Random Sequences Based on the Divisor Pairs Function

TL;DR

This paper explores the randomness characteristics of a divisor pairs function, demonstrating its aperiodicity and strong autocorrelation, with potential applications in cryptography and computer science.

Contribution

It introduces a divisor pairs function with proven aperiodicity and autocorrelation properties, highlighting its suitability for cryptographic applications.

Findings

The function is proven to be aperiodic.

It exhibits excellent autocorrelation properties.

Potential applications in cryptography and key distribution.

Abstract

This paper investigates the randomness properties of a function of the divisor pairs of a natural number. This function, the antecedents of which go to very ancient times, has randomness properties that can find applications in cryptography, key distribution, and other problems of computer science. It is shown that the function is aperiodic and it has excellent autocorrelation properties.