<p>The need for parameter optimization in chaotic systems has become a critical pursuit in communication and control engineering. This paper investigates the parameter optimization of three dimensional Fractional Order (FO) Lorenz, and Chen chaotic systems by minimizing the reciprocal of the positive Lyapunov exponent as an objective function. The parameters of FO chaotic systems are optimized by considering systems with (i) identical fractional order and (ii) different fractional orders. Heuristic algorithms includes cuckoo search, accelerated particle swarm optimization, firefly, and artificial bee colony are used to solve the proposed constrained optimization problem. The performance of the various heuristic algorithms is measured using maximum Lyapunov exponent and speed of convergence. The results show that the FO Chen system with different FO derivatives achieve maximum Lyapunov exponent. Hence, the chaotic characteristics of the FO Chen system are used in the field of cryptography for generating keys. The robustness and cryptographic strength of the generated key is tested using NIST Statistical Test Suite.Furthermore, different symmetric key encryption algorithms are used to encrypt and decrypt the satellite images. The performance of these algorithms is evaluated using various performance metrics such as key space, information entropy, correlation coefficient, mean absolute error, mean squared error, peak signal to noise ratio, number of pixels change rate, and unified average changing intensity. For instance, The proposed FO Chen system based encryption scheme offers highest key space of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2^{608}\)</EquationSource> </InlineEquation> and NPCR of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(99.79\%\)</EquationSource> </InlineEquation>, demonstrating superior performance compared to existing chaos based and conventional encryption methods. In addition to resistance against statistical and differential attacks, the proposed work demonstrates enhanced security against chosen plaintext and chosen ciphertext attacks. An ablation experiment comparing Mersenne Twister RNG, unoptimal and optimal FO Chen system based encryption further validates the effectiveness of the proposed scheme. Moreover, the proposed methodology is tested on speech signals to demonstrate its adaptability and robust efficacy in securing diverse multimedia data.</p>

Fractional order chaotic systems for encrypting/decrypting satellite images in secure communication

期刊论文
发表日期：

2026年1月29日

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K. Meera,
N. Selvaganesan

摘要

The need for parameter optimization in chaotic systems has become a critical pursuit in communication and control engineering. This paper investigates the parameter optimization of three dimensional Fractional Order (FO) Lorenz, and Chen chaotic systems by minimizing the reciprocal of the positive Lyapunov exponent as an objective function. The parameters of FO chaotic systems are optimized by considering systems with (i) identical fractional order and (ii) different fractional orders. Heuristic algorithms includes cuckoo search, accelerated particle swarm optimization, firefly, and artificial bee colony are used to solve the proposed constrained optimization problem. The performance of the various heuristic algorithms is measured using maximum Lyapunov exponent and speed of convergence. The results show that the FO Chen system with different FO derivatives achieve maximum Lyapunov exponent. Hence, the chaotic characteristics of the FO Chen system are used in the field of cryptography for generating keys. The robustness and cryptographic strength of the generated key is tested using NIST Statistical Test Suite.Furthermore, different symmetric key encryption algorithms are used to encrypt and decrypt the satellite images. The performance of these algorithms is evaluated using various performance metrics such as key space, information entropy, correlation coefficient, mean absolute error, mean squared error, peak signal to noise ratio, number of pixels change rate, and unified average changing intensity. For instance, The proposed FO Chen system based encryption scheme offers highest key space of \(2^{608}\) and NPCR of \(99.79\%\) , demonstrating superior performance compared to existing chaos based and conventional encryption methods. In addition to resistance against statistical and differential attacks, the proposed work demonstrates enhanced security against chosen plaintext and chosen ciphertext attacks. An ablation experiment comparing Mersenne Twister RNG, unoptimal and optimal FO Chen system based encryption further validates the effectiveness of the proposed scheme. Moreover, the proposed methodology is tested on speech signals to demonstrate its adaptability and robust efficacy in securing diverse multimedia data.