Direct key while a key established in the path key

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direct key , while a key established in the path key establishment phase is called an indirect key . For simplicity, we assume there are n equal-sized deployment groups with m sensor nodes in each of these groups. The description of our frame- work is given below. For simplicity, we omit the detail of the message format. 3.1. Pre-Distribution For each deployment group G i , we need a key pre-distribution instance D i to take care of the pairwise key establishment in G i . For the sake of pre- sentation, these key pre-distribution instances are called the in-group (key pre-distribution) instances . The in-group instance D i can be the instance of any existing key pre-distribution technique. To handle the pairwise key establishment between sensor nodes in dif- ferent deployment groups, we construct m cross groups { G i } i =1 ,...,m . The requirements on these cross groups are: (1) each cross group includes ex- actly one sensor node from each deployment group, and (2) there are no common sensor nodes between any two different cross groups. In other words, for any i and j with i = j , we have G i G j = φ and | G i G j | = 1. We also generate a key pre-distribution instance D i for the pairwise key establishment in every G i . These instances are called the cross-group (key pre-distribution) instances . By doing this, each cross group provides a potential link for any two deployment groups. Similarly, the cross-group instance D i can be the instance of any key pre-distribution technique. In this chapter, we propose a simple way to construct the deployment groups and cross groups for pairwise key establishment. Basically, each 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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74 D. Liu, P. Ning and W. Du deployment group G i contains the sensor nodes with the IDs { ( i 1) m + j } j =1 ,...,m , while each cross group G i contains the sensor nodes with the IDs { i + ( j 1) m } j =1 ,...,n . By doing this, a sensor node can easily figure out which deployment group or cross group another sensor node belongs to based on the ID of the other node. Figure 2 shows an example of this group construction when n = 4 and m = 3. In this figure, G 1 includes node 1, 4, 7 and 10, G 2 includes node 2, 5, 8 and 11, and G 3 includes node 3, 6, 9 and 12. 1 2 3 4 5 6 7 8 9 10 11 12 G 1 G 2 G 3 G 4 G' 1 G' 2 G' 3 Fig. 2. Example of group construction. 3.2. Direct Key Establishment After the pre-distribution step, each sensor node has the keying materials for two key pre-distribution instances, an in-group instance and a cross- group instance. Hence, the direct key establishment between two neighbor sensor nodes is simple and direct. If they are in the same deployment group, for example, G i , they can follow the direct key establishment of the in-group instance D i . If they are not in the same deployment group
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