New Generalized Cyclotomic Quaternary Sequences with Large Linear Complexity and a Product of Two Primes Period

Jiang Ma,Wei Zhao,Yanguo Jia,Haiyang Jiang

doi:10.3390/info12050193

Abstract

Linear complexity is an important criterion to characterize the unpredictability of pseudo-random sequences, and large linear complexity corresponds to high cryptographic strength. Pseudo-random Sequences with a large linear complexity property are of importance in many domains. In this paper, based on the theory of inverse Gray mapping, two classes of new generalized cyclotomic quaternary sequences with period pq are constructed, where pq is a product of two large distinct primes. In addition, we give the linear complexity over the residue class ring Z4 via the Hamming weights of their Fourier spectral sequence. The results show that these two kinds of sequences have large linear complexity.

Highlights

Pseudo-random sequences with large linear complexity and low nontrivial autocorrelation values are widely applied in spread spectrum communication, radar navigation, cryptography, code division multiple access, especially stream cipher
Pseudorandom sequences with period pq have been taken seriously, as pq is the RSA
The results show that, the first class of the generalized cyclotomic quaternary sequence has lower linear complexity only if η p (r )ηq (r ) = 1, ±2δξ = (1 ± δ)(modr ) and r |(3p + 1) ; the second one has lower linear complexity only if η p (r )ηq (r ) = 1, ±ξ (2 ± δ) = 1(modr ) and r |±σ

Summary

Introduction

Pseudo-random sequences with large linear complexity and low nontrivial autocorrelation values are widely applied in spread spectrum communication, radar navigation, cryptography, code division multiple access, especially stream cipher. Kim et al constructed a class of quaternary sequences with period 2p over Z4 by the use of a Legendre sequence pair They analyzed the autocorrelation properties and the linear complexity of these sequences [10,11]. Yang et al defined a class of quaternary sequence on Z4 by using the Whiteman generalized cyclotomic binary sequence pair and calculated the autocorrelation values [12]. Wang et al established a class of quaternary sequence on Z4 based on the balanced Whiteman generalized cyclotomic binary sequence pair and gave the linear complexity of the sequence [15]. This paper proposes a new class of quaternary sequences with period pq based on the Ding generalized cyclotomic binary sequence and the new.

Preliminaries

The Linear Complexity of the First Class of Generalized Cyclotomic

Conclusions