Hybrid Image Encryption via BCC-Algebraic Dynamic Key Generation and AES-CBC

Traditional chaotic image encryption systems frequently suffer from phase-space periodic degradation and finite-precision limitations. To overcome these inherent vulnerabilities, this paper presents a novel dynamic image encryption framework combining finite BCC-algebraic structures, SHA-256 cryptographic hashing, and an HMAC-based Key Derivation Function (HKDF). The scheme establishes a plaintext-aware key synthesis mechanism utilizing dynamic matrix representations of finite BCC-algebra. Primary key seeds and Initialization Vectors (IVs) are dynamically generated by performing bitwise XOR operations between the SHA-256 hash digest of the input image and vectorized algebraic structures, followed by rigorous HKDF sub-key derivation. Spatial confusion and diffusion are subsequently achieved using the AES-CBC mode. Extensive security evaluations and formal provable security analysis (IND-CPA) demonstrate that the proposed system achieves high resistance against differential, linear, statistical, and Chosen-Plaintext Attacks, with an information entropy consistently approaching the theoretical optimum of 8.0 and optimal NPCR/UACI differential performance.