Abstract
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 F 2.
This paper presents a generalization of Stern’s information-set- decoding algorithm for decoding linear codes over arbitrary finite fields F q 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 F 31 are suggested for which the new information-set-decoding algorithm needs 2128 bit operations.
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Peters, C. (2010). Information-Set Decoding for Linear Codes over F q . In: Sendrier, N. (eds) Post-Quantum Cryptography. PQCrypto 2010. Lecture Notes in Computer Science, vol 6061. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12929-2_7
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DOI: https://doi.org/10.1007/978-3-642-12929-2_7
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