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Communication Dans Un Congrès Année : 2023

Short Signatures from Regular Syndrome Decoding in the Head

Eliana Carozza
  • Fonction : Auteur
Antoine Joux
  • Fonction : Auteur

Résumé

We introduce a new candidate post-quantum digital signature scheme from the regular syndrome decoding (RSD) assumption, an established variant of the syndrome decoding assumption which asserts that it is hard to find w-regular solutions to systems of linear equations over F2 (a vector is regular if it is a concatenation of w unit vectors). Our signature is obtained by introducing and compiling a new 5-round zero-knowledge proof system constructed using the MPC-in-the-head paradigm. At the heart of our result is an efficient MPC protocol in the preprocessing model that checks correctness of a regular syndrome decoding instance by using a share ring-conversion mechanism. The analysis of our construction is non-trivial and forms a core technical contribution of our work. It requires careful combinatorial analysis and combines several new ideas, such as analyzing soundness in a relaxed setting where a cheating prover is allowed to use any witness sufficiently close to a regular vector. We complement our analysis with an in-depth overview of existing attacks against RSD. Our signatures are competitive with the best-known code-based signatures, ranging from 12.52 KB (fast setting, with signing time of the order of a few milliseconds on a single core of a standard laptop) to about 9 KB (short setting, with estimated signing time of the order of 15 ms).
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Dates et versions

hal-04265627 , version 1 (31-10-2023)

Identifiants

Citer

Eliana Carozza, Geoffroy Couteau, Antoine Joux. Short Signatures from Regular Syndrome Decoding in the Head. 42nd Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 2023), Apr 2023, Lyon, France. pp.532-563, ⟨10.1007/978-3-031-30589-4_19⟩. ⟨hal-04265627⟩
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