Wireless devices are characterized by low computational power and memory. In addition to this wireless environment are inherently less secure than their wired counterparts, as anyone can intercept the communication. Hence they require more security. One way to provide more security without adding to the computational load is to use elliptic curve cryptography (ECC) in place of the more traditional cryptosystems such as RSA. As ECC provides the same level of security for far less key sizes, as compared to the traditional cryptosystems, it is ideal for wireless security. In this thesis we will investigate the different ways of implementing ECC on wireless devices such as personal digital assistants (PDAs). We will present our findings and compare the different implementations. In our implementation ECC over the field Fn2 using optimal normal basis representation gives the best results.