RYDE: A Digital Signature Scheme based on Rank-Syndrome-Decoding Problem with MPCitH Paradigm

TL;DR

This paper introduces a digital signature scheme based on the rank syndrome-decoding problem, utilizing multi-party computation and zero-knowledge proofs to enhance security and efficiency.

Contribution

It presents a novel signature scheme leveraging MPC protocols and zero-knowledge proofs within the MPCitH paradigm, improving communication costs and security.

Findings

Two zero-knowledge proof protocols with different efficiency trade-offs.

A signature scheme derived from the proofs using the Fiat-Shamir heuristic.

Enhanced security based on the rank syndrome-decoding problem.

Abstract

We present a signature scheme based on the Syndrome-Decoding problem in rank metric. It is a construction from multi-party computation (MPC), using a MPC protocol which is a slight improvement of the linearized-polynomial protocol used in [Fen22], allowing to obtain a zero-knowledge proof thanks to the MPCitH paradigm. We design two different zero-knowledge proofs exploiting this paradigm: the first, which reaches the lower communication costs, relies on additive secret sharings and uses the hypercube technique [AMGH+22]; and the second relies on low-threshold linear secret sharings as proposed in [FR22]. These proofs of knowledge are transformed into signature schemes thanks to the Fiat-Shamir heuristic [FS86].