Welcome to the resource topic for 2025/1909
Title:
Weak Instances of the Inverse Matrix Code Equivalence Problem
Authors: Jesús-Javier Chi-Domínguez
Abstract:Nowadays, the Matrix Code Equivalence Problem shows potential applicability in constructing efficient and secure advanced digital signatures, focusing on linkable ring signatures, threshold signatures, and blind signatures. Current constructions of these advanced signatures rely on relaxed instantiations of the Matrix Code Equivalence Problem: given two pairs of equivalent matrix codes, find (if it exists) the secret isometry connecting the pairs. For example, the linkable ring signature construction by Chou et al. (AFRICACRYPT, 2023) builds on top of the Inverse Matrix Code Equivalence Problem: given three equivalent matrix codes, where one pair of the codes is connected by the secret isometry and another by the inverse of that isometry, find the secret isometry.
This paper studies the Inverse Matrix Code Equivalence Problem, focusing on the family of instances where the secret isometry is (skew) symmetric. Our main contribution corresponds to a new algorithm for solving these instances of the Inverse Matrix Code Equivalence Problem. As an implication, we identify weak instances of this kind of instantiation of the Inverse Matrix Code Equivalence Problem, for around 70% of the possible parameter set choices (i.e., code dimension k, and code lengths m and n), our algorithm runs (heuristically) in polynomial time. In addition, our results spotlight an additional 35% of parameter sets where the best algorithm for solving the Matrix Code Equivalence Problem, proposed by Couvreur and Levrat (Crypto, 2025), does not apply.
Our results have a crucial security impact on the recent blind signature construction proposed by Kuchta, LeGrow, and Persichetti (ePrint IACR, 2025), whose security is closely related to the hardness of solving these kinds of instances of the Inverse Matrix Code Equivalent Problem.
ePrint: https://eprint.iacr.org/2025/1909
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