Computing the 2-Adic Complexity of Two Classes Generalized Cyclotomic Sequences

Shiwen Sun,Tongjiang Yan,Ming Yan,Yuhua Sun

doi:10.1109/access.2020.3013122

Abstract

This paper contributes to analyze the 2-adic complexity of a class of Ding-Helleseth generalized cyclotomic sequences and a class of Whiteman generalized cyclotomic sequences of periods of N = pq, wherep and q are two odd distinct primes with gcd(p - 1, q - 1) = 2 satisfyingp ≡ q ≡ 3 (mod 4). The results show that the 2-adic complexity of these sequences is at least pq - p - q - 1. Then it is large enough to resist the attacks of rational approximation algorithm.

Highlights

Stream cipher is an important encryption algorithm, which has an important application in the field of communication
Sun and Yan et al obtained a lower bound on the 2-adic complexity of modified Jacobi sequences [6]
In 2013, Li et al proved a new class of Whiteman generalized cyclotomic sequences of order two and length pq have high linear complexity [5]. We show that these sequences have large 2-adic complexity, too

Summary

INTRODUCTION

Stream cipher is an important encryption algorithm, which has an important application in the field of communication. Linear complexity and the autocorrelation, 2-adic complexity is one of the important standards for measuring the pseudo-random properties of key stream sequences. Xiong et al raised a method of determining the 2-adic complexity of binary sequences by circulant matrices [10]. Using this method, they showed that Legendre sequences and Ding-Helleseth sequences with optimal autocorrelation and two other classes of sequences with interleaved structures have maximal 2-adic complexity [10], [11].

PRELIMINARIES

SOME NECESSARY SUBSIDIARY LEMMAS

APPLICATION Example 1

CONCLUSION