Generating Elliptic Curves Modulo p for Cryptography Using Mathematica Software

This paper discussed basic concepts of elliptic curves, from the definition of the elliptic curve defined by the Weierstrass equation up to its application to cryptography. The discussion includes the group operations on the curves, the addition law as well as the doubling formulas and how to generate a good curve cryptographically. These important properties come with some examples with the direction towards illustrating the use of elliptic curves in cryptography with the help of the Mathematica software.