Treffer: MATLAB Implementation of Gray-Scale Image Encryption and Decryption using Elliptic Curve ElGamal Cryptosystem

Elliptic curve algorithms have become increasingly prominent in modern cryptosystems due to their superior computational efficiency and high security, comparable to classical algorithms like RSA. Their use in modern cryptography enables smaller chip-sizes, reduced power-consumption, and enhanced computational speed. In this thesis, we developed several MATLAB codes, along with a graphical user interface, to implement a grayscale image encryption and decryption system based on the elliptic curve variant of the ElGamal Cryptosystem. The codes were optimized to minimize computational load, leveraging the Weierstrass cubic equation to define a suitable elliptic curve.To accelerate encryption and decryption, well-structured submodules—such as fast exponentiation in modular arithmetic—were incorporated. The flexible graphical user interface allows users to adjust elliptic curve parameters, the prime modulus p, and the private keys of both communicating parties. The system generated high-quality cipher images with low mean square error and high peak signal-to-noise ratio. Additionally, the final version of the model integrates a novel algorithm that addresses two practical challenges of the Elliptic Curve ElGamal Cryptosystem, significantly reducing both encryption and decryption times and the size of the transmittedcipher image.