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Fast Algorithms for Determining the Linear Complexity of Period Sequences

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Progress in Cryptology — INDOCRYPT 2002 (INDOCRYPT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2551))

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Abstract

We introduce a fast algorithm for determining the linear complexity and the minimal polynomial of a sequence with period p n over GF(q) , where p is an odd prime, q is a prime and a primitive root modulo p 2; and its two generalized algorithms. One is the algorithm for determining the linear complexity and the minimal polynomial of a sequence with period p mqn over GF(q), the other is the algorithm for determining the k-error linear complexity of a sequence with period p n over GF(q), where p is an odd prime, q is a prime and a primitive root modulo p 2. The algorithm for determining the linear complexity and the minimal polynomial of a sequence with period 2p n over GF(q) is also introduced. where p and q are odd prime, and q is a primitive root (mod p 2). These algorithms uses the fact that in these case the factorization of x N—1 is especially simple for N= p n, 2p n, p nqm.

The work was supported in part by 973 Project(G1999035804) and the Natural Science Foundation of China under Grant 60172015 and 60073051.

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Author information

Authors and Affiliations

  1. National Key Lab of ISN, Xidian University, Xi’an 710071, China

    Guozhen Xiao

  2. Department of Computer Science and Technique, Peking University, 100871, Beijing, China

    Shimin Wei

Authors
  1. Guozhen Xiao
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  2. Shimin Wei
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Editor information

Editors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Alfred Menezes

  2. Applied Statistics Unit, Indian Statistical Institute, 203, B.T. Road, 700108, Kolkata, India

    Palash Sarkar

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© 2002 Springer-Verlag Berlin Heidelberg

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Xiao, G., Wei, S. (2002). Fast Algorithms for Determining the Linear Complexity of Period Sequences. In: Menezes, A., Sarkar, P. (eds) Progress in Cryptology — INDOCRYPT 2002. INDOCRYPT 2002. Lecture Notes in Computer Science, vol 2551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36231-2_2

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  • DOI: https://doi.org/10.1007/3-540-36231-2_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00263-5

  • Online ISBN: 978-3-540-36231-9

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