Conference key establishment protocol using a multivariate polynomial and its applications

In 1992, a non-interactive k-secure m-conference protocol based on an m-variate polynomial has been proposed. Each user needs to store a (m 1)-polynomial having degree k as a private share. A secret conference key involving m users can be computed by each conference member non-interactively using each private share. There is no overhead to exchange information in order to establish a conference key. However, the storage space of each user is exponentially proportional to the group size of the conference. In this paper, we propose a key establishment protocol using a multivariate polynomial in ZN, where N is a RSA modulus. One unique feature of using this special type of polynomials for conference key protocol is that the storage space of each user is fixed and is independent to the group size of the conference. User can use their shares obtained from a key generation center initially to establish conference keys consisting of different users. Furthermore, we propose two applications to demonstrate the importance of using this special type of polynomials to design solutions. One is the private reconstruction of secret in a secret sharing scheme over network, and the other is the secure group communication. Copyright © 2014 John Wiley & Sons, Ltd.