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

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