Design and analysis of a fractional-order based chaotic map with application in image encryption

The increasing need for strong image encryption methods has developed because digital image transmission has expanded rapidly into fields that include medical imaging, surveillance, and secure communication. The existing chaos-based image encryption methods depend on integer-order chaotic maps, which experience digital system limitations because of their finite precision characteristics, their restricted key capacity, and their deficient random pattern generation. The limitations of these systems can be solved through particular methods that serve this purpose. This paper introduces a novel chaotic map, the Fractional-Order Recursive Cosine-Sine Chaotic Map (FORCSCM), which utilizes the property of fractional calculus. The FORCSCM addresses the limitations of traditional chaotic maps by incorporating fractional-order, resulting in superior chaotic behavior with a high Lyapunov exponent and exceptional sensitivity to initial conditions. Time-series analysis and sample entropy evaluations confirm the map’s robustness and unpredictability. By using this novel chaotic map, an image encryption algorithm is introduced. The encryption process involves two phases: confusion, where a FORCSCM-generated chaotic sequence permutes image pixels, and diffusion, where a diffusion mask derived from the map modifies pixel values through an XOR operation. The algorithm demonstrates strong resistance to statistical, differential, and brute-force attacks, as evidenced by experimental analyses. Metrics such as correlation coefficients close to zero, a high entropy value of 7.999 for encrypted images, and uniform histogram distributions validate its efficacy. The proposed method is suitable for secure image communication, digital watermarking, and privacy protection, offering robust encryption and computational efficiency for real-time applications.