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].

翻译：本文提出一种基于秩度量中综合征解码问题的签名方案。该方案采用多方计算（MPC）构建，所使用的MPC协议是对[Fen22]中线性化多项式协议的轻微改进，通过MPCitH范式实现零知识证明。我们利用该范式设计了两种不同的零知识证明：第一种方案通过加法秘密共享结合超立方体技术[AMGH+22]实现较低通信开销；第二种方案则基于[FR22]提出的低阈值线性秘密共享。这些知识证明通过Fiat-Shamir启发式[FS86]转化为签名方案。