A wide spectrum of applications in today’s world use wireless networks since they promise maximum mobility with minimum effort for the user. Due to their use in a numerous number of applications which are diversified, wireless networks are posed to major security threats. Depending upon the utility wireless network security is classified under various domains. Our research mainly focuses on –Network Access Domain Security. This domain addresses authentication mechanisms which ensure that only authorized devices can access a wireless network hence ensuring data integrity and privacy in the network. Various cryptographic algorithms are used to address authentication for wireless networks. Due to the energy constraints in wireless networks which often tend to develop a “Security Processing gap” only a few asymmetric cryptographic algorithms can ensure effective means of mutual authentication and non-repudiation. Performance of cryptographic algorithms can be compared on the basis of their computational requirements. An ideal algorithm for ensuring security in wireless networks would be an algorithm which is hard to break, uses less amount of computation and which uses a small key size. On the basis of these parameters a comparative study of Elliptic Curve Cryptography (ECC) is made with RSA and it is observed that ECC fits well for an efficient authentication mechanism in wireless networks since it offers same level of security for a smaller key size hence reducing the processing overhead.