JSE_V3_N2_RP2 R. Ganesan M. Gobi K. Vivekanandan Journal on Software Engineering 2230 – 7168 3 2 43 48 Cryptography, Elliptic curve cryptography, Hyper-elliptic curve cryptography, Encryption, Decryption, Key generation It has recently been reported that elliptic and hyper-elliptic curve cryptography are the two public key cryptographic techniques used to implement the cryptosystems more efficiently and effectively. Many researches are being done to implement these in both hardware and software fields. In this paper, the basic concepts of elliptic and hyper-elliptic curves are discussed. The algorithms for private key, public key generation, encryption and decryption for both elliptic curve and hyper-elliptic curve cryptography are described. Also, the performance of both ECC and HECC are demonstrated. Finally, the comparative study between these two is analyzed. July - September 2008 Copyright © 2008 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=248