Abstract
Pseudo-random number generators (PRNGs) are one of the building blocks of cryptographic methods and therefore, new and improved PRNGs are continuously developed. In this study, a novel method to generate pseudo-random sequences using coupled map lattices is presented. Chaotic maps only show their chaotic behaviour for a specified range of control parameters, what can restrict their application in cryptography. In this work, generalised symmetric maps with adaptive control parameter are presented. This novel idea allows the user to choose any symmetric chaotic map, while ensuring that the output is a stream of independent and random sequences. Furthermore, to increase the complexity of the generated sequences, a lattice-based structure where every local map is linked to its neighbouring node via coupling factor has been used. The dynamic behaviour and randomness of the proposed system has been studied using Kolmogorov–Sinai entropy, bifurcation diagrams and the NIST statistical suite for randomness. Experimental results show that the proposed PRNG provides a large key space, generates pseudo-random sequences and is computationally suitable for IoT devices.
Highlights
Computers have evolved from large calculating machines to smart handheld devices that have revolutionized human lives [1]
We introduce the concept of Generalised Symmetric Map (GSM) as local map for the coupled map lattices (CMLs) system and propose the concept of adaptive control parameter values that results in highly chaotic and complex Pseudo-random number generators (PRNGs)
The ad function when supplied with accumulation points for GSM, returns ad values such that, the CML system stays above the accumulation points and exhibits chaotic output depending on the type of local map chosen
Summary
Computers have evolved from large calculating machines to smart handheld devices that have revolutionized human lives [1]. The chaotic systems can generate diverging and disorderly sequences, which appear to be random, being deterministic but highly sensitive to initial conditions [10]. These particular characteristics make chaotic systems a good candidate for PRNGs. Chaos based PRNGs have been an active area of research but relatively few chaotic maps have been explored for this purpose [11]. The proposed model introduces additional control parameters which contribute to the generation of highly chaotic sequences with large key space for cryptographic applications.
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