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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 manual before you delete this box.: AAAAAAAAA

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**Types of Bilinear Groups**

Prime Order: Composite Order:

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**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

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Goal Composite Order Groups Prime Order Groups

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**Prior State of Affairs Ad Hoc Results General translation [F10] [OT10]**

[BGN05] [LOSTW10] [KSW08] [BSW06] [W09] Ad Hoc Results General translation [F10]

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Challenge Prime Order Groups Composite Order Groups Proof construction

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**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

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**Building Orthogonality in Prime Order**

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Progress So Far ?

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**Exploiting Coprimality**

Chinese Remainder Theorem attacker simulator

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**Goal Replace coprimality, CRT Alternate mechanism**

for hiding parameters

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

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**Orthogonal Subspaces with DPVS**

Orthogonality across bases, not within!

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**Hidden Parameters with DPVS**

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

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**Expanding/Contracting with DPVS**

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**Demonstration: Boneh-Boyen IBE**

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**Sketch of Proof Dual System Encryption Subspace Assumption Decryption**

Failure! Dual System Encryption

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**Further Applications Lewko-Waters Unbounded HIBE**

Natural prime order construction Security from DLIN Simpler proof

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**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

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**Thanks for your attention.**

Questions?

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