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A Key Management Scheme for Wireless Sensor Networks Using Deployment Knowledge

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  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 • fi(x,y), • Existing key pre-distribution schemes assume • fi(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 Gi,jis deployed from the point (xi,yj) • The resident point of node k in group Gi,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 • Si,j: key pool used by group Gi,j, • |Sc|: size of Si,j ,

  9. Key Pre-distribution Scheme • Step 1: Key pre-distribution • Divide the key pool S into t x n key pools Si,j • Si,j corresponding to deployment group Gi,j • | Si,j | = | Sc|, 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 a A B C a b b D F a a a b b Vertical Diagonal G H I a b

  11. Key Pre-distribution Scheme • Determining |Sc| • Given key pool |S|, overlapping factor a, b • Si,j • Determine

  12. Key Pre-distribution Scheme • Select keys for each key pool Si,j • Global key pool S • Overlapping factor a and b Global Key Pool S |Sc| keys 1-(a+b)|Sc| keys 1-a|Sc| keys a|Sc| keys b|Sc| keys a|Sc| 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 plocal • 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