Distinguisher-Based Attacks on Public-Key Cryptosystems Using Reed-Solomon Codes

Alain Couvreur (1, 2) , Philippe Gaborit (3) , Valérie Gautier (4) , Ayoub Otmani (5) , Jean-Pierre Tillich (6)

1 GRACE - Geometry, arithmetic, algorithms, codes and encryption
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 XLIM-DMI - DMI
4 Departamento de Matematicas
5 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
6 SECRET - Security, Cryptology and Transmissions

The purpose of this paper is to demonstrate that a distinguisher of Reed-Solomon codes based on the square code construction leads to the cryptanalysis of several cryptosystems relying on them. These schemes are respectively (i) a homomorphic encryption scheme proposed by Bogdanov and Lee; (ii) a variation of the McEliece cryptosystem proposed by Baldi et al. which firstly uses Reed-Solomon codes instead of Goppa codes and secondly, adds a rank 1 matrix to the permutation matrix; (iii) Wieschebrink's variant of the McEliece cryptosystem which consists in concatenating a few random columns to a generator matrix of a secretly chosen generalized Reed-Solomon code.

Mots clés: McEliece; Code-based cryptography; coordinatewise product of codes; cryptanalysis

Domaines: Cryptographie et sécurité [cs.CR]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Mathématiques [math]

Alain Couvreur, Philippe Gaborit, Valérie Gautier, Ayoub Otmani, Jean-Pierre Tillich. Distinguisher-Based Attacks on Public-Key Cryptosystems Using Reed-Solomon Codes. International Workshop on Coding and Cryptography - WCC 2013, Apr 2013, Bergen, Norway. pp.181-193. ⟨hal-00830594⟩