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a pairwise key Note also that keys generated in this scheme are all pairwise keys and hence can also be used for authentication purposes as long as the key space is not compromised This scheme exhibits a threshold property similar to the earlier schemes such as the q-composite scheme [39] and the scheme in [41] Thus, when the number of compromised nodes is less than the threshold, the probability that the secure links formed by noncompromised nodes are affected on account of some compromised nodes is close to zero A difference as compared to the q-composite scheme or the basic scheme in [17] is that the thresholds at which this scheme breaks down is much larger For example, the authors show that, in order to eavesdrop successfully on 10 percent of the secure links formed by noncompromised nodes, the adversary has to break ve times as many nodes as he has to break under the q-composite scheme or the basic scheme in [17] Thus, this scheme substantially lowers the initial payoff to the adversary from compromising a small number of nodes Hence, the adversary needs to compromise a signi cant fraction of nodes in the network to be able to also eavesdrop successfully on communication between noncompromised nodes This scheme also allows nodes to be deployed in increments and does not need all nodes to be deployed at the same time The random key schemes that we have seen so far ensure that communication costs per node are constant irrespective of the number of nodes in the network, but these schemes require that the average number of neighbors of a node be above a threshold in order to ensure that secure links can be established by each node in the network Thus such schemes will not be suitable for networks where nodes are not densely distributed nor for networks where the node density is nonuniform This is due to the probabilistic nature of key establishment in such networks This could result in a disconnected network on account of the fact that some critical pairs of nodes could not successfully perform key establishment To address key establishment in such sparse networks, the authors in [44] present a key distribution scheme called Peer Intermediaries for Key Establishment (PIKE) PIKE establishes a key between any pairs of nodes in the network irrespective of the topology or the density of the network as long as the network is not partitioned Under this p scheme every node in the network shares a pairwise key uniquely with each of O( n) other nodes in the network, assuming that the network has n nodes Each key is unique and shared only between two nodes These keys are set up during the predeployment phase After the nodes are deployed, if two nodes A and B need to set up secure communication link between them, they have two options If A and B share a pairwise key set up during predeployment they can use that The second possibility is when A and B do not share any pairwise key In such a case, it would be necessary to nd some node C that shares a unique pairwise key with both A and B Then C is used as a trusted intermediary to establish shared keys between nodes To accomplish this, A encrypts the new key to be shared with B using the key that A shares with C and sends this message to C C decrypts this message and re-encrypts the result using the key that C shares with B and sends the resulting message to B As a result, B is able to get the new key shared with A securely provided that C has not been compromised by the adversary Note that this is also a result of the fact that the pairwise keys are shared between exactly two nodes Note that B can nally send a message to A encrypted using the new key to con rm receipt Thus, the basic idea in PIKE is to use nodes as trusted intermediaries to establish shared keys between nodes
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