A Comparative and Overview Analysis of Elliptic Curve Cryptography over Finite Fields

Abstract

Recently, Finite Fields are the most important security mathematical function in the area of elliptic curve cryptography. In this paper, we classify the finite fields into a prime field and a binary field. The proposed approach offers solution to solve the real time implementation based on the finite fields. One such important property is point doubling that has not been focused previously. Finite fields are used to implement the process in a secure way. It is tedious work for the hackers to hack the function, which is based on elliptic curves over finite fields. Therefore, it is more efficient in Elliptic curves and performance and give a one example for application on EC signature. Finally, an serious discussion about the comparison between ECC and other cryptography algorithm is attempted to shape this article.