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Determining the k-error joint linear complexity spectrum for a binary multisequence with period p n

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Abstract

Recent developments in word-based stream ciphers present the study on multisequences. The joint linear complexity and k-error joint linear complexity are fundamental concepts for the assessment of multisequences. The k-error joint linear complexity spectrum contains all the information about how the joint linear complexity of a multisequence decreases as the number k of allowed bit changes increases. In this paper, we present an efficient algorithm by which the k-error joint linear complexity spectrum for a t-fold p n-periodic binary multisequence can be entirely determined using \(\mathcal {O}(tp^{n}\log p)\) bit operations, where p is an odd prime, 2 is a primitive root modulo p 2 and n is a positive integer.

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Authors and Affiliations

  1. Department of Applied Mathematics, Hefei University of Technology, Hefei, 230009, Anhui, People’s Republic of China

    Fulin Li, Shixin Zhu & Ting Jiang

  2. School of Information Science and Technology, University of Science and Technology of China, Hefei, 230027, Anhui, People’s Republic of China

    Honggang Hu

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  1. Fulin Li
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  2. Shixin Zhu
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  3. Honggang Hu
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  4. Ting Jiang
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Corresponding author

Correspondence to Fulin Li.

Additional information

This research is supported by National Natural Science Foundation of China (No.61271271 and 61370089); Natural Science Foundation of Anhui Province under Grant 1508085MA13; 100Talents Program of Chinese Academy of Science and the Fundamental Research Funds for the Central Universities (J2014HGXJ0075).

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Li, F., Zhu, S., Hu, H. et al. Determining the k-error joint linear complexity spectrum for a binary multisequence with period p n . Cryptogr. Commun. 8, 513–523 (2016). https://doi.org/10.1007/s12095-015-0157-2

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  • DOI: https://doi.org/10.1007/s12095-015-0157-2

Keywords

Mathematics Subject Classfication