Group Theoretic Approach to Elgamal Elliptic Curve Cryptosystem

Due to increase in complexity of cryptographic attacks, this paper explored the ElGamal Elliptic Curve Cryptosystem (EECC) using group theoretic approach with specific focus on understanding its mathematical foundations, security features, potential vulnerabilities and practical applications. The aim is achieved through a detailed analysis, and the study demonstrated how EECC leverages the strengths of elliptic curve cryptography and group theory to offer a secure and efficient alternative to traditional cryptographic systems. The research addressed key questions regarding the operation of ElGamal on elliptic curves, its security advantages, and areas where vulnerabilities may arise. It was concluded that the vulnerabilities identified, particularly concerning side-channel attacks and the looming threat of quantum computing, highlight the need for further research and development in cryptographic techniques and implementations.