A Novel Chaotic DNA-Based Image Cryptosystem Leveraging Euclidean Division, Dynamic Josephus Traversal, and Reservoir Computing

This study presents a new chaotic DNA-based image cryptosystem that combines Euclidean division, dynamic Josephus traversal (DJT), and reservoir computing to address the weaknesses of current methods. Old chaotic DNA cryptosystems usually have problems such as using the same keys for different messages, simple DNA processes, and being vulnerable to attacks where the attacker can choose the input or try many options. The cryptosystem in this study uses a 7D hyperchaotic system that starts with keys created from SHA-512 hashes to produce changing keystreams based on the plaintext, making it very strong against such attacks. The proposed cryptosystem uses a base-4 numeral system instead of traditional DNA encoding, which significantly reduces the amount of computing power required to convert pixels to DNA. Dynamic Josephus traversal introduces an adaptive permutation by dynamically altering the traversal parameters to enhance unpredictability. Simultaneously, reservoir computing selects from 14 new DNA operations, such as upshift, downshift, and composite NOT transformations, to improve data mixing. Thorough security tests show outstanding results: a keyspace of 2860, almost perfect randomness (7.9999), an encryption time of 1.2925 s for a 512×512 image, NPCR (99.6331%), UACI (33.5379%), and high encryption quality. The cryptosystem shows strong resistance to noise and cropping attacks, with PSNR values of 19.2801 dB at 0.1 noise density and 12.3207 dB with 50% data missing, which is better than the best current methods. The NBCR metric (49.98%) confirms that the key sensitivity is almost perfect, meaning that there is almost no link between ciphertexts made with slightly different keys. Comparative studies indicate that it is more resistant to differential, statistical, and adversarial attacks and can encrypt data faster than other DNA-based cryptosystems.