Abstract
Elliptic Curve Cryptography is gaining wide acceptance as an alternative to the conventional cryptosystems (DES, RSA, AES) which tend to be power hungry. Elliptic Curve ciphers require less computational power, memory and communication bandwidth giving it a clear edge over the traditional Crypto- Algorithms. This paper provides an overview of elliptic curves and their use in cryptography. The focus is on the performance advantages to be obtained in the wireless environment by using elliptic curve cryptography instead of a traditional cryptosystem like RSA. Specific applications to secure messaging and identity- based encryption are discussed.