Algebraic Cryptanalysis of McEliece Variants with Compact Keys -- Toward a Complexity Analysis

Abstract : A new algebraic approach to investigate the security of the McEliece cryptosystem has been proposed by Faugère-Otmani-Perret-Tillich in Eurocrypt 2010. This paper is an extension of this work. The McEliece’s scheme relies on the use of error-correcting codes. It has been proved 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 alternant codes. These highly structured algebraic equations allowed to mount an efficient key-recovery attack against two recent variants of the McEliece cryptosystems that aim at reducing public key sizes by using quasi-cyclic or quasi-dyadic structures. Thanks to a very recent development due to Faugère-Safey el Din-Spaenlehauer on the solving of bihomogeneous bilinear systems, we can estimate the complexity of the FOPT algebraic attack. This is a first step toward providing a concrete criterion for evaluating the security of future compact McEliece variants.
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Submitted on : Tuesday, March 15, 2016 - 4:51:30 PM
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  • HAL Id : hal-01288888, version 1


Jean-Charles Faugère, Ayoub Otmani, Ludovic Perret, Jean-Pierre Tillich. Algebraic Cryptanalysis of McEliece Variants with Compact Keys -- Toward a Complexity Analysis. SCC '10: the 2nd International Conference on Symbolic Computation and Cryptography, Jun 2010, London, United Kingdom. pp.45-55. ⟨hal-01288888⟩



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