Cryptanalysis of a system based on twisted Reed–Solomon codes - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Designs, Codes and Cryptography Année : 2020

Cryptanalysis of a system based on twisted Reed–Solomon codes

Résumé

Twisted Reed-Solomon (TRS) codes are a family of codes that contains a large number of maximum distance separable codes that are non-equivalent to Reed--Solomon codes. TRS codes were recently proposed as an alternative to Goppa codes for the McEliece code-based cryptosystem, resulting in a potential reduction of key sizes. The use of TRS codes in the McEliece cryptosystem has been motivated by the fact that a large subfamily of TRS codes is resilient to a direct use of known algebraic key-recovery methods. In this paper, an efficient key-recovery attack on the TRS variant that was used in the McEliece cryptosystem is presented. The algorithm exploits a new approach based on recovering the structure of a well-chosen subfield subcode of the public code. It is proved that the attack always succeeds and breaks the system for all practical parameters in $O(n^4)$ field operations. A software implementation of the algorithm retrieves a valid private key from the public key within a few minutes, for parameters claiming a security level of 128 bits. The success of the attack also indicates that, contrary to common beliefs, subfield subcodes of the public code need to be precisely analyzed when proposing a McEliece-type code-based cryptosystem. Finally, the paper discusses an attempt to repair the scheme and a modification of the attack aiming at Gabidulin-Paramonov-Tretjakov cryptosystems based on twisted Gabidulin codes.

Dates et versions

hal-02884628 , version 1 (30-06-2020)

Identifiants

Citer

Julien Lavauzelle, Julian Renner. Cryptanalysis of a system based on twisted Reed–Solomon codes. Designs, Codes and Cryptography, 2020, 88 (7), pp.1285-1300. ⟨10.1007/s10623-020-00747-6⟩. ⟨hal-02884628⟩
93 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More