CSC 774 Advanced Network Security

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.
2
Membership Operations
Formation
Group partition
Member add
Member leave
Group merge
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

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 ( lt O(log 2 N)), and
  N is the number of users
• Maximum number of exponentiations per node 3d

5
Key Tree (General)
ggn1gn2n3 gn6gn4n5
gn1gn2n3
gn6gn4n5
gn4n5
n6
n1
gn2n3
n4
n5
n2
n3
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Key Tree (n3s view)
GROUP KEY
ggn1gn2n3 gn6gn4n5
gn1gn2n3
ggn6gn4n5
ggn4n5
gn6
gn1
gn2n3
gn4
gn5
gn2
n3
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
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Join (n3s view)
n3
gn4
8
Join (n3s view)
gn3gn1n2
ggn1n2gn3n4
n3
ggn1n2
gn3n4
gn1
gn2
9
Leave (n2s view)
ggn1n2gn3n4
gn1n2
ggn3n4
gn1
n2
10
Leave (n2s view)
ggn1n2gn3n4
gn1n2
ggn3n4
n2
11
Leave (n2s view)
gn2gn3n4
ggn3n4
n2
12
Partition (n5s view)
ggn1gn2n3 gn6gn4n5
ggn1gn2n3
gn6gn4n5
gn4n5
gn1
ggn2n3
gn4
n5
gn3
n5
13
Partition (n5s view)
gn4n5
gn1
gn2n3
gn4
n5
gn3
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Partition (n5s view)
ggn1n3gn4n5
gn4n5
ggn1n3
gn4n5
gn1
gn3
gn4
n5
n5
n5
Change share
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Partition Both Sides
gn1
gn4
n5
gn3
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Partition Both sides (N5 and N6)
ggn1n3gn4n5
gn2n6
gn2
ggn1n3
gn4n5
n6
n6
gn1
gn3
n5
n2
gn4
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Merge (N2s view)
ggn1n2gn5gn3n4
ggn5gn3n4
gn1n2
ggn3n4
gn5
n2
gn1
gn4
gn3
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Merge (to intermediate node)
gggn1n2gn6n7gn5gn3n4
ggn5gn3n4
ggn1n2gn6n7
ggn3n4
gn5
n1
gn1n2
gn4
gn3
n2
gn1
n2
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Tree Management do ones 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 lt 2 log2 N)

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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