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

doi:10.1007/s00224-026-10274-x

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

2026-04-23

PRE

Kareem, Shadman Rahman *

Pirdawood, Mardan Ameen

DOI：10.1007/s00224-026-10274-x

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Abstract

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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 %, UACI 33.4649 %, entropy > 7.9993) compared to existing methods. By combining algebraic map enhancements with hash-based initialization and multi-stage diffusion, the algorithm achieves an optimal balance between security and computational efficiency, making it particularly suitable for real-time image encryption applications while resisting statistical, differential, and chosen-plaintext attacks.

Keywords:

Chaotic encryption

Image security

Hash-based cryptography

3D chaotic map