Smart cards improve the convenience and security of any transaction. They provide tamper-proof storage of user and account identity. Multifunction cards are used to manage network system access, store value and other data. The cards carry personal account, credit and buying-preference information and thus, security becomes a primary issue here. Public Key Cryptography plays an essential role in electronic banking and financial transactions. ECC is one of the best public key techniques for its small key size, high security and is suitable for secure access of smart cards. This article gives principles of public key cryptography, illustrates two cryptographic algorithms RSA and ECC. The elliptic curve cryptography is implemented on smart card using Menezes-Vanstone Elliptic Curve Cryptosystem and Nyberg-Rueppel Signature Scheme [2]. The implementation of these algorithms is done using Java Card technology. The test results are analysed and comparison about the public key sizes and security aspects are also discussed.