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Faster 2-regular information-set decoding. (English) Zbl 1272.94096
Chee, Yeow Meng (ed.) et al., Coding and cryptology. Third international workshop, IWCC 2011, Qingdao, China, May 30 – June 3, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-20900-0/pbk). Lecture Notes in Computer Science 6639, 81-98 (2011).
Summary: Fix positive integers \(B\) and \(w\). Let \(C\) be a linear code over \(\mathbb F_2\) of length \(Bw\). The 2-regular-decoding problem is to find a nonzero codeword consisting of \(w\) length-\(B\) blocks, each of which has Hamming weight 0 or 2. This problem appears in attacks on the FSB (fast syndrome-based) hash function and related proposals. This problem differs from the usual information-set-decoding problems in that (1) the target codeword is required to have a very regular structure and (2) the target weight can be rather high, so that there are many possible codewords of that weight.
In the paper that introduced FSB [Lect. Notes Comput. Sci. 3715, 64–83 (2005; Zbl 1126.94320)], D. Augot et al. presented a variant of information-set decoding tuned for 2-regular decoding. This paper improves the Augot-Finiasz-Sendrier algorithm in a way that is analogous to Stern’s improvement upon basic information-set decoding. The resulting algorithm achieves an exponential speedup over the previous algorithm.
For the entire collection see [Zbl 1214.94002].

MSC:
94B35 Decoding
94B05 Linear codes, general
Software:
McEliece
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