Perfectly-Secure Key Distribution for Dynamic Conferences

Abstract

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.

A new key predistribution scheme for general and grid-group deployment of wireless sensor networks

“…From this coordinate, the destination node finds out the common polynomial that it shares with the broadcasting node if at all. Now, the common key can be calculated using the same method as [5].…”

“…However, in their schemes, only a single node is deployed in a square region as opposed to our scheme where there are a group of nodes deployed in a region. They used the polynomial-based scheme of Blundo et al [5]. The deployment region is broken down into equal-sized squares …”

“…This scheme, though primarily not intended for WSNs, was later used for key establishment in WSN. A symmetric polynomial-based scheme was proposed by Blundo et al in [5]. Key predistribution schemes based on combinatorial design can be found in [6][7][8][9][10][11][12].…”

“…The first scheme called the closest pairwise scheme was a modification of the pairwise key predistribution scheme. The second predistribution scheme uses the polynomial-based key predistribution scheme of Blundo et al [5].…”

Dynamic Cryptographic Context Management (DCCM)

“…• Information-theoretic methods, such as Blundo's Symmetric Polynomials (BSP) [7] and Chiou-Chen's Secure Lock (CSL) [10], require large amounts of space per user and scale exponentially with the number of members in a group. [19].…”