Security is the major concern in nowadays in many applications, many algorithms were proposed majorly categorized into symmetric and asymmetric key cryptographic algorithms. The limitations with symmetric key cryptography are the scope of knowing the shared key between the communicators to intruders. Hence, asymmetric key cryptography algorithms were performed, among those ECC is one best mechanism. This paper is aiming at the analysis of time complexity, efficiency and security levels of Elliptic Curve Cryptography(ECC) and based upon the analysis, further extension to a strong encryption and decryption algorithm. In addition to that ECC will be extended to other ECC based derived algorithms include Hessian algorithm. Due to the many important properties making the model attractive in cryptography, a paper code is implemented in the Magma software to ensure the correctness of formulas in this work. A comparative analysis will be done among the ECC and Hessian algorithm.