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.

The Rise and Fall and Rise of Combinatorial Key Predistribution

“…For many applications this tradeoff is likely to favour the Blom scheme. The Blom key predistribution scheme easily generalises to key predistribution applications where groups of t nodes require common keys [3]. It was further shown that this approach is optimal with respect to node key storage.…”

AK-PPM: An Authenticated Packet Attribution Scheme for Mobile Ad Hoc Networks

“…If an intermediate node u i , whose previous hop is u j , decides to inscribe the packet, it will update the value of F = F ⊕ H ki (M |u i ), here k i is the pairwise key shared between u i and V . Note that a node can easily compute its pairwise key shared with another node given each other's id [15][16][17]. The MAC of M |u i serves as its "footprint" and we will see in the verification phase how it helps detect the marks in Q from being removed starting from the end.…”

“…Nodes can establish trust through either a PKI, a Trusted Third Party (TTP), or predistributed shared keys. Further, any two nodes in the network, as long as knowing each other's id, can efficiently establish a pairwise key based on one of the existing schemes [15][16][17]. The key used in the message authentication code (MAC) generation at an intermediate node is its pairwise key share with the victim node.…”

Compromise-Resilient Anti-jamming for Wireless Sensor Networks

“…Many pairwise key establishment schemes [16][17][18] allow two nodes to establish a pairwise key on the fly as long as they know each other's id. In our work, we choose the Blundo scheme [20] for our solution since the Blundo scheme provides clear security guarantee and eases our presentation. In the Blundo scheme, a bivariate symmetric polynomial f (x, y) with degree of t is chosen in advance and f (i, y) is preloaded on sensor i.…”