Motivation and Contributions Sample Clauses

Motivation and Contributions. In practice one finds local broadcast channels in various networks in the form of LAN (Local Area Network) like an Ethernet or Token ring system. Another example is wireless communication, which is inherently broadcast in nature. A particular case when there is a local broadcast among every three players, that is, a complete (2, 3)-uniform hypergraph, has been studied in [7]. We investigate the strength of arbitrary (2, 3)-uniform hypergraphs in the context of achieving Byzantine agreement. Recall that even over complete (2, 3)-uniform hypergraphs on n processes of which up to t may be Byzantine faulty, Byzantine agreement is achievable if and only if n > 2t [7]. We characterize the (im)possibility of Byzantine agreement on an arbitrary network. − Definition 1. A hypergraph H is said to be (α, β)-hyper-γ-connected if on re- moval of any (γ 1) vertices, for any partition of the remaining vertices into α sets of maximum size β, there exists a hyperedge which has non-empty intersec- tion with every set of the partition. − ≤ In Section 4 we prove that Byzantine agreement among n > 2t processes con- nected via a (2, 3)-uniform hypergraph H is possible if and only if H satisfies the following three conditions: (i) if n = 2t + 1, then H is 2-hyperedge complete; (ii) if n > 2t + 1, then H is (2, n)-hyper-(2t + 1)-connected, and (iii) if 2t < n 3t, then H is (3, t)-hyper-(3t n + 1)-connected. Implicit in the characterization are the principles for fault-tolerant network design using (2, 3)-hyperedges. Nevertheless, we provide explicit constructions of minimally connected optimally tolerant 3-uniform hypergraphs (in Section 5). The impact of our results can be seen from the following implications: Implication 1 For any n > 3t, addition of (any number of ) 3-hyperedges does not reduce the (2t + 1)-connectivity requirement. Remark: Note that any hypergraph H is (2, n)-hyper-(2t + 1)-connected if and only if its underlying graph is (2t + 1)-connected. By underlying graph, we mean the graph obtained by replacing each 3-hyperedge by its corresponding three edges. Implication 2 The optimum of n = (2t + 1) can be achieved even if a consider- able fraction of the 3-hyperedges are absent. Furthermore, the minimum number of 3-hyperedges necessary to facilitate agreement reduces as (n/t) increases.

Motivation and Contributions. Group key management protocols [19, 22] are classified into group key distribution protocols and group key agree- ment protocols. The group key distribution protocols [2] are used to distribute group key to the group participants. In group key agreement, group participants are actively involved in the derivation of group key. Compared with conventional group key agreement protocol, AGKAP is having the advantage of one round efficiency. Many of the popular conventional GKA protocols require two or more rounds for sharing the common secret key. In these protocols, all the participants should be connected con- currently in order to share the key. However, if the partic- ipants are located in different locations with different time zones, it is very difficult for them to be connected concur- rently. But, single round ASGKA protocols [17, 23] have several advantages over the GKA protocols with two or more rounds. The single round ASGKA allows each par- ticipant to publish their public key contribution by hold- ing their respective secret key. The participant need not be connected during the key sharing. To send a message to participants in the group, the sender encrypts the mes- sage commonly using the derived common group public key and generates the cipher text. The protocols devel- oped are efficient but secure against passive attacks only. However, in real world attackers are active attackers, who can control the communication channel to place powerful attacks. Man-in-middle attack and also, with which the active attackers can delay, modify, replay and insert the messages during the execution of the protocol. Hence, it is imperative for an ASGKA protocol to resist against the attacks from active adversaries. Any Authenticated key agreement protocol [9, 10, 15, 20, 27], which ensures that no entities other than intended participant can possibly compute the agreed group ses- sion key, even the attacker is active or passive. In au- thenticated key agreement protocols, each user can ob- tain others certificate, extract other participant’s public key, checks the validity of the certificate and then finally a common group key was computed. Consequently, the management of the certificate incurs overheads compu- tation, storage and communication. To eliminate such overhead costs, Identity Based Public Key Cryptography (IB-PKC) that was introduced by Xxxxxx [21]. The dis- tinct feature of IBPKC is that the public key is derived using the participant identity such as...