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

TL;DR

This paper introduces MIRA, a new digital signature scheme based on the MinRank problem and the MPC-in-the-Head paradigm, achieving improved efficiency and signature sizes through innovative techniques.

Contribution

It presents two novel MPCitH-based signature schemes, MIRA-Additive and MIRA-Threshold, with enhanced efficiency and optimized signature sizes compared to classical methods.

Findings

MIRA-Additive achieves ~5.6kB signature size.

MIRA-Threshold achieves ~8.3kB signature size.

Both schemes are faster than classical MPCitH implementations.

Abstract

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.