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Distinguisher-based attacks on public-key cryptosystems using Reed-Solomon codes
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Couvreur, Alain
Gaborit, Philippe
Gauthier-Umaña, Valérie
Otmani, Ayoub
Tillich, Jean-Pierre
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Fecha
2014
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Kluwer Academic Publishers
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Abstract
Because of their interesting algebraic properties, several authors promote the use of generalized Reed-Solomon codes in cryptography. Niederreiter was the first to suggest an instantiation of his cryptosystem with them but Sidelnikov and Shestakov showed that this choice is insecure. Wieschebrink proposed a 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. More recently, new schemes appeared which are the homomorphic encryption scheme proposed by Bogdanov and Lee, and a variation of the McEliece cryptosystem proposed by Baldi et al. which hides the generalized Reed-Solomon code by means of matrices of very low rank. In this work, we show how to mount key-recovery attacks against these public-key encryption schemes. We use the concept of distinguisher which aims at detecting a behavior different from the one that one would expect from a random code. All the distinguishers we have built are based on the notion of component-wise product of codes. It results in a powerful tool that is able to recover the secret structure of codes when they are derived from generalized Reed-Solomon codes. Lastly, we give an alternative to Sidelnikov and Shestakov attack by building a filtration which enables to completely recover the support and the non-zero scalars defining the secret generalized Reed-Solomon code. © 2014 Springer Science+Business Media New York.
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Keywords
Matrix algebra , Public key cryptography , Recovery , Reed-Solomon codes , Code-based cryptography , Distinguishers , Generalized reed-solomon codes , Ho-momorphic encryptions , Key-recovery , Codes (symbols) , Code-based cryptography , Distinguisher , Generalized Reed-Solomon codes , Homomorphic encryption , Key-recovery
