Conference Key Establishment Using Polynomials

In 1992, Blundo et al. have proposed a non-interactive k-secure m-conference protocol based on an m-variate polynomial over a finite field Fp. The key distribution center (KDC) is responsible to pick a symmetric m-variate polynomial of degree k and generate shares for users. Each share is a symmetric polynomial involving m− 1 variables of degree k, and needs to store the coefficients of such a symmetric polynomial. The storage space of each user is exponentially proportional to both the size of the conference and the security level. This makes their protocol impractical except for the case of the pairwise key distribution of m = 2. In this paper, we propose a non-interactive k-secure m-conference protocol based on a special type of multivariate polynomials of degree k. The advantage of using this type of multivariate polynomials can limit the storage space of each user to be k + 1, the number of the coefficients of a univariate polynomial of degree k, which is independent of the conference size. Furthermore, the shares generated for a k-secure m-conference protocol can support any conference with size t where t ≤ m. We show that the proposed protocol is information-theoretic secure in terms of a concept of homomorphic random source and can resist known shares and known conference keys attacks.