A distinguisher for high rate McEliece cryptosystems

The Goppa Code Distinguishing (GCD) problem consists in distinguishing the matrix of a Goppa code from a random matrix. Up to now, it is widely believed that the GCD problem is a hard decisional problem. We present the first technique allowing to distinguish alternant and Goppa codes over any field....

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Detalles Bibliográficos
Autores Principales: Faugère, Jean-Charles, Gauthier-Umanã, Valérie, Otmani, Ayoub, Perret, Ludovic, Tillich, Jean-Pierre
Formato: Capítulo de libro (Book Chapter)
Lenguaje:Inglés (English)
Publicado: IEEE 2011
Materias:
Acceso en línea:https://repository.urosario.edu.co/handle/10336/28909
https://doi.org/10.1109/ITW.2011.6089437
Descripción
Sumario:The Goppa Code Distinguishing (GCD) problem consists in distinguishing the matrix of a Goppa code from a random matrix. Up to now, it is widely believed that the GCD problem is a hard decisional problem. We present the first technique allowing to distinguish alternant and Goppa codes over any field. Our technique can solve the GCD problem in polynomial-time provided that the codes have rates sufficiently large. The key ingredient is an algebraic characterization of the key-recovery problem. The idea is to consider the dimension of the solution space of a linearized system deduced from a particular polynomial system describing a key-recovery. It turns out that experimentally this dimension depends on the type of code. Explicit formulas derived from extensive experimentations for the value of the dimension are provided for “generic” random, alternant, and Goppa code over any alphabet. Finally, we give explanations of these formulas in the case of random codes, alternant codes over any field and binary Goppa codes.