Original title: A Hybrid Elliptic Curve Cryptography Hill Cipher with Bézier like Coefficient Matrix for Secure Image Encryption
Syed Ahmad Aidil Adha Said Mad Zain, Md Yushalify Misro, Hailiza Kamarulhaili, Muhammad Rezal Kamel Ariffin · September 2026
Sending pictures securely over public networks needs strong codes that computers can run quickly. Older methods combine elliptic curve math with a matrix-based code called a Hill Cipher. A matrix is a grid of numbers used to mix up data. But these older systems rely on only one mixing step. This limit leaves them with weaker variety in their secret keys and less ability to spread image details around. To solve this, researchers added a second mixing layer using a Bézier-like coefficient matrix. A controllable shape setting builds these new number grids. This tool gives users a wider variety of secret keys and scrambles pixel values much more thoroughly. The new two-stage system keeps calculations fast while securing pictures. Tests showed it achieves near ideal entropy, creates uniform scrambled images, reacts sharply to tiny key changes, and recovers images steadily under moderate noise.
Imagine stirring a pot of soup with one spoon. You stir once, and the ingredients barely mix; the flavor stays in one spot. Now suppose you could change the shape of the spoon as you stir, so each turn pushes the soup in a different pattern. In this paper, the first stir is the old way of mixing, and the shape-changing second stir is the new layer that scrambles the picture's dots more thoroughly.
Anyone sending images over public networks needs encryption that resists attacks yet runs on ordinary hardware. This scheme adds a second, shape-controlled matrix layer to an existing cipher, so a tiny key change scrambles the whole image and statistical or differential attacks get much harder — without a big speed penalty.
The abstract doesn't say much about limitations, but it only claims stable recovery under moderate noise and compares only against the conventional ECC Hill Cipher, so stronger noise and other modern ciphers are not addressed.
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A Hybrid Elliptic Curve Cryptography Hill Cipher with Bézier like Coefficient Matrix for Secure Image Encryption — Syed Ahmad Aidil Adha Said Mad Zain, Md Yushalify Misro, Hailiza Kamarulhaili et al. — Mathematics — doi:10.3390/math14183431
Abstract licence: CC BY
Explanation generated by Synthesis from the abstract — it is not the original paper.