Pseudorandom number generator based on novel 2D Hénon-Sine hyperchaotic map with microcontroller implementation

Daniel Murillo-Escobar; Miguel Ángel Murillo-Escobar; César Cruz-Hernández; Adrian Arellano-Delgado; Rosa Martha López-Gutiérrez

doi:10.1007/s11071-022-08101-2

Pseudorandom number generator based on novel 2D Hénon-Sine hyperchaotic map with microcontroller implementation

Nonlinear Dyn. 2023;111(7):6773-6789. doi: 10.1007/s11071-022-08101-2. Epub 2022 Nov 27.

Authors

Daniel Murillo-Escobar¹, Miguel Ángel Murillo-Escobar¹, César Cruz-Hernández², Adrian Arellano-Delgado³, Rosa Martha López-Gutiérrez¹

Affiliations

¹ Engineering, Architecture and Design Faculty, Autonomous University of Baja California (UABC), Ensenada, Baja California Mexico.
² Electronics and Telecommunication Department, Scientific Research and Advanced Studies Center of Ensenada (CICESE), Ensenada, Baja California Mexico.
³ Engineering, Architecture and Design Faculty, CONACYT-UABC Autonomous University of Baja California (UABC), Ensenada, Baja California Mexico.

Abstract

Recently, chaotic maps have been considered to design pseudorandom number generator (PRNG). However, some chaotic maps present security disadvantages, such as low uniformity and low randomness properties. Nowadays, chaos-based PRNGs are used as the main source for the development of cryptographic algorithms. In this work, to overcome such weaknesses, a novel 2D hyperchaotic map is proposed based on discrete-time feedback by using Hénon map and Sine map. In addition, the dynamics of the hyperchaotic map are enhanced by using the remainder after division function (rem), where better random statistical properties are obtained. A comparison is made between the enhanced Hénon-Sine hyperchaotic map (EHSHM) and the Hénon-Sine hyperchaotic map through Lyapunov exponent analysis, attractor trajectory, histograms and sensitivity at initialization. Then, 8-bit pseudorandom number generator based on the proposed hyperchaotic map (PRNG-EHSHM) is designed and the initial seed of the PRNG is calculated by a secret key of 60 hexadecimal characters. It is implemented in both MATLAB and Arduino Mega microcontroller for experimental results. A complete security analysis is presented from a cryptographic point of view, such as key space, floating frequency, histograms and entropy of the information. Moreover, the randomness is verified with the tests of the National Institute of Standards and Technology (NIST 800-22). Based on the security results obtained, the proposed PRNG-EHSHM can be implemented in embedded cryptographic applications based on chaos.

Keywords: 2D Hénon-Sine hyperchaotic map; Chaos; Microcontroller implementation; Pseudorandom number generator; Security analysis.

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