Outline

1. A Key Pre-Distribution Scheme Using Deployment Knowledge for Wireless Sensor NetworksZhen Yu & Yong GuanDepartment of Electrical and Computer EngineeringIowa State UniversitySep. 15, 2004

2. Outline • Introduction • Related work • Our scheme • Evaluation and simulation • Conclusions

3. Bootstrapping Problem (1) Need to encrypt communications between sensor nodes against eavesdropping and node capture. Bootstrapping problem: How to set up secret keys among nodes

4. Bootstrapping Problem (2) • Limitations of wireless sensor networks: • Limited power resource; • Limited computation capacity; • Limited memory size; • Limited transmission range r. • General methods cannot be used: • Public-key cryptography consumes more energy and needs longer time; • No trusted third party for online key management; • Storing N-1 pairwise keys is not suitable for large sensor networks; • Solution: key pre-distribution scheme.

5. Basic Scheme k Key Pool m keys k • Each node picks k secret keys from a large key pool of size m. • Two neighboring nodes can establish secure connection if sharing at least one common key.

6. Du’s Deployment Knowledge Scheme (1) • Group-based deployment model: • Drop nodes from a helicopter hanging above some deployment point; • Divide sensor field into equal-size square grids; • Divide sensor nodes into groups equally; • The center of each grid is a deployment point, the expected location of a group of nodes; • Each group is deployed into a corresponding grid; • The real location of nodes of each group i follows a normal distribution:

7. Du’s Deployment Knowledge Scheme (2) Global Key Pool Global Key Pool A B C 1 a D E 1-a Divide a global key pool into multiple key pools Key assignment for all the key pools Shared keys between neighboring key pools

8. Each node i stores the i-th row of A and the i-th column of G; • Node i and j exchange their columns of G in plaintext and derive Kij = Kji; • So G is public, while A is kept secret • A can be broken after rows compromised. Preliminary: Blom’s Scheme • Dis symmetric • Public matrix G • Secret matrix A • A = (DG)T = GTD • Kis symmetric • K = AG = GTDG

9. Our Scheme: Overview • Observation: Most neighbors come from the same group or neighboring groups • Hexagonal deployment • One public matrix G. • Multiple secret matrices As and Bs. • Each node picks rows from A and B. Assignment of A: Each group has a distinct A. Assignment of B: Any two neighboring groups share some common B(s). A:in-group communications. B:inter-group communications. Nodes from the same group or neighboring groups can always find common keys.

10. Our Scheme: Assignment of B (1) • Cluster: 7 neighboring groups • At most 2 basic groups / cluster • At most 2 rows / node • At most 13 affected groups

11. Our Scheme: Assignment of B (2) • At most 3 basic groups / cluster • At most 3 rows / node • At most 16 affected groups

12. Our Scheme: Assignment of B (3) • At most 1 basic groups / cluster • At most 3 rows / node • Max # of affected groups: large

13. Our Scheme: Assignment of B (4) • Cluster: 9 neighboring groups • At most 3 basic groups / cluster • At most 3 rows / node • At most 21 affected groups

14. Our Scheme: Performance Metrics • Connectivity: • The probability that the deployed network is connected • Resilience against node capture: • The fraction of links compromised over the total number of links given some number of nodes are compromised • Memory requirement: • The number of keys stored

15. Our Scheme: Connectivity Analysis (1) MN, the longest edge of a random Minimum Spanning Tree If set , we have where Pc is the probability that the network is connected when N approaches infinite.

16. Our Scheme: Connectivity Analysis (2) When nodes are not uniformly distributed, use the lowest node density over sensor field. Lowest node density area Normal distribution over 4x4 hexagonal grids

17. Our Scheme: Connectivity Analysis (3) • Constrain neighbors coming from neighboring groups • Normal distribution: 99.87% nodes reside within 3σ of deployment point; • Let any two non-neighboring groups be farther away than 6σ; • So we set ( ) for hexagonal (square) grids. • Deploy 104 nodes into 103x103m2 field with Pc = 0.9999: • Our scheme: r = 31.25 m; • The basic scheme and Du’s scheme: r = 40 m.

18. Our Scheme: Security Metrics • Global security: • The fraction of links compromised given some nodes are compromised over the entire sensor field. • Local security: • The fraction of links compromised given some nodes are compromised in some local area. • Simulation: • For local security: suppose nodes are uniformly distributed in each grid and the compromised nodes come from the same grid. • Deploy 104 nodes into 103x103m2 sensor field with Pc = 0.9999

19. Our Scheme: Local Security • Larger memory size brings a larger ; • Hexagonal deployment is better than square one due to less affected groups.

20. Our Scheme: Global Security • Better performance in security than other schemes; • A lower memory requirement to achieve Pc = 0.9999.

21. Conclusions • A novel key pre-distribution scheme; • Hexagonal deployment; • Smaller transmission range with the same connectivity; • Better performance in security; • Lower memory requirement.

22. References • L. Eschenauer, et al., ''A Key-Management Scheme for Distributed Sensor networks'', in ACM CCS, 2002. • W. Du, et al., ''A Key Management Scheme for Wireless Sensor Networks Using Deployment Knowledge'', in IEEE INFOCOM, 2004. • R. Blom, ''An Optimal Class of Symmetric Key Generation Systems'', in Advances in Cryptology: Proceedings of EUROCRYPT 84, LNCS, vol. 209, pp.335-338, 1985. • W. Du, et al., ''A Pairwise Key Pre-distribution Scheme for Wireless Sensor Networks'', in ACM CCS, 2003. • M. D. Penrose, ''The Longest Edge of the Random Minimum Spanning Tree'', in The Annals of Applied Probability, Vol. 7, No. 2, pp. 340-361, 1997.