1. A Key Management Scheme for Wireless Sensor Networks Using Deployment Knowledge Wenliang Du et al.

2. Outline Introduction Modeling deployment knowledge Key pre-distribution using deployment knowledge Performance evaluation Conclusion

3. Introduction Problem –Key pre-distribution in sensor network Previous work –Random key pre-distribution scheme –Improvement to random scheme q-composite scheme Polynomial-based scheme Common assumption –No deployment knowledge is available

4. New assumption In many practical scenarios –Certain deployment knowledge may be available What is deployment knowledge –How are sensors deployed? –Are they uniformly randomly distributed? Deployment method –Uniformly randomly distributed No deployment knowledge –Non-uniform distribution Deployed by groups Possible to know where a node is more likely to reside Useful –Most communications are between neighbors –Deployment knowledge helps us to know which nodes are more likely to be neighbors for each node

5. Modeling deployment knowledge Probability density function (pdf) General Deployment Model –Deployment area 2-dimensional rectangular area X x Y –pdf for the location of node i, i = 1,…,N f i (x,y), Existing key pre-distribution schemes assume –f i (x,y) = 1/XY –All sensor nodes are uniformly distributed over the deployment region

6. Modeling deployment knowledge (Cont’d) Group-based Deployment Model –N sensor nodes are divided into t x n groups Probability node is in a certain group is (1 / tn) –Group G i,j is deployed from the point (x i,y j ) –The resident point of node k in group G i,j follow the pdf Example of pdf f(x,y): 2-dimensional Guassian distribution Deployment Points

7. Modeling deployment knowledge (Cont’d) Deployment distribution used in paper –2-dimensional Gaussian distribution for each group –Overall distribution over the entire deployment region

8. Modeling deployment knowledge (Cont’d) Why use group-based model –Easy to determine which nodes are more likely to be close to each other Distance between two deployment points increases  Probability for two nodes from these two groups become neighbors decreases –Different groups can use different key pools Key pool size is smaller  better connectivity Two groups are far away  overlap between their key pools becomes smaller Notations –S i,j : key pool used by group G i,j, –|S c |: size of S i,j,

9. Key Pre-distribution Scheme Step 1: Key pre-distribution –Divide the key pool S into t x n key pools S i,j S i,j corresponding to deployment group G i,j | S i,j | = | S c |, for any i, j Nearby key pools share more key Far away key pools share less or no key –Two horizontally or vertically neighboring key pools share exactly a|Sc| key spaces, 0 <= a <= 0.25 –Two diagonally neighboring key pools share exactly b|Sc| key spaces, 0 <= b <= 0.25 –Two non-neighboring key pools share no key spaces

10. Key Pre-distribution Scheme Key sharing among key pools Horizontal VerticalDiagonal a ab b bb b A C F HI D G a aa a B

11. Key Pre-distribution Scheme Determining |S c | –Given key pool |S|, overlapping factor a, b –S i,j –Determine

12. Key Pre-distribution Scheme Select keys for each key pool S i,j –Global key pool S –Overlapping factor a and b Global Key Pool S 11-a 1-(a+b)1-2(a+b) 1-(2a+b) 1-(a+b)1-2(a+b) 1-(2a+b) 1-(a+b)1-2(a+b) 1-(2a+b) |S c | keys a|S c | keys 1-a|S c | keys a|S c | keys b|S c | keys 1-(a+b)|S c | keys t = 4, n = 4

13. Key Pre-distribution Scheme Effects of the Overlapping Factors –Best overlapping factors Combination of a and b that maximizes the local connectivity

14. Key Pre-distribution Scheme Step 2: Shared-key discovery –After deployment, every node will find out whether it shares keys with its neighbors Step 3: Path-key establishment –Two neighboring nodes cannot find any common key –Use secure channels that have already been established

15. Performance Evaluation Performance metrics: –Local connectivity p local The prob. of any two neighboring nodes sharing at least one key –Resilience against node capture The fraction of additional communications (communications among uncaptured nodes) that an adversary can compromise based on the information retrieve from x captured nodes –Communication overhead When two neighboring nodes cannot find a common key ph(l): prob. That the smallest number of hops needed to connect two neighboring nodes is l

16. Performance Evaluation Local connectivity

17. Performance Evaluation Resilience against node capture

18. Performance Evaluation Communication overhead

19. Conclusion Use pdf to model deployment knowledge Propose a key pre-distribution scheme using deployment knowledge –Sensors carry less key –Achieves same level of connectivity –Improves network’s resilience against node capture