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.

• Type: Conference
• Year: 2010
• Where: PQCRYPTO
• Authors: Christiane Peters
• Keywords: Algorithm, Code-based Cryptosystems, Cryptology, Information-set-decoding Algorithm, PQCRYPTO 2010