Abstract
In this paper, we consider Ding-Helleseth generalized cyclotomic sequences of length pq where p and q are odd distinct primes. We derive symmetric 2-adic complexity of these sequences for any p, q and show that they have high symmetric 2-adic complexity. These results generalize known conclusions of Yan et al. (IEEE Access, 2020, https://doi:10.1109/ACCESS.2020.3012570) about 2-adic complexity of Ding-Helleseth sequences of order 2 and of length pq.
V. Edemskiy were supported by RFBR-NSFC according to the research project No. 19-51-53003, C. Wu was partially supported by the Projects of International Cooperation and Exchange NSFC-RFBR No. 61911530130, by the National Natural Science Foundation of China No. 61373140, 61772292 and by the Natural Science Foundation of Fujian Province No. 2020J01905.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ding, C., Helleseth, T.: New generalized cyclotomy and its applications. Finite Fields Appl. 4(2), 140–166 (1998)
Edemskiy, V., Sokolovskiy, N.: Notes about the linear complexity of Ding-Helleseth generalized cyclotomic sequences of length pq over the finite field of order \(p\) or \(q\). In: ITM Web of Conferences, vol. 9, p. 01005 (2017)
Golomb, S.W.: Shift Register Sequences. Holden-Day, San Francisco (1967)
Hofer, R., Winterhof, A.: On the 2-adic complexity of the two-prime generator. IEEE Trans. Inf. Theory 64(8), 5957–5960 (2018)
Hu, H.: Comments on “a new method to compute the 2-adic complexity of binary sequences”. IEEE Trans. Inform. Theory 60, 5803–5804 (2014)
Hu, H., Feng, D.: On the 2-adic complexity and the k-error 2-adic complexity of periodic binary sequences. IEEE Trans. Inf. Theory 54(2), 874–883 (2008)
Ireland, K., Rosen, M.: A Classical Introduction to Modern Number Theory. Graduate Texts in Mathematics. Springer, New York (1990). https://doi.org/10.1007/978-1-4757-2103-4
Klapper, A., Goresky, M.: Cryptanalysis based on 2-adic rational approxiamtion. In: CRYPTO 1995, LNCS, vol. 963, pp. 262–273 (1995)
Klapper, A., Goresky, M.: Feedback shift registers, 2-adic span, and combiners with memory. J. Cryptol. 10(2), 111–147 (1997). https://doi.org/10.1007/s001459900024
Li, S., Chen, Z., Sun, R., Xiao, G.: On the randomness of generalized cyclotomic sequences of order two and length \(pq\). IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences E90-A(9), 2037–2041 (2007)
Li, S., Chen, Z., Fu, X., Xiao, G.: The autocorrelation values of new generalized cyclotomic sequences of order two and length \(pq\). J. Comput. Sci. Technol. 22(6), 830–834 (2007). https://doi.org/10.1007/s11390-007-9099-2
Sun, Y., Wang, Q., Yan, T.: The exact autocorrelation distribution and 2-adic complexity of a class of binary sequences with almost optimal autocorrelation. Cryptography and Communications 10(3), 467–477 (2017). https://doi.org/10.1007/s12095-017-0233-x
Sun, Y., Yan, T., Chen, Z., Wang, L.: The 2-adic complexity of a class of binary sequences with optimal autocorrelation magnitude. Cryptography and Communications 12(4), 675–683 (2019). https://doi.org/10.1007/s12095-019-00411-4
Sun, Y., Wang, Q., Yan, T.: A lower bound on the 2-adic comeplxity of the modified Jacobi sequences. Cryptogr. Commun. 11(2), 337–349 (2019). https://doi.org/10.1007/s12095-018-0300-y
Whiteman, A.L.: A family of difference sets. Illinois J. Math. 6, 107–121 (1962)
Xiao, Z., Zeng X., Sun, Z.: 2-Adic complexity of two classes of generalized cyclotomic binary sequences. Internationl Journal of Foundations of Comput. Sci. 27(7), 879–893 (2016)
Xiong, H., Qu, L., Li, C.: A new method to compute the 2-adic complexity of binary sequences. IEEE Trans. Inform. Theory 60, 2399–2406 (2014)
Yan, T., Sun, R., Xiao, G.: Autocorrelation and linear complexity of the new generalized cyclotomic sequences. IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences E90-A (4), 857–864 (2007)
Yan, T., Chen, Z., Xiao, G.: Linear complexity of Ding generalized cyclotomic sequences. Journal of Shanghai University 11(1), 22–26 (2007). https://doi.org/10.1007/s12095-018-0343-0
Yang, M., Feng, K.: Determination of 2-adic complexity of generalized binary sequences of order 2. arXiv:2007.15327
Yan, M., Yan, T., Li, Y.: Computing the 2-adic complexity of two classes of Ding-Helleseth generalized cyclotomic sequences of period of twin prime products. arXiv:1912.06134
Yan, M., Yan, T., 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). https://doi.org/10.1109/ACCESS.2020.3012570
Zhang, L., Zhang, J., Yang, M., Feng, K.: On the 2-Adic complexity of the Ding-Helleseth-Martinsen binary sequences. IEEE Trans. Inform. Theory (2020). https://doi.org/10.1109/TIT.2020.2964171
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Edemskiy, V., Wu, C. (2021). Symmetric 2-Adic Complexity of Ding-Helleseth Generalized Cyclotomic Sequences of Period pq. In: Wu, Y., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2020. Lecture Notes in Computer Science(), vol 12612. Springer, Cham. https://doi.org/10.1007/978-3-030-71852-7_21
Download citation
DOI: https://doi.org/10.1007/978-3-030-71852-7_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-71851-0
Online ISBN: 978-3-030-71852-7
eBook Packages: Computer ScienceComputer Science (R0)