Computing the 2-adic complexity of two classes of Ding-Helleseth generalized cyclotomic sequences of periods of twin prime products

This paper contributes to compute the 2-adic complexity of two classes of Ding-Helleseth generalized cyclotomic sequences. Results show that the 2-adic complexity of these sequences is good enough to resist the attack by the rational approximation algorithm.

[1]  Arne Winterhof,et al.  On the 2-Adic Complexity of the Two-Prime Generator , 2018, IEEE Transactions on Information Theory.

[2]  Mark Goresky,et al.  Feedback shift registers, 2-adic span, and combiners with memory , 1997, Journal of Cryptology.

[3]  C. Ding,et al.  Stream Ciphers and Number Theory , 1998 .

[4]  V. Edemskiy,et al.  Notes about the linear complexity of Ding-Helleseth generalized cyclotomic sequences of length pq over the finite field of order p or q , 2017 .

[5]  Dongdai Lin,et al.  Generalized cyclotomic numbers of order two and their applications , 2015, Cryptography and Communications.

[6]  Qiang Wang,et al.  A lower bound on the 2-adic complexity of the modified Jacobi sequence , 2018, Cryptography and Communications.

[7]  Mark Goresky,et al.  Cryptanalysis Based on 2-Adic Rational Approximation , 1995, CRYPTO.

[8]  Qiang Wang,et al.  The exact autocorrelation distribution and 2-adic complexity of a class of binary sequences with almost optimal autocorrelation , 2018, Cryptography and Communications.

[9]  Chao Li,et al.  2-Adic complexity of binary sequences with interleaved structure , 2015, Finite Fields Their Appl..

[10]  K. Williams,et al.  Gauss and Jacobi sums , 2021, Mathematical Surveys and Monographs.

[11]  Wen-Feng Qi,et al.  2-adic Complexity of Binary M-sequences , 2010, IEEE Trans. Inf. Theory.

[12]  Chao Li,et al.  A New Method to Compute the 2-Adic Complexity of Binary Sequences , 2014, IEEE Transactions on Information Theory.

[13]  Honggang Hu.  Comments on “A New Method to Compute the 2-Adic Complexity of Binary Sequences” , 2014, IEEE Transactions on Information Theory.