1. Informal Security Seminar: Key Pre-distribution Scheme for Wireless Sensor Networks Joengmin Hwang Dept. Computer Science Univ. of Minnesota, Twin Cities

2. 2 Overview  An optimal class of symmetric key generation systems – Blom sheme  A pairwise key pre-distribution scheme for wireless sensor networks – Wenliang Du  A key pre-distribution scheme using deployment knowledge for wireless sensor networks

3. 3 Blom Schme  Pair-wise Key Approach Need to store N-1 keys for each node when network size N Security is perfect. Need a lot of memory  Blom ’ s Scheme Need to store ((k+2) key size) secrete information ( k+1 << N - 1 ) Any pair of nodes can directly find a secret key Tolerate compromise up to k nodes

4. 4 Blom Scheme  Basic Block Public matrix G Private matrix D (symmetric). D G k+1 N

5. 5 Blom Scheme X = A = (D G) T G K i j i j K ji K ij N k+1 N N G: Public, D: Private and Symmetric K = A G = (D G) T G = G T D T G = G T D G = (A G) T = K T K: Symmetric ( K ij = K ji )

6. 6 Blom Scheme X = A = (D G) T G K i j i j K ji K ij N k+1 N N Node i carries: Node j carries: K ij K ji

7. 7 Key Pre-Distribution  Goal: Loading Keys into sensor nodes prior to deployment, s.t. any two nodes can find a secret key between them after deployment  Basic model: Eschenauer & Gligor Scheme  Optimization: Blom’s schme Pairwise Key Using Deployment Knowledge

8. 8 A Pairwise Key Pre-distribution Scheme for Wireless Sensor Networks  Based on Blom’s Scheme: One key space (D, G)  To increase network’s resilience against node capture without using more memory  Using multiple key space (D 1,…, D , G)

9. 9 Multiple Space Scheme (D 1, G) (D 2, G) (D 3, G) Key-Space Pool: (D 1, G) (D 2, G),…,(D , G) (D 1, G) (D 4, G) (D 5, G) (D 4, G) (D 6, G) (D 7, G) Store j-th row of (D i G) T  spaces (ex.  =3)

10. 10 Multiple Space Scheme (D 1, G) (D 2, G) (D 3, G) Key-Space Pool: (D 1, G) (D 2, G),…,(D , G) (D 1, G) (D 4, G) (D 5, G) (D 4, G) (D 6, G) (D 7, G) Store j-th row of A i = (D i G) T K random

11. 11 Resilience (p = 0.33, m=200) Blom

12. 12 A Key Pre-Distribution Scheme Using Deployment Knowledge  Group based deployment model  Based on Blom’s scheme  Using deployment knowledge, reduce memory requirement  Rearrange transmission range

13. 13 A Key Pre-Distribution Scheme Using Deployment Knowledge F1 F1 F2 F1 F3 A1 A2 A3 Common Matrix G Secret Matrix Ai used to connect two nodes in the same group Secret Matrix Fj used to connect two nodes in the different groups

14. 14 A Key Pre-Distribution Scheme Using Deployment Knowledge F1 F1 F2 F1 F3 A1 A2 A3 Common Matrix G Secret Matrix Ai used to connect two nodes in the same group Secret Matrix Fj used to connect two nodes in the different groups

15. 15 A Key Pre-Distribution Scheme Using Deployment Knowledge F1 F1 F2 F1 F3 A1 A2 A3 Common Matrix G Secret Matrix Ai used to connect two nodes in the same group Secret Matrix Fj used to connect two nodes in the different groups

16. 16 A Key Pre-Distribution Scheme Using Deployment Knowledge  Assignment of F

17. 17 A Key Pre-Distribution Scheme Using Deployment Knowledge  Assignment of F

18. 18 A Key Pre-Distribution Scheme Using Deployment Knowledge

19. 19 A Key Pre-Distribution Scheme Using Deployment Knowledge