The 2-adic complexity of Yu-Gong sequences with interleaved structure and optimal autocorrelation magnitude

TL;DR

This paper investigates the 2-adic complexity of Yu-Gong sequences with optimal autocorrelation, demonstrating they have high complexity values that can reach the maximum, indicating strong resistance to certain cryptanalytic attacks.

Contribution

It provides a detailed analysis of the 2-adic complexity of Yu-Gong sequences, showing they can attain maximum complexity with appropriate parameters, enhancing their cryptographic strength.

Findings

2-adic complexities are larger than N - 2⎡log₂N⎤ + 4

Complexities can reach the maximum value N

Sequences are resistant to the Rational Approximation Algorithm

Abstract

In 2008, a class of binary sequences of period $N=4(2^k-1)(2^k+1)$ with optimal autocorrelation magnitude has been presented by Yu and Gong based on an $m$-sequence, the perfect sequence $(0,1,1,1)$ of period $4$ and interleaving technique. In this paper, we study the 2-adic complexities of these sequences. Our results show that they are larger than $N-2\lceil\mathrm{log}_2N\rceil+4 $ (which is far larger than $N/2$) and could attain the maximum value $N$ if suitable parameters are chosen, i.e., the 2-adic complexity of this class of interleaved sequences is large enough to resist the Rational Approximation Algorithm.