1. Tools for Simulating Features of Composite Order Bilinear Groups in the Prime Order Setting
Allison Lewko
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2. Types of Bilinear Groups
Prime Order:
Composite Order:

3. Pros and Cons Composite Order Groups: Prime Order Groups:
Smaller group order
Orthogonal Subgroups
Faster pairings
Coprime Orders
Simple assumptions
Large group order
Lack of extra structure
Slow pairings

4. Goal
Composite Order
Groups
Prime Order
Groups

5. Prior State of Affairs Ad Hoc Results General translation [F10] [OT10]
[BGN05]
[LOSTW10]
[KSW08]
[BSW06]
[W09]
Ad Hoc Results
General translation [F10]

6. Challenge
Prime Order
Groups
Composite Order
Groups
Proof
construction

7. What Features Do Proofs Need?
Orthogonal Subgroups:
Expand/Contract
With Computational
Assumptions
Hidden Parameters:
Public Parameters
V|PP - random variable
- has some entropy
Internal View V
Simulator
Attacker

8. Building Orthogonality in Prime Order

9. Progress So Far ?

10. Exploiting Coprimality
Chinese
Remainder
Theorem
attacker
simulator

11. Goal Replace coprimality, CRT Alternate mechanism
for hiding parameters

12. Tool: Dual Pairing Vector Spaces [OT08,09]

13. Orthogonal Subspaces with DPVS
Orthogonality across bases, not within!

14. Hidden Parameters with DPVS
Can’t detect change!
Not Everything!
What can be determined about hidden vectors?

15. Expanding/Contracting with DPVS

16. Demonstration: Boneh-Boyen IBE

17. Sketch of Proof Dual System Encryption Subspace Assumption Decryption
Failure!
Dual System Encryption

18. Further Applications Lewko-Waters Unbounded HIBE
Natural prime order construction
Security from DLIN
Simpler proof

19. Summary Dual pairing vector spaces 1. orthogonality
2. parameter hiding
Subspace assumption
1. simulated subgroup decision
2. implied by DLIN
General tools for translating dual system encryption proofs

20. Thanks for your attention.
Questions?