Dynamic analysis and FPGA implementation of a 2D fractional sine-cosine map for image encryption using bit-level permutation and genetic algorithm

This paper introduces a novel 2D fractional sine-cosine (2D-FSC) hyperchaotic map and its application in a robust image encryption scheme. Through comprehensive dynamic analysis including bifurcation diagrams, Lyapunov exponents, butterfly effect, Shannon entropy, and phase space visualization, it is demonstrated the map's superior chaotic characteristics compared to conventional 1D chaotic systems. The proposed encryption framework employs a three-stage diffusion-permutation-confusion architecture enhanced by two key innovations: (1) a genetic algorithm optimizing diffusion and confusion processes to maximize entropy (7.998 ± 0.002) and minimize correlation coefficients (|cc| < 0.004) of the encrypted image, and (2) a novel chaos-based pixel fusion technique for efficient bit-level permutation. Hardware implementation on a Cyclone IV FPGA (6057 logic elements, 34.29 MHz max frequency) validates the practical feasibility of the chaotic map. Security analysis confirms resistance against brute-force (key space > 2750), statistical (χ² < 184.2), differential (NPCR 99.61 ± 0.04 %, UACI 33.46 ± 0.09 %), and noise/clipping attacks. The algorithm processes 256× 256 images in 0.32 s which is 28–42 % faster than comparable schemes, while maintaining consistent performance across grayscale, color, and edge-case images. These advancements establish a new benchmark for chaos-based cryptosystems in applications requiring both high security and computational efficiency.