Paper 2024/252

Short Signatures from Regular Syndrome Decoding, Revisited

Abstract

We revisit the construction of signature scheme using the MPC-in-the-head paradigm, and focus in particular on constructions from the regular syndrome decoding assumption, a well-known variant of the syndrome decoding assumption. 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 provably secure in the multi-instance 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. Our improved PPRF can be used to speed up many MPC-in-the-head signatures, and illustrate it on two signatures: the recent SDitH (submitted to the NIST), and a new signature scheme that we introduce. – 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.