MinRank in the Head: Short Signatures from Zero-Knowledge Proofs.

In recent years, many digital signature scheme proposals have been built from the so-called MPC-in-the-head paradigm. This has shown to be an outstanding way to design efficient signatures with security based on hard problems. MinRank is an NP-complete problem extensively studied due to its applications to cryptanalysis since its introduction in 1999. However, only a few schemes base their security on its intractability, and their signature size is large compared with other proposals based on NP problems. This paper introduces the first MinRank-based digital signature scheme that uses the MPC-in-the-head paradigm, allowing to achieve small signature sizes and running times. For NIST’s category I parameter set, we obtain signatures of 6.5KB, which is competitive with the shortest proposals in the literature that are based on non-structured problems.