Periodic autocorrelation of sequences

TL;DR

This paper demonstrates that the periodic autocorrelations of random binary sequences are concentrated around a specific point, highlighting their potential cryptographic resistance.

Contribution

It extends previous results on autocorrelations of Boolean functions to the periodic autocorrelations of random binary sequences.

Findings

Periodic autocorrelations are concentrated around a point.

Supports cryptographic resistance of random binary sequences.

Extends understanding of autocorrelation behavior in sequences.

Abstract

The autocorrelation of a sequence is a useful criterion, among all, of resistance to cryptographic attacks. The behavior of the autocorrelations of random Boolean functions (studied by Florian Caullery, Eric F\'erard and Fran\c{c}ois Rodier [4]) shows that they are concentrated around a point. We show that the same is true for the evaluation of the periodic autocorrelations of random binary sequences.