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2-Adic complexity of two constructions of binary sequences with period 4N and optimal autocorrelation magnitude

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Abstract

Three constructions of binary sequences with period 4N and optimal autocorrelation value or optimal autocorrelation magnitude have been presented by Tang and Gong based on interleaving technique. In this paper, the 2-adic complexity of the sequences with optimal autocorrelation magnitude constructed from the Legendre sequence pair or the twin-prime sequence pair is investigated. With the method proposed by Hu, we completely determine the 2-adic complexity of the sequences by calculating the exact autocorrelation distribution of the sequences and discussing the greatest common divisors. Results show that the 2-adic complexity of these sequences is either maximum or very close to maximum.

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References

  1. Arasu, K., Ding, C., Helleseth, T., Kumar, P., Martinsen, H.: Almost difference sets and their sequences with optimal autocorrelation. IEEE Trans. Inf. Theory 47(7), 2934–2943 (2001)

    Article  MathSciNet  Google Scholar 

  2. Cai, Y., Ding, C.: Binary sequences with optimal autocorrelation. Theor. Comput. Sci. 410(24), 2316–2322 (2009)

    Article  MathSciNet  Google Scholar 

  3. Ding, C.: Autocorrelation values of generalized cyclotomic sequences of order two. IEEE Trans. Inf. Theory 44(4), 1699–1702 (1998)

    Article  MathSciNet  Google Scholar 

  4. Fan, C.: The linear complexity of a class of binary sequences with optimal autocorrelation. Des. Codes Cryptogr. 86(10), 2441–2450 (2018)

    Article  MathSciNet  Google Scholar 

  5. Gong, G.: Theory and applications of q-ary interleaved sequences. IEEE Trans. Inf. Theory 41(2), 400–411 (1995)

    Article  MathSciNet  Google Scholar 

  6. Hu, H.: Comments on a new method to compute the 2-adic complexity of binary sequences. IEEE Trans. Inf. Theory 60(9), 5803–5804 (2014)

    Article  MathSciNet  Google Scholar 

  7. Hofer, R., Winterhof, A.: On the 2-adic complexity of two-prime generator. IEEE Trans. Inf. Theory 64(8), 5957–5960 (2018)

    Article  MathSciNet  Google Scholar 

  8. Klapper, A., Goresky, M.: 2-Adic shift registers, Fast Software Encryption, volume 809 of LNCS, pp. 174–178. Springer, Cambridge (1994)

  9. Klapper, A., Goresky, M.: Cryptanalysis based on 2-adic rational approximation, Advances in Cryptology, CRYPTO’95, volume 963 of LNCS, pp. 262–273. Springer, Santa Barbara (1995)

  10. Klapper, A., Goresky, M.: Feedback shift registers, 2-adic span, and combiners with memory. Cryptology 10(2), 111–147 (1997)

    Article  MathSciNet  Google Scholar 

  11. Li, N., Tang, X.: On the linear complexity of binary sequences of period 4N with optimal autocorrelation value/magnitude. IEEE Trans. Inf. Theory 57(11), 7597–7604 (2011)

    Article  MathSciNet  Google Scholar 

  12. Su, W., Yang, Y., Fan, C.: New optimal binary sequences with period 4p via interleaving Ding-Helleseth-Lam sequences. Des. Codes Cryptogr. 86(6), 1329–1338 (2018)

    Article  MathSciNet  Google Scholar 

  13. Sun, S., Yan, T., Sun, Y., Yan, M.: Computing the 2-adic complexity of two classes generalized cyclotomic sequences. IEEE Access 8, 140478–140485 (2020)

    Article  Google Scholar 

  14. Sun, Y., Wang, Q., Yan, T.: The exact autocorrelation distribution and 2-adic complexity of a class of binary sequences with almost optimal autocorrelation. Cryptogr. Commun. 10(3), 467–477 (2018)

    Article  MathSciNet  Google Scholar 

  15. Sun, Y., Yan, T., Chen, Z., Wang, L.: The 2-adic complexity of a class of binary sequences with optimal autocorrelation magnitude. Cryptogr. Commun. 12(4), 675–683 (2020)

    Article  MathSciNet  Google Scholar 

  16. Tang, X., Gong, G.: New constructions of binary sequences with optimal autocorrelation value/magnitude. IEEE Trans. Inf. Theory 56 (3), 1278–1286 (2010)

    Article  MathSciNet  Google Scholar 

  17. Whiteman, A. L.: A family of difference sets. Illionis J. Math. 6(1), 107–121 (1962)

    MathSciNet  MATH  Google Scholar 

  18. Xiong, H., Qu, L., Li, C.: A new method to compute the 2-adic complexity of binary sequences. IEEE Trans. Inf. Theory 60(4), 2399–2406 (2014)

    Article  MathSciNet  Google Scholar 

  19. Xiong, H., Qu, L., Li, C.: 2-Adic complexity of binary sequences with interleaved structure. Finite Fields Appl. 33, 14–28 (2015)

    Article  MathSciNet  Google Scholar 

  20. Xiao, Z., Zeng, X., Sun, Z.: 2-Adic complexity of two classes of generalized cyclotomic binary sequences. Int. J. Found. Comput. Sci. 27(7), 879–893 (2016)

    Article  MathSciNet  Google Scholar 

  21. Yan, T., Yan, M., Sun, Y., Sun, S.: The 2-adic complexity of Ding-Helleseth generalized cyclotomic sequences of order 2 and period pq. IEEE Access 8, 140682–140687 (2020)

    Article  Google Scholar 

  22. Yang, M., Zhang, L., Feng, K.: On the 2-adic complexity of a class of binary sequences of period 4p with optimal autocorrelation magnitude, arXiv:1904.13012 (2019)

  23. Yu, N., Gong, G.: New binary sequences with optimal autocorrelation magnitude. IEEE Trans. Inf. Theory 54(10), 4771–4779 (2008)

    Article  MathSciNet  Google Scholar 

  24. Zhang, L., Zhang, J., Yang, M., Feng, K.: On the 2-adic complexity of the Ding-Helleseth-Martinsen binary sequences. IEEE Trans. Inf. Theory 66 (7), 4613–4620 (2020)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank the Editors and the anonymous referees for their valuable comments and helpful suggestions. This work was supported by the National Natural Science Foundation of China (Nos. 62072161, 12061027) and the Application Foundation Frontier Project of Wuhan Science and Technology Bureau (No. 2020010601012189)

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Authors and Affiliations

  1. College of Science, Wuhan University of Science and Technology, Wuhan, 430081, China

    Zibi Xiao

  2. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, 430062, China

    Xiangyong Zeng

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  1. Zibi Xiao
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  2. Xiangyong Zeng
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Correspondence to Xiangyong Zeng.

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Xiao, Z., Zeng, X. 2-Adic complexity of two constructions of binary sequences with period 4N and optimal autocorrelation magnitude. Cryptogr. Commun. 13, 865–885 (2021). https://doi.org/10.1007/s12095-021-00498-8

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  • DOI: https://doi.org/10.1007/s12095-021-00498-8

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