A New Parallel Fuzzy Multi Modular Chaotic

Logistic Map for Image Encryption

Mahmoud Gad¹, Esam Hagras², Hasan Soliman¹, and Noha Hikal¹

¹Faculty of Computers and Information Sciences, Mansoura University, Egypt

²Faculty of Engineering, Delta University for Science and Technology, Egypt

Abstract: This paper introduces a new image encryption algorithm based on a Parallel Fuzzy Multi-Modular Chaotic Logistic Map (PFMM-CLM). Firstly, a new hybrid chaotic system is introduced by using four parallel cascade chaotic logistic maps with a dynamic parameter control to achieve a high Lyapunov exponent value and completely chaotic behavior of the bifurcation diagram. Also, the fuzzy set theory is used as a fuzzy logic selector to improve chaotic performance. The proposed algorithm has been tested as a Pseudo-Random Number Generator (PRNG). The randomness test results indicate that system has better performance and satisfied all random tests. Finally, the Arnold Cat Map with controllable iterative parameters is used to enhance the confusion concept. Due to excellent chaotic properties and good randomization test results, the proposed chaotic system is used in image encryption applications. The simulation and security analysis indicate that this proposed algorithm has a very high security performance and complexity.

Keywords: Image encryption, parallel multi modular chaotic maps, pseudo-random number generation, fuzzy logic selector.

Received August 24, 2019; accepted September 7, 2020
https://doi.org/10.34028/iajit/18/2/12

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