Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Short Transitive Signatures For Directed Trees

441 views

Published on

Slides

Published in: Business, Technology
  • Be the first to comment

  • Be the first to like this

Short Transitive Signatures For Directed Trees

  1. 1. San Francisco, Feb 27-Mar 2 2012Short Transitive Signatures for Directed TreesPhilippe Camacho and Alejandro Hevia University of Chile
  2. 2. How do we sign a graph? a b
  3. 3. Trivial solutions
  4. 4. Transitive signature schemes [MR02,BN05,SMJ05] Combiner
  5. 5. Landscape
  6. 6. Transitive Signatures for Directed Trees
  7. 7. Previous Work
  8. 8. Our ResultsExamplesTime tosignedge /verifypathsignatureTime to compute apathsignatureSize of pathsignature
  9. 9. Security [MR02]σBC E
  10. 10. BASIC CONSTRUCTION
  11. 11. Pre/Post Order Tree Traversal a b h d i j k c e f g Pre order: a b c d e f g h i j k Post order: c e f g d b i j k h a
  12. 12. Property of Pre/Post order Traversal• Proposition [Dietz82] a b h d c i j k e f g Pre order: a b c d e f g h i j k Post order: c e f g d b i j k h a
  13. 13. Idea a b h d c i j k e f g How do we avoidPosition 1 2 3 4 5 6 7 8 9 10 11 recomputing a lot ofPre a b c d e f g h h i i j j k k signatures when an element is inserted?Post c e f g d d b b i i j j k k h h a a
  14. 14. Order Data Structure
  15. 15. Trivial Order Data Structure A Toy ExampleElements -∞ d a e b c +∞ 0 250 1000 500 675 750 875Labels
  16. 16. a b dc Pre a b c d +∞-∞ 0 500 750 875 937 1000 Post c d b a +∞-∞ 0 125 187 250 500 1000
  17. 17. Trivial Order Data Structure-∞ d a b c +∞0 250 500 750 875 1000 New CRHF! It allows to: • compress the strings • efficiently compare them from their hashes
  18. 18. HASHING WITH COMMON PREFIXPROOFS
  19. 19. The Idea
  20. 20. Security
  21. 21. n-BDHI assumption [BB04]
  22. 22. The hash function
  23. 23. Generating & Verifying Proofs
  24. 24. Generating & Verifying Proofs
  25. 25. Security• Proposition: If the n-BDHI assumption holds then the previous construction is a secure HCPP family.• Proof (idea)
  26. 26. CRHF is incremental
  27. 27. Comparing strings
  28. 28. FULL CONSTRUCTION
  29. 29. Trivial Order Data Structure d a b c0 250 500 750 875 1000
  30. 30. New Order Data Structure d e a b c Use a binary tree to obtain a 1an «incremental» order data structure d 0 b 1 1 e c
  31. 31. a b dc ODPre ODPost a a 1 0 b b 1 0 c c 1 1 d d
  32. 32. Trade off
  33. 33. Conclusion and Open Problems• Efficient transitive signature scheme for directed trees• Possible to balance the time to compute and to verify the proof• Based on a general new primitive HCPP• New constructions / applications for HCPP• Can we improve the trade off?• Stateless transitive signatures for directed trees

×