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.: AAAAAAAAA

Types of Bilinear Groups Prime Order: Composite Order:

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

Goal Composite Order Groups Prime Order Groups

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

Challenge Prime Order Groups Composite Order Groups Proof construction

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

Building Orthogonality in Prime Order

Progress So Far ?

Exploiting Coprimality Chinese Remainder Theorem attacker simulator

Goal Replace coprimality, CRT Alternate mechanism for hiding parameters

Tool: Dual Pairing Vector Spaces [OT08,09]

Orthogonal Subspaces with DPVS Orthogonality across bases, not within!

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

Expanding/Contracting with DPVS

Demonstration: Boneh-Boyen IBE

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

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

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

Thanks for your attention. Questions?