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containing a signed list of K key identi ers for the key ring to be revoked. To sign the list of key identi ers, the controller generates a signature key Ke and unicasts it to each node by encrypting it with a key Kci . After obtaining the signature key, each node veri es the signature of the signed list of key identi ers, locates those identi ers in its key ring, and removes the corresponding keys. Once the keys are removed from key rings, some links may disappear and the affected nodes need to recon gure those links by restarting the shared-key discovery and possibly path-key establishment. Re-keying is described as self-revocation of a key by a node if its life is expired. After removal of the expired key, affected nodes restart the shared-key discovery and path-key establishment process. Resiliency to Sensor Node Capture. There are two levels of threats posed by the node capture. The rst level of threat is manipulation of sensor s data when an adversary injects the fake data in sensor network. Detecting this nature of attack requires of ine data correlation analysis and data anomaly detection by collection and processing nodes. The second level of threat occurs when physically a sensor node is in control of the adversary. This level of active threat includes data manipulation of captured node and other nodes on the network. Countermeasures to node capture threats are tamper-detection technologies [14] to shield the sensors in such a way that vandalism of nodes causes the erasure of a sensor s key ring, eventually disabling the sensor s operation. 16.6.3 Extended Random Key Pre-distribution Scheme Chan et al. [15] extended the idea of Eschenauer and Gligor [1] and developed three key pre-distribution schemes; q-composite, multipath reinforcement, and randompairwise keys schemes to over come the weakness of basic random key predistribution scheme. In the q-composite scheme, q common keys (q > 1) are needed, instead of just one. In this scheme the key pool size S is reduced and multiple keys are used to establish communications instead of just one. To compute the key pool size, let p(i) be the probability that any two nodes have exactly i keys in common. Let Pconnect be the probability of any two nodes sharing suf cient keys from a secure connection. P connect = 1 (probability that the two nodes share insuf cient keys to form a connection), hence P connect = 1 (p(0) + p(1) + . . . + p(q 1)). For a given key ring size m, minimum key overlap q, and minimum connection probability p, the largest |S| is chosen such that P connect p. To initialize the key setup, a set of S of random keys out of the total key space is picked. For each node, m random keys are selected from S (where m is the number of keys each node can carry in its key ring) and store them into the node s key ring. In the key setup phase, each node discovers all common keys it possesses with each of its neighbors. q-composite key scheme strengthens the network resilience against node capture when the number of nodes captured is small. However, if the large number of nodes
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have been captured, the q-composite keys scheme tends to reveal a larger fraction of network to the adversary. In the multipath key reinforcement scheme, Chan et al. [15] present a method to strengthen the security of an established link key by establishing the link key through multiple paths. Assuming that key setup has been completed, there are now many secure links formed through the common keys in the various nodes key rings. Suppose node A has a secure link to node B after key setup. This link is secured using a single key k from the key pool S. k may be residing in the key ring memory of some other nodes elsewhere in the network. If any of those nodes are captured, the security of the link between nodes A and B is jeopardized. To address this, the communication key is updated to a random value after key setup. However, key update cannot be coordinated using the direct link between nodes A and B since if the adversary has been recording all key-setup traf c, it could decrypt the key update message after it obtained k and still obtain the new communication key. In this approach, key update is coordinated over multiple independent paths. Assume that enough routing information can be exchanged such that node A knows all disjoint paths to node B created during initial key setup that are h hops or less. The more paths between two nodes A and B, the more security multipath key reinforcement provides from the link between A and B. However, for any given path, the probability that the adversary can eavesdrop on the path increases with the length of the path since if any one link on the path is insecure, then the entire path is made insecure. Furthermore, it is increasingly expensive in terms of communication overhead to nd multiple disjoint paths that are very long. To address this issue, a 2-hop multipath key reinforcement scheme is presented where paths of only 2 links are considered. The effectiveness of 2-hop multipath key reinforcement is evaluated by simulating the random deployment of 10,000 sensor nodes on a square planar eld. Successfully implementing multipath key reinforcement on the key management scheme of Eschenauer and Gligor [1] enables it to outperform the q-composite scheme for q 2 even when the q-composite scheme is supplemented by key reinforcement. However, compounding both schemes compounds their weaknesses: The smaller key pool size of the q-composite keys scheme undermines the effectiveness of multipath key reinforcement by making it easier to build up a critically larger collection of keys. The third mechanism introduced in this scheme is a random pairwise scheme where node-to-node authentication is established. The random pairwise scheme introduces the following properties: r r r r r Resilience against node capture Node-to-node identity authentication Distributed node revocation Resistence to node replication and generation Comparable scalability
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In random key pool distribution schemes like q-composite and multipath, keys can be issued multiple times out of the key pool, and the node-to-node authentication
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