We revisit the construction of signature schemes using the MPC-in-the-head paradigm. We obtain two main contributions:

-We observe that previous signatures in the MPC-in-the-head paradigm must rely on a salted version of the GGM puncturable pseudorandom function (PPRF) to avoid collision attacks. We design a new efficient PPRF construction that is provably secure in the multiinstance setting. The security analysis of our PPRF, in the ideal cipher model, is quite involved and forms a core technical contribution of our work. While previous constructions had to rely on a hash function, our construction uses only a fixed-key block cipher and is considerably more efficient as a result: we observe a 12× to 55× speed improvement for a recent signature scheme (Joux and Huth, Crypto'24). Our improved PPRF can be used to speed up many MPC-in-the-head signatures. -We introduce a new signature scheme from the regular syndrome decoding assumption, based on a new protocol for the MPC-in-the-head paradigm, which significantly reduces communication compared to previous works. Our scheme is conceptually simple, though its security analysis requires a delicate and nontrivial combinatorial analysis.

breaks the scheme using 2 40 signatures in time 2 69 ). The authors later fixed this issue in their NIST submission [AFG + 23], using a proper salted GGM tree instantiated with a hash function.