A Discussion on Elliptic Curve Cryptography and Its Applications

Elliptic curve cryptography (ECC) is a kind of public key cryptosystem like RSA. But it differs from RSA in its quicker evolving capacity and by providing attractive and alternative way to researchers of cryptographic algorithm. The security level which is given by RSA can be provided even by smaller keys of ECC (for example, a 160 bit ECC has roughly the same security strength as 1024 bit RSA). In this paper, we will present some ECC algorithms and also gives mathematical explanations on the working of these algorithms.