1, matches the message initially signed by the honest participant, raising questions about its classification as a forgery. Conversely, sigma_2, associated with MuSig2-IAS, unambiguously constitutes a forgery since it verifies a message not signed by the legitimate key holder, clearly breaching the EUF-CMA-TK security model outlined in the DahLIAS paper.

This differentiation underscores the nuanced nature of security within cryptographic protocols and the importance of defining clear security models. Although the MuSig2 paper does not provide a specific model for evaluating the security of tweaked multisignatures, the discussion hints at the possibility of developing such a framework. Whether sigma_1 should be considered a forgery hinges on the abstract security notion adopted, illustrating the complexity of assessing vulnerabilities in cryptographic systems.

Furthermore, the practical implications of this vulnerability for MuSig2 remain uncertain. While theoretically conceivable, scenarios leading to significant issues appear contrived. Nonetheless, acknowledging and addressing these potential vulnerabilities in formal documentation, such as the Bitcoin Improvement Proposal (BIP), could enhance the security and robustness of the protocol, ensuring it remains resilient against sophisticated attack vectors. This conversation not only highlights the depth of analysis required to secure cryptographic mechanisms but also emphasizes the collaborative effort in the development community to identify and mitigate possible threats.