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International Conference on Coding and Cryptology

IWCC 2011: Coding and Cryptology pp 81–98Cite as

Faster 2-Regular Information-Set Decoding

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6639))

Abstract

Fix positive integers B and w. Let C be a linear code over 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.

Augot, Finiasz, and Sendrier, in the paper that introduced FSB, 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.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Chicago, Chicago, IL, 60607–7045, USA

    Daniel J. Bernstein

  2. Department of Mathematics and Computer Science Technische, Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, Netherlands

    Tanja Lange & Christiane Peters

  3. Institute of Information Science Academia Sinica, 128 Section 2 Academia Road, Taipei, 115-29, Taiwan

    Peter Schwabe

Authors
  1. Daniel J. Bernstein
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  2. Tanja Lange
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  3. Christiane Peters
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  4. Peter Schwabe
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Editor information

Editors and Affiliations

  1. School of Physical and Mathematical Sciences, Division of Mathematical Sciences, Nanyang Technological University, 637371, Singapore

    Yeow Meng Chee , San Ling , Huaxiong Wang  & Chaoping Xing , ,  & 

  2. College of Information Engineering, Qingdao University, 266071, Shandong, P.R. China

    Zhenbo Guo

  3. Qingdao University, 266071, Shandong, P.R. China

    Fengjing Shao

  4. School of Mathematical Sciences, Yangzhou University, 225002, Jiangsu, P.R. China

    Yuansheng Tang

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Bernstein, D.J., Lange, T., Peters, C., Schwabe, P. (2011). Faster 2-Regular Information-Set Decoding. In: Chee, Y.M., et al. Coding and Cryptology. IWCC 2011. Lecture Notes in Computer Science, vol 6639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20901-7_5

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  • DOI: https://doi.org/10.1007/978-3-642-20901-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20900-0

  • Online ISBN: 978-3-642-20901-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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