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.

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