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Tools for Simulating Features of Composite Order Bilinear Groups in the Prime Order Setting Allison Lewko TexPoint fonts used in EMF. Read the TexPoint.

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Presentation on theme: "Tools for Simulating Features of Composite Order Bilinear Groups in the Prime Order Setting Allison Lewko TexPoint fonts used in EMF. Read the TexPoint."— Presentation transcript:

1 Tools for Simulating Features of Composite Order Bilinear Groups in the Prime Order Setting Allison Lewko TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA A A A A

2 Types of Bilinear Groups Prime Order: Composite Order:

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

4 Composite Order Groups Composite Order Groups Prime Order Groups Prime Order Groups Goal

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

6 Challenge Proof construction Composite Order Groups Composite Order Groups Prime Order Groups Prime Order Groups

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

8 Building Orthogonality in Prime Order

9 Progress So Far ?

10 Exploiting Coprimality attacker simulator Chinese Remainder Theorem

11 Goal Replace coprimality, CRT Alternate mechanism for hiding parameters

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

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

14 Hidden Parameters with DPVS What can be determined about hidden vectors? Not Everything! Cant detect change!

15 Expanding/Contracting with DPVS

16 Demonstration: Boneh-Boyen IBE

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

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?


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