Distinguisher-Based Attacks on Public-Key Cryptosystems Using Reed-Solomon Codes

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 \textit{al.} which hides the Generalized Reed-Solomon code by means of matrices of very low rank.