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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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References

  1. Berlekamp, E.: Algebraic Coding Theory. McGraw-Hill, New York (1968)

  2. Massey, J.: Shift register synthesis and BCH decoding. IEEE Trans. Inf. Theory 15(1), 122–127 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  3. Stamp, M., Martin, C.F.: An algorithm for the k-error linear complexity of binary sequences with period 2n. IEEE Trans. Inf. Theory 39, 1389–1401 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ding, C., Xiao, G., Shan, W.: The stability theory of stream ciphers. Lecture Notes in Computer Science, vol. 561. Springer, Berlin (1991)

  5. Ding, C.: Lower bounds on the weight complexities of cascaded binary sequences, in advances in Cryptology-AVSCRYPT’90. Lecture Notes in Computer Science. In: Seberry, J., Pieprzyk, J. (eds.) , vol. 453, pp 39–43. Springer, Berlin (1991)

  6. Niederreiter, H.: Periodic sequences with the large k-error linear complexity. IEEE Trans. Inf. Theory 49, 501–505 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Meidl, W.: How many bits have to be changed to decrease the linear complexity ?. Des. Codes Cryptogr. 109–122, 33 (2004)

    MathSciNet  MATH  Google Scholar 

  9. Xiao, G.Z., Wei, S.M., et al.: A fast algorithm for determining the linear complexity of a sequence with period p n over F q . IEEE Trans. Inf. Theory 46(6), 2203–2206 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lauder, A., Paterson, K.: Computing the error linear complexity spectrum of a binary sequence of period 2n. IEEE Trans. Inf. Theory 49(1), 273–280 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang, L.P., Zhu, Y.F.: On the lattice basis reduction multisequences synthesis algorithm. IEEE Trans. Inf. Theory 50(11), 2905–2910 (2004)

    Article  MATH  Google Scholar 

  12. Sidorenko, V.R., Schmidt G.: A linear algebraic approach to multisequence shift-register synthesis. Probl. Inf. Transm. 47(2), 149–165 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Xing, C.P., Ding, Y.: Multisequences linear with large field, k-error linear complexity from Hermitian function. IEEE Trans. Inf. Theory 55(8), 3858–3863 (2009)

    Article  MathSciNet  Google Scholar 

  14. Niederreiter, H., Venkateswarlu, A.: Periodic multisequences with large error linear complexity. Des Codes Cryptogr. 49, 33–45 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Meidl, W., Niederreiter, H., Venkateswarlu, A.: Error linear complexity measures for multisequences. J. Complexity 23(169), 192 (2007)

    MathSciNet  MATH  Google Scholar 

  16. Fulin, L.I., Shixin, Z.H.U.: Computing the k-error joint linear complexity of binary periodic multisequences. The Journal of China Universities of Posts and Telecommunications 20(6), 96–101 (2013)

    Article  Google Scholar 

  17. Sethumadhavana, M. , Sindhua, M., Srinivasana, C., Kavithaa, C.: An algorithm for k-error joint linear complexity of binary multisequences. J. Discret. Math. Sci. Cryptogr. 11(3), 297–304 (2008)

    Article  MathSciNet  Google Scholar 

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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

Authors
  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

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