Today security is the challenging aspect in internet and network application. Cryptography is the study of mathematical techniques related to various aspects of information security, such as confidentiality or privacy, data integrity and entity authentication. Cryptography is one of the main constituents of computer security. Public cryptography is the art of protecting information by transforming it (encrypting it) into an unreadable format, called cipher text. Only those who possess a secret key can decrypt the message into plain text. This paper reviews five commonly used asymmetric key cryptography algorithms namely RSA, Diffie - Hellman, ElGamal, DSA and ECC and present their comparative study.