With the rapid growth in the exchange of digital data, the problem of protecting images has become essential, particularly in sectors such as medicine, surveillance and secure communications. Traditional encryption techniques, such as DES, AES and RSA, are effective for text, but often ineffective for images, due to high redundancy and high correlation between pixels. We suggest a novel image encryption algorithm based on chaotic maps and the variable-step Josephus problem to get over these restrictions and increase the encryption resilience. This algorithm uses Kepler Chaotic Optimisation Algorithm (CKOA) to select the most suitable chaotic maps, guaranteeing optimal diffusion and complex pixel confusion. Key generation is enhanced with MD5 and SHA-256 hash functions, providing increased resistance to collisions and attacks. In addition, Discrete Wavelet Transform (DWT) is integrated to compress images and reduce processing time, while maintaining a high average entropy of 7.999 for encrypted images. Experimental tests demonstrate strong resistance against cryptographic attacks, including 99.6% as pixel change rate and 33.31% as unified average change intensity, ensuring optimum security. Compared with other image-based encryption schemes, our method stands out for its speed and reduced computational complexity, while offering superior security.
Ghouate et al. (2025) studied this question.