With the explosion of the Internet as well as the wireless and mobile communications, it faces a growing need for security. Both for secure web transaction and for secure messaging, an efficient public key system is required. The Elliptic Curve Cryptography delivers the highest security strength per bit of key in any known public key system. It well suits to the applications such as the smart card systems and the wireless/mobile communications. In this work, we apply the ECC and the bilinear pairings on elliptic curve to the authentication and the group security. There are four ECC-based...