1. CSC 774 Advanced Network Security
Topic 5.2 Tree-Based Group Diffie Hellman Protocol
Acknowledgment: Slides were originally provided by Dr. Yongdae Kim at University of Minnesota.
Dr. Peng Ning
CSC 774 Adv. Net. Security

2. Membership Operations
Formation
Group partition
Member add
Member leave
Group merge
Dr. Peng Ning
CSC 774 Adv. Net. Security

3. Membership Operations
Join: a prospective member wants to join
Leave: a member wants to (or is forced to) leave
Partition: a group is split into smaller groups
Network failure: network event causes disconnectivity
Explicit partition: application decides to split the group
Merge: two or more groups merge to form one group
Network fault heal: previously disconnected partitions reconnect
Explicit merge: application decides to merge multiple pre-existing groups into a single group
Dr. Peng Ning
CSC 774 Adv. Net. Security

4. Tree-Based Group Diffie Hellman
Simple: One function is enough to implement it
Fault-tolerant: Robust against cascade faults
Secure
Contributory
Provable security
Key independence
Efficient
d is the height of key tree ( < O(log 2 N)), and N is the number of users
Maximum number of exponentiations per node 3d
Dr. Peng Ning
CSC 774 Adv. Net. Security

5. Key Tree (General) ggn1gn2n3 gn6gn4n5 gn1gn2n3 gn6gn4n5 n1 gn2n3 gn4n5
Dr. Peng Ning
CSC 774 Adv. Net. Security

6. Key Tree (n3’s view) = ggn1gn2n3 gn6gn4n5 ggn6gn4n5 ggn6gn4n5 n3 gn2n3
GROUP KEY
Key-path: Set of nodes on the path from member node to root node
GROUP KEY
= ggn1gn2n3 gn6gn4n5
gn1
gn2
ggn6gn4n5
Co-path: Set of siblings of nodes on the key-path
gn1gn2n3
ggn6gn4n5
gn1
gn2n3
ggn4n5
gn6
gn2 n3
gn4
gn5
Any member who knows blinded keys on every nodes and
its session random can compute the group key.
Member knows all keys on the key-path and all blinded keys
Dr. Peng Ning
CSC 774 Adv. Net. Security

7. Join (n3’s view) n3 gn1 gn2 ggn1n2 gn3gn1n2 n3 Tree(n4) gn4
Dr. Peng Ning
CSC 774 Adv. Net. Security

8. Join (n3’s view) gn3gn1n2 ggn1n2gn3n4 n3 ggn1n2 n3 gn3n4 gn4 gn1 gn2
Dr. Peng Ning
CSC 774 Adv. Net. Security

9. Leave (n2’s view) ggn1n2gn3n4 gn1n2 ggn3n4 gn1 n2 gn3 gn4 gn1 n2
Dr. Peng Ning
CSC 774 Adv. Net. Security

10. Leave (n2’s view) ggn1n2gn3n4 gn1n2 ggn3n4 n2 gn3 gn4 n2 Dr. Peng Ning
CSC 774 Adv. Net. Security

11. Leave (n2’s view) gn2’gn3n4 n2’ ggn3n4 gn3 gn4 Dr. Peng Ning
CSC 774 Adv. Net. Security

12. Partition (n5’s view) ggn1gn2n3 gn6gn4n5 ggn1gn2n3 gn6gn4n5 gn1 gn6
ggn2n3
gn4n5
gn3
gn4 n5 n5
Dr. Peng Ning
CSC 774 Adv. Net. Security

13. Partition (n5’s view) gn1 gn2n3 gn4n5 gn3 gn4 n5 Dr. Peng Ning
CSC 774 Adv. Net. Security

14. Partition (n5’s view) ggn1n3gn4n5’ ggn1n3 gn4n5 gn4n5’ gn1 gn3 n5 gn3
Change share
Dr. Peng Ning
CSC 774 Adv. Net. Security

15. Partition: Both Sides gn1 gn6 gn2 gn3 gn4 n5 Dr. Peng Ning
CSC 774 Adv. Net. Security

16. Partition: Both sides (N5 and N6)
ggn1n3gn4n5’
gn2n6’
ggn1n3
gn4n5’
gn2 n6
n6’
gn1
gn3 n2
gn4
n5’
Dr. Peng Ning
CSC 774 Adv. Net. Security

17. Merge (N2’s view) ggn1n2gn5gn3n4 gn7 gn6 gn1 gn1n2 gn1n2 ggn5gn3n4 gn1
Dr. Peng Ning
CSC 774 Adv. Net. Security

18. Merge (to intermediate node)
gggn1n2gn6n7gn5gn3n4
ggn1n2gn6n7
ggn5gn3n4 n1
gn1n2
ggn6n7
gn7
gn6
ggn3n4
gn5
gn1 n2 n2
gn3
gn4
Dr. Peng Ning
CSC 774 Adv. Net. Security

19. Tree Management: do one’s best
Join or Merge Policy
Join to leaf or intermediate node, if height of the tree will not increase.
Join to root, if height of the tree increases.
Leave or Partition policy
No one can expect who will leave or be partitioned out.
No policy for leave or partition event
Successful
Still maintaining logarithmic (height < 2 log2 N)
Dr. Peng Ning
CSC 774 Adv. Net. Security

20. Discussion Efficiency
Average number of mod exp: 2 log2 n
Maximum number of round: log2 n
Robustness is easily provided due to self-stabilization property
Dr. Peng Ning
CSC 774 Adv. Net. Security