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We exploit the idea of [Fen22] which proposes to build an efficient signaturescheme based on a zero-knowledge proof of knowledge of a solution of a MinRankinstance. The scheme uses the MPCitH paradigm, which is an efficient way tobuild ZK proofs. We combine this idea with another idea, the hypercubetechnique introduced in [AMGH+22], which leads to more efficient MPCitH-basedscheme. This new approach is more efficient than classical MPCitH, as it allowsto reduce the number of party computation. This gives us a first scheme calledMIRA-Additive. We then present an other scheme, based on low-threshold secretsharings, called MIRA-Threshold, which is a faster scheme, at the price oflarger signatures. The construction of MPCitH using threshold secret sharing isdetailed in [FR22]. These two constructions allows us to be faster thanclassical MPCitH, with a size of signature around 5.6kB with MIRA-Additive, and8.3kB with MIRA-Threshold. We detail here the constructions and optimizationsof the schemes, as well as their security proofs.

MIRA: a Digital Signature Scheme based on the MinRank problem and the MPC-in-the-Head paradigm