A suite of algorithms for key distribution and authentication in centralized secure multicast environments

The Extended Euclidean algorithm provides a fast solution to the problem of finding the greatest common divisor of two numbers. In this paper, we present three applications of the algorithm to the security and privacy field. The first one allows one to privately distribute a secret to a set of recipients with only one multicast communication. It can be used for rekeying purposes in a Secure Multicast scenario. The second one is an authentication mechanism to be used in environments in which a public-key infrastructure is not available. Finally, the third application of the Extended Euclidean algorithm is a zero-knowledge proof that reduces the number of messages between the two parts involved, with the aid of a central server.