Information-Set Decoding for Linear Codes over Fq

The best known non-structural attacks against code-based cryptosystems are based on information-set decoding. Stern's algorithm and its improvements are well optimized and the complexity is reasonably well understood. However, these algorithms only handle codes over F2. This paper presents a generalization of Stern's information-set- decoding algorithm for decoding linear codes over arbitrary finite fields Fq and analyzes the complexity. This result makes it possible to compute the security of recently proposed code-based systems over non-binary fields. As an illustration, ranges of parameters for generalized McEliece cryptosystems using classical Goppa codes over F31 are suggested for which the new information-set-decoding algorithm needs 2128 bit operations.

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