MiRitH (from MinRank-in-the-Head) is a project in collaboration between the Technology Innovation Institute of Abu Dhabi (UAE) and the Politecnico di Torino (Italy).
MiRitH is a Digital Signature Scheme (DSS) whose security is based on the hardness of solving the MinRank problem. MiRitH has been submitted to the NIST Call for Additional Digital Signature Schemes for the Post-Quantum Cryptography Standardization Process (https://csrc.nist.gov/projects/pqc-dig-sig) . The scheme allows high flexibility in the parameters choice and several trade-offs between signature size and sign/verification time.
Informally, the MinRank problem asks to find a non-trivial low-rank linear combination of some given matrices over a finite field. The construction of MiRitH starts from an MPC-in-the-Head (MPCitH) Zero-Knowledge Proof of Knowledge (ZKPoK) of a solution to the MinRank problem, which is then used to construct a 5-pass identification scheme, which in turn is converted into a non-interactive signature scheme via the Fiat-Shamir transform.
MiRitH is built on top of the MinRank-based signature scheme proposed by Adj, Rivera-Zamarripa, and Verbel [ARZV], which introduced a Multi-Party Computation (MPC) protocol P to verify solutions to the MinRank problem using the Kipnis--Shamir modeling and checking that a triple of shared matrices (Z, X, Y) satisfies Z = X.Y.
MiRitH introduces two optimizations over [ARZV], namely:
More details can be found in the technical specifications document.
As an example, for several variants of MiRitH, we report key/signature sizes and constant-time AVX2 implementation benchmarks on an 11th Gen Intel(R) Core(TM) i7-1165G7 @ 2.80GHz (Turbo Boost disabled). Other variants of the scheme and related performances can be found in the specifications document.
This numbers are dependent on the eXtended Keccak Code Package (XKCP) compiled with AVX2 enabled (https://github.com/XKCP/XKCP).
|Set||Variant||Public key [bytes]||Secret key [bytes]||Signature (avg) [bytes]||KeyGen[Clock Cycles]||Sign [Clock Cycles]||Verify [Clock Cycles]|