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Periodic Sequences with Maximal Linear Complexity and Large k-Error Linear Complexity

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Abstract

The linear complexity and the k-error linear complexity are important concepts for the theory of stream ciphers in cryptology. Keystreams that are suitable for stream ciphers must have large values of these complexity measures. We study periodic sequences over an arbitrary finite field 𝔽 q and establish conditions under which there are many periodic sequences over 𝔽 q with period N, maximal linear complexity N, and k-error linear complexity close to N. The existence of many such sequences thwarts attacks against the keystreams by exhaustive search.

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Authors and Affiliations

  1. Temasek Laboratories, National University of Singapore, Engineering Drive 3, 10 Kent Ridge Crescent, Singapore, 119260, Republic of Singapore

    Wilfried Meidl

  2. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Harald Niederreiter

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  1. Wilfried Meidl
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  2. Harald Niederreiter
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Correspondence to Harald Niederreiter.

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Meidl, W., Niederreiter, H. Periodic Sequences with Maximal Linear Complexity and Large k-Error Linear Complexity. AAECC 14, 273–286 (2003). https://doi.org/10.1007/s00200-003-0134-4

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  • DOI: https://doi.org/10.1007/s00200-003-0134-4

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