Code equivalence is a well-known concept in coding theory. Re-cently, literature saw an increased interest in this notion, due to the intro-duction of protocols based on the hardness of finding the equivalence between two linear codes. In this paper, we analyze the security of code equivalence, with a special focus on the hardest instances, in the interest of cryptographic usage. Our work stems from a thorough review of existing literature, identifies the various types of solvers for the problem, and provides a precise complexity analysis, where previously absent. Furthermore, we are able to improve on the state of the art, providing more efficient algorithm variations, for which we include numerical simulation data. In the end, the goal of this paper is to provide a complete, single point of access, which can be used as a tool for designing schemes that rely on the code equivalence problem.
On the Computational Hardness of the Code Equivalence Problem in Cryptography / Barenghi, A.; Biasse, J. -F.; Persichetti, E.; Santini, P.. - In: ADVANCES IN MATHEMATICS OF COMMUNICATIONS. - ISSN 1930-5346. - 17:1(2023), pp. 23-55. [10.3934/amc.2022064]
On the Computational Hardness of the Code Equivalence Problem in Cryptography
Persichetti E.;
2023
Abstract
Code equivalence is a well-known concept in coding theory. Re-cently, literature saw an increased interest in this notion, due to the intro-duction of protocols based on the hardness of finding the equivalence between two linear codes. In this paper, we analyze the security of code equivalence, with a special focus on the hardest instances, in the interest of cryptographic usage. Our work stems from a thorough review of existing literature, identifies the various types of solvers for the problem, and provides a precise complexity analysis, where previously absent. Furthermore, we are able to improve on the state of the art, providing more efficient algorithm variations, for which we include numerical simulation data. In the end, the goal of this paper is to provide a complete, single point of access, which can be used as a tool for designing schemes that rely on the code equivalence problem.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.