Batch Rekeying for Secure Group Communications

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Batch Rekeying for Secure Group Communications

• By X.S. Li, Y.R. Yang, M.G. Gouda, and S.S.Lam
• presented by Lori Flynn

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Motivation

• Secure group communications is important Internet
  design issue for profitable applications and
  privacy of communications.
• Messages made secure using keys, making rekeying
  efficient is important.

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Motivation

• When nodes leave the group, the privacy of future
  messages must be assured by rekeying
• When nodes join the group, the privacy of
  previous messages must be assured by rekeying

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Motivation

• Problems with individual rekeying
• inefficiency
• out-of-sync problem between keys and data
• This paper proposes solutions to these problems.

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Rekeying

• Straightforward rekeying requires 2 encryptions
  for a join and N-1 encryptions for a leave
• Join new group key sent to members via multicast
  (using the previous group key) and via unicast to
  new member (encrypted using its individual key)

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Rekeying

• Straightforward rekeying requires 2 encryptions
  for a join and N-1 encryptions for a leave
• Leave previous group key cannot be used (or it
  would compromise future communications) so the
  new group key must be encrypted with each
  individual key.

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Rekeying

• Straightforward rekeying requires 2 encryptions
  for a join and N-1 encryptions for a leave
• More scalable rekeying uses a key graph approach.

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Key Graph

• Nodes are each given multiple keys.
• For a single leave request, key tree reduces
  server processing cost to O(log N)

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Key Tree Costs

• Join 2 log_d(N)
• Leave d log_d(N) -1

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Key Star rekeying cost

• Join 2
• Leave N-1

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Key Star u4 leaves
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Batch Rekeying

• Wait an interval, then the key server processes
  all joins and leaves at once
• Leave positions cant be controlled, but joins
  can be placed optimally in the key tree.

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Key Stars batch rekeying server cost
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Key Tree Rekeying Cost
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Example (fig. 6) u4 and u9 leave, u10 joins.
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(case 1 continued, JL)
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N1024, d 2
N4096, d4
Leaves
Leaves
Joins
Joins
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Case 1 J L
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Case 2 J lt L
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Case 3 J gt L and L 0
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Case 4 J gt L and L gt 0
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Rekeying batch vs. individual with key star
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Key Tree batch rekeying costs
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N4096, d4
N1024, d2
L
L
J
J
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N4096, d 4
N1024, d2
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N4096, d4
N1024, d2
L
L
J
J
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N4096, d4
N1024, d2
L
Joins
Joins
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N4096
N1024
J
J
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N1024, JL
N4096, JL
L
L
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N4096, J0
N1024, J0
L
L
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N4096
N1024
D4 better than d2,32
D4 better than d2,8,16
J
J
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Contribution

• Concept of periodic batch rekeying which can
  improve efficiency and alleviate out-of-sync
  problem
• Marking algorithm to process batch of join/leave
  requests
• Analysis of key servers processing cost for
  rekeying which shows substantial savings.

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Contribution (contd)

• Show that when number of requests in a batch is
  not large, best tree degree is four. Otherwise,
  key star is best.

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Conclusion

• Two problems were identified with rekeying
• inefficiency
• out-of-sync problems
• Periodic batch rekeying improves the key servers
  performance substantially
• The marking algorithm is efficient

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Conclusion(contd)

• When number of requests is not large in a batch,
  four is the best tree degree. Otherwise, tree
  star is better.

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Thats all.

• Questions?