Il Prof. Ludovic Perret, dell'Université Pierre et Marie Curie, Paris, sarà ospite del Dipartimento di Matematica dal 13 al 16 Settembre, e terrà un seminario Martedì 14 settembre alle ore 16 in Sala Seminari

MARTEDI' 14 SETTEMBRE 2010

SEMINARIO 16:00-17:30, Sala Seminari (Dip. Matematica) Algebraic Cryptanalysis of McEliece Variants with Compact Keys Prof. Ludovic Perret ('Université Pierre et Marie Curie,' Paris)

Abstract:

In this talk, we will present a new approach to investigate the security of the McEliece cryptosystem. We recall that this cryptosystem relies on the use of error-correcting codes. Since its invention thirty years ago, no efficient attack had been devised that managed to recover the private key. We prove that the private key of the cryptosystem satisfies a system of bi-homogeneous polynomial equations.This property is due to the particular class of codes considered which are alternanting codes.We have used these highly structured algebraic equations to mount an efficient key-recovery attack against two recent variants of the McEliece cryptosystems that aim at reducing public key sizes. These two compact variants of McEliece managed to propose keys with less than 20,000 bits.To do so, they proposed to use quasi-cyclic or dyadic structures.

An implementation of our algebraic attack in the computer algebra system Magma allows to find the secret-key in a negligible time (less than one second) for almost all the proposed challenges. For instance, a private key designed for a 256-bit security has been found in 0.06 seconds with about 2^17.8 operations. joint work with Jean-Charles Faugère, Ayoub Otmani, and Jean-Pierre Tillich)

Liviana Paoletti Segreteria Scientifica Dipartimento di Matematica "L. Tonelli" Universita' di Pisa tel. 0502213251 e-mail paoletti@dm.unipi.it

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