Therefore if a sensor node i wants to establish a key

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Therefore, if a sensor node i wants to establish a key with node j after deployment, it can easily determine whether they are in the same group (either deployment group or cross group). If they are not in the same group, they will follow the path key establishment protocol that is discussed at the beginning of this section to establish an indirect key; otherwise, both of node i and node j can easily figure out the direct key shared between them using the following algorithm. If Pos( i ) < Pos( j ) and (Pos( i )+Pos( j )) mod 2 = 1, node i can compute the shared key H ( K i || j ), while node j has already been pre-distributed with this key. 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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80 D. Liu, P. Ning and W. Du If Pos( i ) < Pos( j ) and (Pos( i ) + Pos( j )) mod 2 = 0, node i has the pre-distributed key H ( K j || i ), while node j can compute this key easily. If Pos( i ) > Pos( j ) and (Pos( i ) + Pos( j )) mod 2 = 1, node i has the pre-distributed key H ( K j || i ), while node j can compute this key easily. If Pos( i ) > Pos( j ) and (Pos( i )+Pos( j )) mod 2 = 0, node i can compute the shared key H ( K i || j ), while node j has already been pre-distributed with this key. From the above discussion, we can clearly see that a sensor node can immediately determine the direct key shared with another sensor node in the same group. There is no additional communication overhead. Since any two sensor nodes in the same group shared a unique key, there is no need to implement the path key establishment inside a group. In addition, we can also see that every shared key between two sensor nodes is only known by these two related sensor nodes. Hence, the com- promise of sensor nodes does not lead to the compromise of any direct key between two non-compromised sensor nodes. As a result, the above scheme guarantees the perfect security property in the presence of node compromise attacks. Now let us estimate the storage space for the keying materials at sensor nodes. Consider any sensor node i in a deployment group G . There are Pos( i ) 1 sensor nodes with smaller IDs and n Pos( i ) sensor nodes with larger IDs. When Pos( i ) is an odd number, we can easily see that node i will get pre-distributed Pos( i ) 1 2 keys for the sensor nodes with smaller IDs, and n P os ( i ) 2 keys for the sensor nodes with larger IDs. Therefore, the overall number of pre-distributed pairwise keys to node i for the deployment group G is Pos( i ) 1 2 + n Pos( i ) 2 n 2 . (2) Similarly, if Pos( i ) is even, the number of pre-distributed pairwise keys to node i is approximately n 2 . When node i belongs to a cross group G , we can also estimate the number of pre-distributed pairwise keys as m 2 in a similar way. Thus, the total number of pairwise keys that are pre- distributed to a sensor node for both of its deployment group and cross
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