Linear complexity of quaternary sequences over Z4 based on Ding-Helleseth generalized cyclotomic classes

TL;DR

This paper analyzes quaternary sequences over Z4 constructed from Ding-Helleseth cyclotomic classes, demonstrating they have high linear complexity and potential cryptographic strength.

Contribution

It introduces a new family of sequences over Z4 based on Ding-Helleseth classes and determines their linear complexity through polynomial and Fourier transform analysis.

Findings

Sequences have large linear complexity

Sequences are suitable for cryptographic applications

Linear complexity is explicitly computed

Abstract

A family of quaternary sequences over Z4 is defined based on the Ding-Helleseth generalized cyclotomic classes modulo pq for two distinct odd primes p and q. The linear complexity is determined by computing the defining polynomial of the sequences, which is in fact connected with the discrete Fourier transform of the sequences. The results show that the sequences possess large linear complexity and are good sequences from the viewpoint of cryptography.