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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 topics involved. §Remote authentication: ECC-based remote authentication scheme with smart card for open distributed system. §Group oriented access: ECC-based group-oriented smart card access scheme merged with shared-secret scheme, cheating detection and cheater identification. §Secure multicast: ECC-based secure multicast scheme endowed with authentication for transmitted message and sender.§Group key agreement: ECC-based group key agreement scheme with authentication for secure group communications.
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