This chapter provides a framework and two efficient

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This chapter provides a framework and two efficient instantiations to es- tablish pairwise keys between sensor nodes. The overhead of using such keys in security protocols (e.g., encryption or authentication) depends on the real applications. Thus, in this chapter, we only focus on the overhead involved in establishing these keys. In particular, we focus on the overhead of the two instantiations. As we discussed earlier, the storage overhead for the hash key-based instantiation is approximately n (since m = n ), while the storage overhead for the polynomial-based instantiation is 2 t . In both instantiations, any two sensor nodes in the same deployment group or the same cross group can establish a direct key between each other, and there is no communication overhead involved in the establishment of the direct keys between sensor nodes. When two sensor nodes are in different deployment groups and different cross groups, they need to establish an indirect key to protect the commu- nication between them. According to the protocol description, the path key establishment may involve one intermediate node, which is either in the same deployment group as the source node or in the same deployment group as the destination node, or two intermediate nodes, where one is in the same deployment group as the source node and the other is in the same deployment group as the destination node. Hence, in practice, the commu- nication overhead for path key establishment is limited in two deployment groups. In addition, every sensor node only needs to discover the list of the nearby sensor nodes in its local area for the path key establishment. This only incurs a small amount of communication overhead. 5.2. Establishing Direct Keys Consider a particular sensor node u in the deployment group G i at position ( x , y ). Let A denote its communication area in which any other sensor node can directly communicate with node u . In this chapter, we assume A is a circle centered at ( x , y ) with radius R , where R is the signal range of a sensor node. Thus, the average number of the sensor nodes in any deployment group G j , including G i , that finally reside in A can be estimated as n i,j ( x , y ) = n A f ( x x j , y y j )d x d y. (3) 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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84 D. Liu, P. Ning and W. Du For any deployment group G j other than G i , we know that there is only one sensor node u in G j that shares the same cross group G k with node u . Thus, the probability of this node u being deployed in A can be estimated as n i,j ( x ,y ) n . This indicates that among all those sensor nodes deployed in A , the average number of sensor nodes that belong to the deployment groups other than G i but share the same cross group G k with node u can be estimated as n i ( x , y ) = n j =1 ,j = i n i,j
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