A Class of Random Sequences for Key Generation

TL;DR

This paper explores the randomness and autocorrelation properties of Fibonacci and Gopala-Hemachandra sequences modulo m, proposing their suitability for key distribution due to their non-complex generation process.

Contribution

It introduces a novel method to generate binary sequences from Fibonacci-based sequences for cryptographic key distribution, analyzing their randomness and autocorrelation properties.

Findings

Sequences modulo prime have better autocorrelation.

Binary sequences derived are suitable for key distribution.

Generation process is computationally simple.

Abstract

This paper investigates randomness properties of sequences derived from Fibonacci and Gopala-Hemachandra sequences modulo m for use in key distribution applications. We show that for sequences modulo a prime a binary random sequence B(n) is obtained based on whether the period is p-1 (or a divisor) or 2p+2 (or a divisor). For the more general case of arbitrary m, we use the property if the period is a multiple of 8 or not. The sequences for prime modulo have much better autocorrelation properties. These are good candidates for key distribution since the generation process is not computationally complex.