Further results on the 2-adic complexity of a class of balanced generalized cyclotomic sequences

TL;DR

This paper establishes a lower bound on the 2-adic complexity of balanced generalized cyclotomic sequences, demonstrating their robustness against certain cryptanalytic attacks and identifying conditions for maximal complexity.

Contribution

It provides a new lower bound on the 2-adic complexity of these sequences, extending previous work and confirming their cryptographic strength.

Findings

2-adic complexity is at least pq - p - q - 1

Sequences are resistant to rational approximation attacks

Maximal complexity achieved with suitable parameters

Abstract

In this paper, the 2-adic complexity of a class of balanced Whiteman generalized cyclotomic sequences of period $pq$ is considered. Through calculating the determinant of the circulant matrix constructed by one of these sequences, we derive a lower bound on the 2-adic complexity of the corresponding sequence, which further expands our previous work (Zhao C, Sun Y and Yan T. Study on 2-adic complexity of a class of balanced generalized cyclotomic sequences. Journal of Cryptologic Research,6(4):455-462, 2019). The result shows that the 2-adic complexity of this class of sequences is large enough to resist the attack of the rational approximation algorithm(RAA) for feedback with carry shift registers(FCSRs), i.e., it is in fact lower bounded by $pq-p-q-1$, which is far larger than one half of the period of the sequences. Particularly, the 2-adic complexity is maximal if suitable parameters are chosen.