This paper presents efficient protocols for establishing securegroup-oriented communication channels in Internet environments based ona geometric method. Since the data encryption/decryption requires acommon secret session key between two communicating parties, finding anefficient way to distribute the group-oriented secret session key inInternet environments has become a nontrivial task. We assume that theInternet environments consist of many hosts, and each host has manyusers attached to it. The scheme proposed in this paper incorporates thepublic-key distribution and the trigonometry concepts as the basictheory. Since this scheme does not need any trusted key distributioncenter to distribute the common secret session key between two groups,it is quite suitable to be used in Internet environments so that the keydistribution is convenient, time-saving and reparable. Furthermore, anauthentication protocol is also proposed. Such a protocol can not onlyidentify both the sender and the receiver of a group correctly but alsomake sure that the transmitted message reaches its destination safely
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