A Hybrid Elliptic Curve Cryptography Hill Cipher with Bézier like Coefficient Matrix for Secure Image Encryption

Secure image communication over public networks requires encryption methods that provide strong security guarantees while maintaining computational efficiency for practical deployment. Existing Elliptic Curve Cryptography Hill Cipher schemes offer efficient matrix-based encryption with compact key representation and low computational cost. However, their security performance is closely tied to elliptic curve parameter selection and relies on a single linear transformation, which may limit key diversity and diffusion capability. This paper presents a hybrid image encryption scheme that strengthens the conventional Elliptic Curve Cryptography Hill Cipher by incorporating a Bézier-like Coefficient Matrix as an additional transformation layer. The proposed matrix is generated through a controllable shape parameter, enabling the construction of diverse transformation matrices that expand the effective key space and act as diffuse to randomize the pixel values of ciphered image. The resulting two-stage encryption framework improves the diffusion process and enhances the complexity of the ciphered image while preserving computational efficiency. Security and performance are evaluated through key sensitivity analysis, information entropy, histogram distribution, differential attack resistance, statistical randomness, and robustness against noise interference. Experimental results show that the proposed method achieves near ideal entropy, uniform ciphered image distributions, high sensitivity to minor key variations, and stable image recovery under moderate noise conditions. Comparative analysis further demonstrates improved diffusion characteristics and enhanced resistance to statistical and differential attacks over the conventional Elliptic Curve Cryptography Hill Cipher. These results indicate that the proposed framework provides a secure and computationally efficient solution for image protection and secure multimedia communication.