Protocols for designing a fast and perfect group-oriented secret key sharing in distributed systems

This paper presents a fast and perfect secret key sharing scheme based on a simple geometric method to solve group-oriented secret sharing problems in distributed systems. This scheme does not need the existence of the trusted authority and can reduce the needed time of sending messages to a group of receivers due to multiplication operations only. The scheme can be shown to be very secure, because it is not only a perfect secret sharing but also when the cryptanalyst tries to compute secret values, he must solve the simultaneous trigonometric equations with t-1 equations, where t is the threshold value in the secret key sharing scheme as presented in this paper and the number of unknown valves are much more than the number of equations so that he will obtain no exact solution. Furthermore, it can dynamically insert or delete any participant in a group without affecting these original participants, and it is easy to change the shares without changing the original secret key