On the 2-Adic Complexity of the Ding-Helleseth-Martinsen Binary Sequences

TL;DR

This paper calculates the 2-adic complexity of Ding-Helleseth-Martinsen binary sequences using advanced number theory tools, providing insights into their cryptographic strength and structure.

Contribution

It introduces a method to determine the 2-adic complexity of DHM sequences via cyclotomic numbers, Gauss periods, and quadratic Gauss sums.

Findings

Exact 2-adic complexity values for DHM sequences are obtained.

The analysis links sequence complexity to properties of finite fields and cyclotomic numbers.

Results enhance understanding of the cryptographic robustness of DHM sequences.

Abstract

We determine the 2-adic complexity of the Ding-Helleseth-Martinsen (DHM) binary sequences by using cyclotomic numbers of order four, "Gauss periods" and "quadratic Gauss sum" on finite field $\mathbb{F}_q$ and valued in $\mathbb{Z}_{2^N-1}$ where $q \equiv 5\pmod 8$ is a prime number and $N=2q$ is the period of the DHM sequences.