1 the source node u first tries the bridge involving

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(1) The source node u first tries the bridge involving itself to establish an indirect key with the destination node v . Assume this bridge is u, v . Node u first sends a request to v if it can establish a direct key with v . If node v can also establish a (direct or indirect) key with the destination node v , node v forwards this request to the destination node v to establish an indirect key. (2) If the first step fails, node u will try the bridge involving the destination node v . Assume the bridge is u , v . In this case, node u sends a request to node u if it can establish a (direct or indirect) key with u . If node Copyright © 2010. World Scientific Publishing Company. All rights reserved. May not be reproduced in any form without permission from the publisher, except fair uses permitted under U.S. or applicable copyright law. EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 2/16/2016 3:46 AM via CGC-GROUP OF COLLEGES (GHARUAN) AN: 340572 ; Beyah, Raheem, Corbett, Cherita, McNair, Janise.; Security in Ad Hoc and Sensor Networks Account: ns224671
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76 D. Liu, P. Ning and W. Du u can establish a direct key with node v , it forwards the request to the destination node v to establish an indirect key. Note that if nodes u and v are in the same cross group, this step can be skipped, since step 1 and step 2 compute the same bridge. (3) When both of the above steps fail, node u has to try other bridges. Basically, it randomly chooses a bridge u , v other than the above two, assuming u is in the same deployment group with u , and v is in the same deployment group with v . Node u then sends a request to u if it can establish a (direct or indirect) key with u . Once u receives this request, it forwards the request to v in the bridge if they share a direct key. If v can establish a (direct or indirect) key with the destination node v , it forwards the request to node v to establish an indirect key. We use the same example as in Figure 2 to illustrate the above algo- rithm. When node 1 wants to establish an indirect pairwise key with node 12, it first tries the bridge 1 , 10 . If this fails, it tries the bridge 3 , 12 . If both bridges fail, it needs to try the bridge 2 , 11 . If none of these bridges works, the path key establishment fails. In our later analysis, we will see that it is usually unlikely that none of those bridges works. When one of the bridges works, the two sensor nodes involved in this bridge will be used as the intermediate nodes by node 1 and node 12 to establish the indirect key. In the above approach, the path key establishment in a cross-group instance has never been used. The reason is that the sensor nodes in a cross group usually spread over the entire deployment field, which makes it expensive to perform path key establishment in a cross group. 4. Seeking Efficient Instantiations In the proposed framework, as long as a key pre-distribution technique can provide pairwise key establishment between sensor nodes for a group of sensor nodes, it can be used as the basic building block to construct a group-based scheme. This implies that our framework can be applied to any existing key pre-distribution technique.
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