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The 4-adic complexity of interleaved quaternary sequences of even period with optimal autocorrelation

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Abstract

Su, Yang, Zhou, and Tang proposed several new classes of optimal autocorrelation interleaved quaternary sequences with period 2n from the twin-prime sequence pairs or GMW sequence pairs. In this paper, we determine the 4-adic complexity of these quaternary sequences by using the correlation function. Our results show that the 4-adic complexity of these quaternary sequences exceeds \(\frac{2n-16}{6}\), so that they are safe enough to resist the attack of the rational approximation algorithm.

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References

  1. Edemskiy, V., Chen, Z.: On the 4-adic complexity of the two-prime quaternary generator. J. Appl. Math. Comput. 68, 3565–3585 (2022)

    Article  MathSciNet  Google Scholar 

  2. Jang, J.W., Kim, Y.S., Kim S.H., No J.S.: New quaternary sequences with ideal autocorrelation constructed from binary sequences with ideal autocorrelation. In: IEEE Intern. Symp. Inf. Theory Proceedings-ISIT 2009, pp. 278-281 (2009)

  3. Kim, Y.S., Jang, J.W., Kim, S.H., No J.S.: New construction of quaternary sequences with ideal autocorrelation from Legendre sequences. In: IEEE Intern. Symp. Inf. Theory Proceedings-ISIT 2009, pp. 282-285 (2009)

  4. Kim, Y.S., Jang, J.W., Kim, S.H., No J.S.: New quaternary sequences with optimal autocorrelation. In: IEEE Intern. Symp. Inf. Theory Proceedings-ISIT 2009, pp. 286-289 (2009)

  5. Klapper, A.: A survey of feedback with carry shift registers. Lecture Notes Comput. Sci. 3486, 56–71 (2005)

    Article  Google Scholar 

  6. Klapper, A., Xu, J.: Register synthesis for algebraic feedback shift registers based on non-primes. Des. Codes Cryptogr. 31(3), 227–250 (2004)

    Article  MathSciNet  Google Scholar 

  7. Lüke, H.D., Schotten, H.D., Hadinejad-Mahram, H.: Generalised Sidelnikov sequences with optimal autocorrelation properties. Electron Lett. 36(6), 525–527 (2000)

    Article  Google Scholar 

  8. Qiang, S., Li, Y., Yang, M., Feng. K.: The 4-adic complexity of a class of quaternary cyclotomic sequences with period \(2p\). arXiv:2011.11875

  9. Qiang, S., Jing, X., Yang, M., Feng. K: 4-Adic complexity of interleaved quaternary sequences. arXiv:2105.13826

  10. Su, W., Yang, Y., Zhou, Z., Tang, X.: New quaternary sequences of even length with optimal auto-correlation. Sci. China Inf. Sci. 61(2), 1–13 (2018)

    Article  MathSciNet  Google Scholar 

  11. Tang, X., Ding, C.: New classes of balanced quaternary and almost balanced binary sequences with optimal autocorrelation value. IEEE Trans. Inf. Theory 56(12), 6398–6405 (2010)

    Article  MathSciNet  Google Scholar 

  12. 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 

  13. Yang, M., Qiang, S., Jing, X., Feng. K., Lin. D.: On the 4-adic complexity of quaternary sequences with ideal autocorrelation. In: IEEE Intern. Symp. Inf. Theory Proceedings-ISIT 2022, pp. 528-531 (2022)

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Funding

This work is supported by the N.S.F.(11971381, 12371007) of P. R. China and Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No. 22JSY007).

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Authors and Affiliations

  1. Research Center for Number Theory and Its Applications, Northwest University, Xi’an, 710127, China

    Xiaoyan Jing & Zhefeng Xu

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  1. Xiaoyan Jing
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  2. Zhefeng Xu
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All authors wrote the main manuscript text and reviewed the manuscript.

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Correspondence to Zhefeng Xu.

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Jing, X., Xu, Z. The 4-adic complexity of interleaved quaternary sequences of even period with optimal autocorrelation. Cryptogr. Commun. 16, 613–628 (2024). https://doi.org/10.1007/s12095-023-00690-y

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  • DOI: https://doi.org/10.1007/s12095-023-00690-y

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