SECURE SCHEMES FOR SECRET SHARING AND KEY DISTRIBUTION USING PELL'S EQUATION

A key distribution scheme for dynamic conferences is a method by which initially an trusted server distributes private individual pieces of in- formation to a set of users. Later each member of any group of users of given size can compute a common secure group key. In this setting any group of t users can compute a common key by each user computing using only his pri- vate initial piece of information and the identities of the other t − 1 users in the group. Keys are secure against coalition of to k users, that is, even if k users pool together their pieces they cannot compute anything about a key of any t-size conference comprised of other users. In this paper, we introduce an algorithm for such perfectly secure scheme by using Pell's equation.