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A Fast Algorithm for Determining the Linear Complexity of Periodic Sequences over GF(3)

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Cryptology and Network Security (CANS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4301))

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Abstract

A fast algorithm is derived for determining the linear complexity and the minimal polynomial of periodic sequences over GF(3) with period 3n p m, where p is a prime number, and 3 is a primitive root modulo p 2 . The algorithm presented here generalizes the fast algorithm to determine the linear complexity of a sequence over GF(q) with period p m, where p is a prime, q is a prime and a primitive root modulo p 2.

The research is supported by Natural Science Foundation of Anhui Education Bureau (No. 2006KJ238B).

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References

  1. Games, R.A., Chan, A.H.: A fast algorithm for determining the complexity of a binary sequence with period 2n. IEEE Trans on Information Theory 29(1), 144–146 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ding, C.S., Xiao, G.Z., Shan, W.J.: The Stability Theory of Stream Ciphers, pp. 85–88. Springer, Heidelberg (1991)

    MATH  Google Scholar 

  3. Blackburn, S.R.: A generalization of the discrete Fourier transform: determining the minimal polynomial of a periodic sequence. IEEE Trans on Information Theory 40(5), 1702–1704 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. Wei, S.M., Xiao, G.Z., Chen, Z.: Fast algorithms for determining the linear complexity of periodic sequences. Journal of China Institute of Communications 22(12), 48–54 (2001) (in Chinese)

    Google Scholar 

  5. Wei, S.M., Xiao, G.Z., Chen, Z.: A fast algorithm for determining the complexity of a binary sequence with period 2n p m. Science in China (Series F) 32(3), 401–408 (2002)

    Google Scholar 

  6. Wei, S.M., Xiao, G.Z., Chen, Z.: A fast algorithm for determining the minimal polynomial of a sequence with period 2p n over GF(q). IEEE Trans. on Information Theory 48(10), 2754–2758 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. Massey, J.L.: Shift register synthesis and BCH decoding. IEEE Trans. on Information Theory 15(1), 122–127 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  8. McEliece, R.J.: Finite Fields for Computer Scientists and Engineers. Kluwer Academic Publishers, Boston (1987)

    MATH  Google Scholar 

  9. Rosen, K.H.: Elementary Number Theory and its Applications. Addison-Wesley, Reading (1988)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Anhui Univ. of Technology, Ma’anshan, 243002, China

    Jianqin Zhou & Qiang Zheng

Authors
  1. Jianqin Zhou
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  2. Qiang Zheng
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Editor information

Editors and Affiliations

  1. Ecole Normale Supérieure – LIENS/CNRS/INRIA,, France

    David Pointcheval

  2. Centre for Computer and Information Security Research School of Computer Science and Software Engineering, University of Wollongong, Australia

    Yi Mu

  3. Department of Computer Science and Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

    Kefei Chen

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© 2006 Springer-Verlag Berlin Heidelberg

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Zhou, J., Zheng, Q. (2006). A Fast Algorithm for Determining the Linear Complexity of Periodic Sequences over GF(3). In: Pointcheval, D., Mu, Y., Chen, K. (eds) Cryptology and Network Security. CANS 2006. Lecture Notes in Computer Science, vol 4301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11935070_15

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  • DOI: https://doi.org/10.1007/11935070_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49462-1

  • Online ISBN: 978-3-540-49463-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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