New image encryption approach using a dynamic-chaotic variant of Hill cipher in Z/4096Z

Abstract

Currently, digital communication generates a considerable amount of data from digital images. Preserving the confidentiality of these images during transmission through network channels is of crucial importance. To ensure the security of this data, this article proposes an image encryption approach based on enhancing the Hill cipher by constructing pseudo-random matrices operating in the ring Z/2¹²Z injected into a controlled affine transformation. This approach relies on the use of chaotic maps for generating matrices used in the encryption process. The use of the ring Z/2¹²Z aims to expand the key space of our cryptosystem, thus providing increased protection against brute-force attacks. Moreover, to enhance security against differential attacks, a matrix of size (4×4), not necessarily invertible, is also integrated into a diffusion phase. The effectiveness of our technique is evaluated through specific tests, such as key space analysis, histogram analysis, entropy calculation, NPCR and UACI values, correlation analysis, as well as avalanche effect assessment.