A distinguisher for high rate McEliece cryptosystems

Jean Charles Faugère, Valérie Gauthier-Umaña, Ayoub Otmani, Ludovic Perret, Jean Pierre Tillich

Research output: Chapter in Book/ReportConference contribution

56 Scopus citations


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.

Original languageEnglish (US)
Title of host publication2011 IEEE Information Theory Workshop, ITW 2011
Number of pages5
StatePublished - 2011
Externally publishedYes
Event2011 IEEE Information Theory Workshop, ITW 2011 - Paraty, Brazil
Duration: Oct 16 2011Oct 20 2011

Publication series

Name2011 IEEE Information Theory Workshop, ITW 2011


Conference2011 IEEE Information Theory Workshop, ITW 2011

All Science Journal Classification (ASJC) codes

  • Information Systems


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