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Languages wit Efficient Zer i SZK are in SZK
MOHAMMAD MA DAVID XIAO
h
- -Knowledge PCP
HMOODY (CORNELL) (LIAFA)
Probabilistically Proofs (PCPs) y Checkable y
accept / reject
Languages wit h Efficient Zer o-Knowledge PCP are in SZK i SZK - - PowerPoint PPT Presentation
Languages wit h Efficient Zer o-Knowledge PCP are in SZK i SZK - - PowerPoint PPT Presentation
Languages wit h Efficient Zer o-Knowledge PCP are in SZK i SZK MOHAMMAD MA HMOODY (CORNELL) DAVID XIAO (LIAFA) Probabilistically y Checkable y Proofs (PCPs) accept / reject Z Zero-Knowledge PC K l d PC CPs CP statisti ically
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Z K l d PC Zero-Knowledge PC
actual statisti (default Def: View of any efficient verifier can be efficientl execution (default Def: View of any efficient verifier can be efficientl
- Harder to achieve zero‐knowledge PCPs (than pr
- Easier to achieve sound PCPs (than provers)
- Easier to achieve sound PCPs (than provers).
[Kilian‐Petrank‐Tardos’97] NEXP has (statistical) ze I h tl f l i l l th ( f
- Inherently of super‐polynomial length (even for
CP CPs
generated ically close in this talk) SIM y “simulated” (similar to ZK interactive proofs) generated efficiently in this talk) y simulated (similar to ZK interactive proofs) rovers) verifier can read any PCP answers. ero‐knowledge PCPs NP) NP)
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Efficient Zero-Kn Efficient Zero-Kn nowledge PCPs nowledge PCPs
accept / reject
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Main Q estion A th efficie Main Question: Are there efficient ( t ti ti l) ZK PCP f NP ? nt (statistical) ZK PCPs for NP ?
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Motivation: Basin Motivation Basin Proof Hardware
[Kat07, MS08, CGS08,
ng Crypto on Tamper ng Crypto on Tamper
GKR08, GISVW10, Kol10, GIMS10, ... ]
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Motivation: Reset Zero-Knowledge
give me answer to q FORGET q and FORGET q and answer to p
ttable Statistical
answer to q d answer p d answer p
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Limits of Efficie Limits of Efficie Zero-Knowledge PC
Main Question: Are there efficient [Ishai‐M‐Sahai’12] Any language w [Ishai M Sahai 12] Any language w non‐adaptive verifier is in co‐AM Corollary: No efficient ZK for NP us l h l i l i hi unless the polynomial‐time hierarc
ent (statistical) ent (statistical) CPs?
t ZK PCPs for NP ? with an efficient ZK PCP using a with an efficient ZK PCP using a sing a non‐adaptive verifier h ll [BHZ’87] chy collapses [BHZ’87]
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Our Result
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Id b hi d Ideas behind th f d the proof
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Approach of [IMS’ Approach of [IMS’12] 12]
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Naïve Approach Naïve Approach
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Our Approach Our Approach
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Our Approach Our Approach
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Our Approach Our Approach
Conditional Entropy Approxim py pp in SZK [Vadhan’04] mation:
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Putting Things To Putting Things To
- gether
- gether
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Summary
Theorem: No efficient statistical Z hi h ll i th hierarchy collapses ‐‐ removing th Open: Characterize languages wit Conjecture: All of SZK (sufficient Open: Number of messages (2 or Open: Number of messages (2 or efficient PCP (hardware token) to ZK PCP for NP unless polynomial‐tim h d ti it b i f [IMS’12 he non‐adaptivity barrier of [IMS’12 th efficient ZK PCPs. to make compiler of [GOVW] efficie r 3 or 4) needed in addition to an r 3 or 4) needed in addition to an
- get statistical zero‐knowledge for N
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