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Published byIliana Piggott Modified over 2 years ago

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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.: AAAAA A A A A

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Types of Bilinear Groups Prime Order: Composite Order:

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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

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

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

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

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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

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Building Orthogonality in Prime Order

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Progress So Far ?

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Exploiting Coprimality attacker simulator Chinese Remainder Theorem

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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 orthogonal Orthogonality across bases, not within!

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

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Expanding/Contracting with DPVS

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Demonstration: Boneh-Boyen IBE

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Sketch of Proof Decryption Failure! Dual System Encryption Subspace Assumption

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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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