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Bounds for the Multicovering Radii of Reed-Muller Codes with Applications to Stream Ciphers

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Abstract

The multicovering radii of a code are recentgeneralizations of the covering radius of a code. For positivem, the m-covering radius of C is the leastradius t such that everym-tuple of vectors is contained in at least one ball of radiust centered at some codeword. In this paper upper bounds arefound for the multicovering radii of first order Reed-Muller codes. These bounds generalize the well-known Norse bounds for the classicalcovering radii of first order Reed-Muller codes. They are exactin some cases. These bounds are then used to prove the existence of secure families of keystreams against a general class of cryptanalytic attacks. This solves the open question that gave rise to the study ofmulticovering radii of codes.

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Authors and Affiliations

  1. Dept. of Mathematics, University of Turku, 20014, Turku, Finland

    I. Honkala

  2. Dept. of Computer Science, University of Kentucky, 763H Anderson Hall, Lexington, KY, 40506-0046

    A. Klapper

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  1. I. Honkala
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  2. A. Klapper
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Honkala, I., Klapper, A. Bounds for the Multicovering Radii of Reed-Muller Codes with Applications to Stream Ciphers. Designs, Codes and Cryptography 23, 131–146 (2001). https://doi.org/10.1023/A:1011291913974

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