Image encryption algorithm based on 2D-CICFM using cross-granularity sinusoidal-Joseph coupled permutation and bidirectional interleaved-bitplane diffusion

With the explosive growth of digital multimedia communication, the secure transmission of image data has become a critical issue. However, existing image encryption schemes still face significant challenges in terms of security and efficiency. To address the dynamical degradation inherent in low-dimensional chaotic systems, a novel 2D coupling infinite collapse-fuch map (2D-CICFM) is developed, whose complex dynamic properties, high sensitivity to initial conditions, and chaotic behaviors are rigorously validated through Lyapunov exponents, bifurcation diagrams, sample entropy, permutation entropy, and the NIST SP 800-22 test suite. Furthermore, to overcome the structural vulnerabilities arising from single-granularity permutation coupled with inefficient linear diffusion, an image encryption algorithm based on a cross-granularity strategy is designed. In the algorithm design, a sinusoidal-Joseph coupled permutation mechanism is proposed to thoroughly disrupt spatial correlations through the alternating execution of bit-level and byte-level transformations. Moreover, a bidirectional interleaved-bitplane diffusion strategy is proposed to guarantee a global avalanche effect. Experimental results confirm near-ideal information entropy and correlation coefficients, successful NPCR and UACI hypothesis tests, and strong robustness against noise and occlusion attacks. Complexity analysis further validates its low computational overhead and minimal memory requirements, achieving an optimal trade-off between security and real-time performance.