The 2-adic complexity of a class of binary sequences with optimal autocorrelation magnitude

TL;DR

This paper investigates the 2-adic complexity of a recently constructed class of binary sequences with optimal autocorrelation, demonstrating that their 2-adic complexity is sufficiently high to resist certain cryptanalytic attacks.

Contribution

It provides the first analysis of the 2-adic complexity for this class of sequences, showing it exceeds half of the period, enhancing their cryptographic strength.

Findings

2-adic complexity is at least half the sequence period

Sequence's 2-adic complexity resists Rational Approximation Algorithm

Confirms the sequence's cryptographic robustness

Abstract

Recently, a class of binary sequences with optimal autocorrelation magnitude has been presented by Su et al. based on interleaving technique and Ding-Helleseth-Lam sequences (Des. Codes Cryptogr., https://doi.org/10.1007/s10623-017-0398-5). And its linear complexity has been proved to be large enough to resist the B-M Algorighm (BMA) by Fan (Des. Codes Cryptogr., https://doi.org/10.1007/s10623-018-0456-7). In this paper, we study the 2-adic complexity of this class of binary sequences. Our result shows that the 2-adic complexity of this class of sequence is no less than one half of its period, i.e., its 2-adic complexity is large enough to resist the Rational Aproximation Algorithm (RAA).