An Encryption Application and FPGA Realization of a Fractional Memristive Chaotic System

The work in this paper extends a memristive chaotic system with transcendental nonlinearities to the fractional-order domain. The extended system's chaotic properties were validated through bifurcation analysis and spectral entropy. The presented system was employed in the substitution stage of an image encryption algorithm, including a generalized Arnold map for the permutation. The encryption scheme demonstrated its efficiency through statistical tests, key sensitivity analysis and resistance to brute force and differential attacks. The fractional-order memristive system includes a reconfigurable coordinate rotation digital computer (CORDIC) and Grunwald-Letnikov (GL) architectures, which are essential for trigonometric and hyperbolic functions and fractional-order operator implementations, respectively. The proposed system was implemented on the Artix-7 FPGA board, achieving a throughput of 0.396 Gbit/s.

Automated summary

This paper extends a memristive chaotic system with transcendental nonlinearities to the fractional-order domain. The chaotic properties of the extended system are validated through bifurcation analysis and spectral entropy. The presented system is employed in the substitution stage of an image encryption algorithm, demonstrating its efficiency through statistical tests, key sensitivity analysis, and resistance to brute force and differential attacks. The proposed system includes reconfigurable coordinate rotation digital computer (CORDIC) and Grunwald-Letnikov (GL) architectures for trigonometric and hyperbolic functions and fractional-order operator implementations, respectively. It achieved a throughput of 0.396 Gbit/s on the Artix-7 FPGA board.