Algebraically Enhanced 3D Chaotic Map with Hash-Based Initialization for Secure Image Encryption

With the rapid growth of image-based communication and storage, ensuring secure image transmission has become a critical challenge. This paper presents a secure image encryption scheme based on an algebraically enhanced 3D chaotic map with hash-based initialization, addressing the growing need for robust image security in modern communication systems. The proposed method employs SHA-256 hashing to generate secure initial conditions, feeding into an algebraically deformed 3D chaotic map with improved non-linear dynamics for enhanced chaotic behavior. The encryption process implements a three-stage approach: first, chaotic x-value sequences permute pixel positions; second, Gray code transformations combined with chaotic XOR operations achieve bit-level diffusion; and finally, multi-channel diffusion establishes inter-pixel dependencies across color channels. The scheme demonstrates strong cryptographic properties, with theoretical analysis confirming its chaotic characteristics and experimental results showing superior performance (NPCR 99.6120