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].
@article{arxiv.2307.08726,
title = {RYDE: A Digital Signature Scheme based on Rank-Syndrome-Decoding Problem with MPCitH Paradigm},
author = {Loïc Bidoux and Jesús-Javier Chi-Domínguez and Thibauld Feneuil and Philippe Gaborit and Antoine Joux and Matthieu Rivain and Adrien Vinçotte},
journal= {arXiv preprint arXiv:2307.08726},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2307.08575