Secure Encryption of Biomedical Images Based on Arneodo Chaotic System with the Lowest Fractional-Order Value

Abstract

Fractional-order (FO) chaotic systems exhibit richer and more complex dynamic behaviors compared to integer-order ones. This inherent richness and complexity enhance the security of FO chaotic systems against various attacks in image cryptosystems. In the present study, a comprehensive examination of the dynamical characteristics of the fractional-order Arneodo (FOAR) system with cubic nonlinearity is conducted. This investigation involves the analysis of phase planes, bifurcation diagrams, Lyapunov exponential spectra, and spectral entropy. Numerical studies show that the Arneodo chaotic system exhibits chaotic behavior when the lowest fractional-order (FO) value is set to 0.55. In this context, the aim is to securely encrypt biomedical images based on the Arneodo chaotic system with the lowest FO value using the Nvidia Jetson Nano development board. However, though the lowest FO system offers enhanced security in biomedical image encryption due to its richer dynamic behaviors, it necessitates careful consideration of the trade-off between high memory requirements and increasing complexity in encryption algorithms. Within the scope of the study, a novel random number generator (RNG) is designed using the FOAR chaotic system. The randomness of the random numbers is proven by using internationally accepted NIST 800-22 and ENT test suites. A biomedical image encryption application is developed using pseudo-random numbers. The images obtained as a result of the application are evaluated with tests such as histogram, correlation, differential attack, and entropy analyses. As a result of the study, it has been shown that encryption and decryption of biomedical images can be successfully performed on a mobile Nvidia Jetson Nano development card in a secure and fast manner.