Binary Prime Tableau Sequences

TL;DR

This paper introduces binary primes tableau sequences, a new class of sequences with promising autocorrelation properties, potentially useful for cryptography and communications, derived from prime-marked tableaux and their duals.

Contribution

It presents a novel construction of binary prime tableau sequences and analyzes their autocorrelation properties, expanding the toolkit for sequence design in cryptography.

Findings

PT sequences exhibit excellent autocorrelation properties

Dual sequences derived from tableau also show promising features

Potential applications in cryptography and secure communications

Abstract

This paper proposes a new class of random sequences called binary primes tableau (PT) sequences that have potential applications in cryptography and communications. The PT sequence of rank p is obtained from numbers arranged in a tableau with p columns where primes are marked off until each column has at least one prime and where the column entries are added modulo 2. We also examine the dual to the PT sequences obtained by adding the rows of the tableau. It is shown that PT sequences have excellent autocorrelation properties.