Encryption scheme for the security of digital images based on Josephus Traversal and Chaos theory

Abstract

A synergistic approach based on the Josephus traversal and chaos theory is suggested for the security of digital images. To encrypt the digital images, a combination of the Josephus Traversal principle and the 2-dimensional Hénon map is employed for the secure transmission of digital data. The two distinct key matrices are used in the Josephus principle to cause bit-level shuffling throughout the image. These two distinct key matrices are effectively formed by the chaotic streams generated by the two-dimensional Hénon map. The system becomes more unpredictable because the Josephus traversal employs a different key set for every individual pixel to scramble it at the bit level. Moreover, the image is shuffled and diffused at the pixel level using the same streams produced by chaotic structure. The test images are used to determine the strength of the suggested system. The numerical results and comparative findings of the various quality parameters such as key space, information entropy, correlation coefficient, histogram analysis, differential attack indicators (NPCR and UACI) verify the strength of the encryption system. The acceptable key space, numerical values of entropy approaches to ideal value, correlation coefficient values close to 0, and satisfactory results of theoretical value tests verify the robustness of the employed scheme to resist various types of cryptanalytical attacks.