Hyperelliptic Curve Cryptography (HECC) is one of the public key cryptography requires only 80 bit key length to provide same level of security as other public key cryptosystem such as RSA-1024, ECC-160. So many researchers put their effort to develop many authentication schemes for constrained environment. Our proposed scheme helps to achieve better security by employing Hyperelliptic Curve Cryptography. This paper shows the procedure to obtain mutual authentication between smart card and server. Finally we achieve the authentication with lesser number of communication bit and less computational complexity. Simulation results shows processing time taken to execute authentication process between server and smart card with respect to key size. © Research India Publications.