2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption

Abstract This study presents a novel approach to generating high-quality random numbers using a two-dimensional logistic map with a unit transfer function (2DLMUTF). The method is built upon the chaotic dynamics of the logistic map, where the parameter $$\:r$$ governs the system’s behavior, exhibiti...

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Main Authors: Raiz Ahmad, Ghawar Said, Aymen Flah, Habib Kraiem, Claude Ziad El bayeh, Yousaf Hameed Khattak, Faisal Baig
Format: Article
Language:English
Published: Nature Portfolio 2025-06-01
Series:Scientific Reports
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Online Access:https://doi.org/10.1038/s41598-025-04702-0
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Summary:Abstract This study presents a novel approach to generating high-quality random numbers using a two-dimensional logistic map with a unit transfer function (2DLMUTF). The method is built upon the chaotic dynamics of the logistic map, where the parameter $$\:r$$ governs the system’s behavior, exhibiting chaotic nature in the range of 3.57 to 4. By applying a unit transfer function and modulus operation, the system’s output is constrained within the [0, 1] range, altering the phase space dynamics compared to traditional 2D logistic maps. Numerical simulations in MATLAB, with parameters $$\:{r}_{1}$$ =4, $$\:{r}_{2}$$ =3.8, and initial seed values $$\:{x}_{0}$$ =0.2350 and $$\:{y}_{0}$$ =0.3500, were run for $$\:{10}^{6}$$ iterations. Statistical testing using the NIST SP 800 − 22 test suite showed superior randomness, with the method passing all 15 tests. Additionally, uniformity, autocorrelation, cross-correlation, and entropy analyses confirmed the method’s suitability for cryptographic applications. The generated random numbers were used to create substitution boxes (S-boxes) for image encryption, demonstrating strong encryption performance. Overall, 2DLMUTF offers a computationally efficient and secure solution for random number generation which is suitable for cryptographic and image encryption applications.
ISSN:2045-2322