The 4-Adic Complexity of Interleaved Quaternary Sequences of Even Length with Optimal Autocorrelation

TL;DR

This paper calculates the 4-adic complexity of certain interleaved quaternary sequences with optimal autocorrelation, demonstrating their robustness against rational approximation attacks.

Contribution

It determines the 4-adic complexity of new classes of quaternary sequences using correlation functions and Gauss sums, ensuring their cryptographic security.

Findings

Sequences have high 4-adic complexity, resistant to rational approximation attacks.

Method involves correlation functions, Gauss periods, and quadratic Gauss sums.

Results confirm the sequences' cryptographic strength.

Abstract

Su et al. proposed several new classes of quaternary sequences of even length with optimal autocorrelation interleaved by twin-prime sequences pairs, GMW sequences pairs or binary cyclotomic sequences of order four in \cite{S1}. In this paper, we determine the 4-adic complexity of these quaternary sequences with period $2n$ by using correlation function and the "Gauss periods" of order four and "quadratic Gauss sums" on finite field $\mathbb{F}_n$ and valued in $\mathbb{Z}^{*}_{4^{2n}-1}$. Our results show that they are safe enough to resist the attack of the rational approximation algorithm.