A key distribution scheme for dynamic conferences is a method by which initially an (off-line) trusted server distributes private individual pieces of information to a set of users. Later any group of users of a given size (a dynamic conference) is able to compute a common secure key. In this paper we study the theory and applications of such perfectly secure systems, In this setting, any group of t users can compute a common key by each user computing using only his private piece of information and the identities of the other t-1 group users. Keys are secure against coalitions of up to k users, that is, even if E users pool together their pieces they cannot compute anything about a key of any t-size conference comprised of other users. First we consider a non-interactive model where users compute the common key without any interaction. We prove a lower bound on the size of the user's piece of information of ("2; ') times the size of the common key. W e then establish the optimality of this bound, by describing and analyzing a scheme which exactly meets this limitatioii (the construction extends the one in [2]). Then, we consider the model where interaction is allowed in the common key computation phase, and show a gap between the models by exhibiting an interactive scheme in which the user's information is only k + t-1 times the size of the common key. We further show various applications and useful modifications of our basic scheme. Finally, we present its adaptation to network topologies with neighborhood constraints.

{ amir , st asio .huge, moti}0oatson. ibm. t o m Abstract. Secret sharing schemes protect secrets by distributing them over different locations (share holders). In particular, in k out of R threshold schemes, security is assured if throughout the entire lifetime of the secret the adversary is restricted to compromise less than k of the n locations. For long-lived and sensitive secrets this protection may be insufficient. We propose an efficient proactive secret sharing scheme, where shares are periodically renewed (without changing the secret) in such a way that information gained by the adversary in one time period is useless for attacking the secret after the shares are renewed. Hence, the adversary willing to learn the secret needs to break to all k locations during the same time period (e.g., one day, a week, etc.). Furthermore, in order to guarantee the availability and integrity of the secret, we provide mechanisms to detect maliciously (or accidentally) corrupted shares, aa well a8 mechanisms to secretly recover the correct shares when modification is detected.

A key distribution scheme for dynamic conferences is a method by which initially an (off-line) trusted server distributes private individual pieces of information to a set of users. Later any group of users of a given size (a dynamic conference) is able to compute a common secure key. In this paper we study the theory and applications of such perfectly secure systems, In this setting, any group of t users can compute a common key by each user computing using only his private piece of information and the identities of the other t-1 group users. Keys are secure against coalitions of up to k users, that is, even if E users pool together their pieces they cannot compute anything about a key of any t-size conference comprised of other users. First we consider a non-interactive model where users compute the common key without any interaction. We prove a lower bound on the size of the user's piece of information of ("2; ') times the size of the common key. W e then establish the optimality of this bound, by describing and analyzing a scheme which exactly meets this limitatioii (the construction extends the one in [2]). Then, we consider the model where interaction is allowed in the common key computation phase, and show a gap between the models by exhibiting an interactive scheme in which the user's information is only k + t-1 times the size of the common key. We further show various applications and useful modifications of our basic scheme. Finally, we present its adaptation to network topologies with neighborhood constraints.

server.We describe our implementation, which can be used as an extension of a web server or as a separate server with interface to applications.

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