The grid based scheme arranges 200 polynomials on a

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pool to each sensor node. The grid-based scheme arranges 200 polynomials on a 100 × 100 grid, and each sensor node also gets two polynomial shares. For the closest pairwise keys scheme, we assume the same storage over- head as our hash key-based instantiation. Hence, every sensor node can store 100 keys, which means that it shares keys with 200 sensor nodes that are closest to itself in terms of the expected locations. In addition, we also assume the sensor nodes are deployed in the same way as our group-based model. The deployment field is equally partitioned into 10 × 10 cells with one group for each cell. The expected location of every deployment group is the center of the corresponding cell, which is known by every sensor 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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Key Pre-Distribution for Sensor Networks Using Group Deployment Knowledge 87 Figure 3 shows the results of comparison. We can see that our schemes have a significantly higher probability of establishing a direct key between two neighbor sensor nodes than the random subset assignment scheme and the pairwise keys scheme. This indicates that our schemes can support larger sensor networks under the same network settings. Therefore, we believe that our framework can substantially improve the performance of existing key pre-distribution techniques. Figure 3 also shows that the closest pairwise keys scheme can achieve better performance than the proposed schemes. The reason is that this scheme assume the knowledge of sensors’ expected locations, which is not required by our schemes. As discussed before, the expected locations could be difficult to obtain in real-world scenarios. We therefore strongly believe that the group-based model is a more realistic deployment model. On the other hand, the performance of our schemes are actually not significantly worse than the closest pairwise keys scheme. 5.3. Establishing Indirect Keys In the following, we estimate the probability of having an indirect key between two neighbor sensor nodes when they cannot establish a direct key. Note that the key pre-distribution instances in both instantiations guarantee that any two nodes in the same group can establish a direct key. Thus, the need for establishing indirect keys only happens when two sensor nodes are in different deployment group and different cross group. In this case, they have to find a valid bridge between these two deploy- ment groups to establish an indirect key. Since there are m cross groups and the nodes in the same group can always establish a direct key in our proposed instantiations, there are totally m valid bridges. Any one of these bridges can help the source node to setup an indirect key with the desti- nation node. On the other hand, the two sensor nodes involved in each of
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