  We exploit the idea of [Fen22] which proposes to build an efficient signature
scheme based on a zero-knowledge proof of knowledge of a solution of a MinRank
instance. The scheme uses the MPCitH paradigm, which is an efficient way to
build ZK proofs. We combine this idea with another idea, the hypercube
technique introduced in [AMGH+22], which leads to more efficient MPCitH-based
scheme. This new approach is more efficient than classical MPCitH, as it allows
to reduce the number of party computation. This gives us a first scheme called
MIRA-Additive. We then present an other scheme, based on low-threshold secret
sharings, called MIRA-Threshold, which is a faster scheme, at the price of
larger signatures. The construction of MPCitH using threshold secret sharing is
detailed in [FR22]. These two constructions allows us to be faster than
classical MPCitH, with a size of signature around 5.6kB with MIRA-Additive, and
8.3kB with MIRA-Threshold. We detail here the constructions and optimizations
of the schemes, as well as their security proofs.
