Linear Complexity and Autocorrelation of two Classes of New Interleaved Sequences of Period $2N$

TL;DR

This paper constructs new binary sequences with optimal autocorrelation and high linear complexity using interleaving techniques, suitable for cryptographic applications.

Contribution

It introduces a novel interleaving method to generate sequences with optimal autocorrelation and provides analysis of their autocorrelation distribution and linear complexity.

Findings

Sequences have low autocorrelation values.

Linear complexity meets cryptographic standards.

Sequences are constructed with period 2N using interleaving.

Abstract

The autocorrelation and the linear complexity of a key stream sequence in a stream cipher are important cryptographic properties. Many sequences with these good properties have interleaved structure, three classes of binary sequences of period $4N$ with optimal autocorrelation values have been constructed by Tang and Gong based on interleaving certain kinds of sequences of period $N$. In this paper, we use the interleaving technique to construct a binary sequence with the optimal autocorrelation of period $2N$, then we calculate its autocorrelation values and its distribution, and give a lower bound of linear complexity. Results show that these sequences have low autocorrelation and the linear complexity satisfies the requirements of cryptography.