Security analysis of ZKPoK based on MQ problem in the multi-instance setting

Bidoux and Gaborit introduced a new general technique to improve zero-knowledge ( ) proof-of-knowledge ( ) schemes for a large set of well-known post-quantum hard computational problems such as the syndrome decoding, the permuted kernel, the rank syndrome decoding, and the multivariate quadratic ( )...

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Bibliographic Details
Published inJournal of mathematical cryptology Vol. 19; no. 1; pp. 188 - 94
Main Authors Kahrobaei, Delaram, Perret, Ludovic, Vigorito, Martina
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 15.04.2025
Walter de Gruyter GmbH
Subjects
11T06
11T55
11T71
12E20
Algorithms
Decoding
MQ problem
Multivariate analysis
multivariate cryptography
Polynomials
Security
ZkPok protocol
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Summary:Bidoux and Gaborit introduced a new general technique to improve zero-knowledge ( ) proof-of-knowledge ( ) schemes for a large set of well-known post-quantum hard computational problems such as the syndrome decoding, the permuted kernel, the rank syndrome decoding, and the multivariate quadratic ( ) problems. In particular, the authors’ idea in the study of Bidoux and Gaborit was to use the structure of these problems in the multi-instance setting to minimize the communication complexity of the resulting schemes. The security of the new schemes is then related to new hard problems. In this article, we focus on the new multivariate-based and the corresponding new underlying problem: the so-called . We present a new efficient probabilistic algorithm for solving the which is polynomial-time if . We also present experimental results showing that the algorithm is efficient in practice.
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ISSN:1862-2984
1862-2976
1862-2984
DOI:10.1515/jmc-2024-0046