Software Implementation of Cyclic Abelian Elliptic Curve using Matlab

of products and standards that use public-key cryptography for encryption and digital signature use RSA. The key length for secure RSA has increased over recent years ,and this has put heavier processing load on applications using RSA. Recently, a competing system has begun to challenge RSA: Elliptic curve cryptography (ECC).The principle attraction of ECC, compared to RSA, is that it appears to offer equal security for a far smaller key size, thereby reducing processor overhead. Cryptographers are interested only in elliptic curve that belongs to cyclic abelian group. This paper implements cyclic abelian elliptic curve in MATLAB. The properties of abelian group is proved over the coordinates satisfying the curve. Base points of elliptic curve are generated to prove that the elliptic curve belongs to cyclic abelian group.