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RYDE: a digital signature scheme based on rank syndrome decoding problem with MPC-in-the-Head paradigm.

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Title: RYDE: a digital signature scheme based on rank syndrome decoding problem with MPC-in-the-Head paradigm.
Authors: Bidoux, Loïc, Chi-Domínguez, Jesús-Javier, Feneuil, Thibauld, Gaborit, Philippe, Joux, Antoine, Rivain, Matthieu, Vinçotte, Adrien
Source: Designs, Codes & Cryptography; May2025, Vol. 93 Issue 5, p1451-1486, 36p
Subject Terms: DIGITAL signatures, CRYPTOGRAPHY, CRYPTOCURRENCIES, CONFERENCES & conventions, STANDARDIZATION
Abstract: We present a signature scheme based on the syndrome decoding (SD) 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 Feneuil (Cryptology ePrint Archive, Report 2022/1512, 2022), allowing to obtain a zero-knowledge proof thanks to the MPCitH (MPC-in-the-Head) paradigm. We design two different zero-knowledge proofs exploiting this paradigm: the first, which reaches the lower communication costs, relies on additive secret sharing and uses the hypercube technique (Aguilar-Melchor et al., in: Cryptology ePrint Archive, Report 2022/1645, 2022); and the second relies on low-threshold linear secret sharing as proposed in Feneuil (Cryptology ePrint Archive, Report 2022/1512, 2022). These proofs of knowledge are transformed to signature schemes thanks to the Fiat–Shamir transform (Fiat and Shamir, in: International Cryptology Conference (CRYPTO), 1986) and the resulting schemes have signatures of size less than 6 kB. These performances prompted us to propose this signature scheme to the post-quantum cryptography standardization process organized by NIST. [ABSTRACT FROM AUTHOR]
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Abstract:We present a signature scheme based on the syndrome decoding (SD) 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 Feneuil (Cryptology ePrint Archive, Report 2022/1512, 2022), allowing to obtain a zero-knowledge proof thanks to the MPCitH (MPC-in-the-Head) paradigm. We design two different zero-knowledge proofs exploiting this paradigm: the first, which reaches the lower communication costs, relies on additive secret sharing and uses the hypercube technique (Aguilar-Melchor et al., in: Cryptology ePrint Archive, Report 2022/1645, 2022); and the second relies on low-threshold linear secret sharing as proposed in Feneuil (Cryptology ePrint Archive, Report 2022/1512, 2022). These proofs of knowledge are transformed to signature schemes thanks to the Fiat–Shamir transform (Fiat and Shamir, in: International Cryptology Conference (CRYPTO), 1986) and the resulting schemes have signatures of size less than 6 kB. These performances prompted us to propose this signature scheme to the post-quantum cryptography standardization process organized by NIST. [ABSTRACT FROM AUTHOR]
ISSN:09251022
DOI:10.1007/s10623-024-01544-1