An efficient and authenticated group-oriented cryptoscheme based on a geometric method in Internet environments

Based on a geometric method, this paper presents an efficient and authenticated cryptoscheme for establishing secure group-oriented data communications in Internet environments. We assume that the Internet environments consist of many hosts, and each host has many users attached to it. The secure group-oriented communication scheme proposed in this paper incorporates the public-key distribution and the trigonometry concepts as the basic theory. Since this scheme does not need any trusted key distribution center to distribute the common secret session key between two parties and can reduce the computation time needed for securely sending messages to a group of receivers by using multiplication operations instead of modular exponentiation, it is quite suitable to be used in Internet environments so that the key distribution is convenient, time-saving and reparable. Furthermore, an authentication protocol is also proposed. Such a protocol can not only identify both the sender and the receiver of a group correctly, but can also make sure the transmitted message has reached its destination safely