Narayana Sequences for Cryptographic Applications

TL;DR

This paper explores the cryptographic potential of Narayana sequences modulo prime p, demonstrating their favorable randomness, autocorrelation, and cross-correlation properties suitable for secure key generation.

Contribution

It provides new insights into the period and correlation properties of Narayana sequences for cryptographic use, which were not previously studied.

Findings

Sequence period is either p*p+p+1 or p*p-1 or a divisor

Exhibits strong autocorrelation properties

Has good cross-correlation properties

Abstract

This paper investigates the randomness and cryptographic properties of the Narayana series modulo p, where p is a prime number. It is shown that the period of the Narayana series modulo p is either p*p+p+1 (or a divisor) or p*p-1 (or a divisor). It is shown that the sequence has very good autocorrelation and crosscorrelation properties which can be used in cryptographic and key generation applications.