Languages witEfficient Zer

i SZKare in SZKMOHAMMAD MA

DAVID XIAO

h o-Knowledge PCP

HMOODY (CORNELL)

(LIAFA)

ProbabilisticallyyProofs (PCPs)

y Checkable y

accept / reject

Z K l d PCZero-Knowledge PC

actualstatisti(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 

CPCPs

generatedically closein 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)

Efficient Zero-KnEfficient Zero-Knnowledge PCPsnowledge PCPs

accept / reject

Main Q estion A th efficieMain Question: Are there efficient ( t ti ti l) ZK PCP f NP ?nt (statistical) ZK PCPs for NP ?

Motivation: BasinMotivation BasinProof Hardware[Kat07, MS08, CGS08, 

ng Crypto on Tamperng Crypto on TamperGKR08, GISVW10, Kol10, GIMS10, ... ]

Motivation: ResetZero-Knowledge

give me 

answer to q

FORGET q andFORGET q andanswer to p

ttable Statistical

answer to q

d answer pd answer p

Limits of EfficieLimits of EfficieZero-Knowledge PCMain Question: Are there efficient

[Ishai‐M‐Sahai’12] Any language w[Ishai M Sahai 12] Any language wnon‐adaptive verifier is in co‐AM

Corollary: No efficient ZK for NP usl h l i l i hiunless the polynomial‐time hierarc

ent (statistical)ent (statistical) CPs?t ZK PCPs for NP ?

with an efficient ZK PCP using awith an efficient ZK PCP using a 

sing a non‐adaptive verifierh ll [BHZ’87]chy collapses [BHZ’87]

Our Result

Id b hi dIdeas behindd th fd the proof

Approach of [IMS’Approach of [IMS’12]12]

Naïve ApproachNaïve Approach

Our ApproachOur Approach

Our ApproachOur Approach

Our ApproachOur Approach

Conditional Entropy Approximpy ppin SZK [Vadhan’04]

mation:

Putting Things ToPutting Things Toogetherogether

Summary

Theorem: No efficient statistical Zhi h ll i thhierarchy collapses ‐‐ removing th

Open: Characterize languages witConjecture: All of SZK (sufficient 

Open: Number of messages (2 orOpen: Number of messages (2 orefficient PCP (hardware token) to

ZK PCP for NP unless polynomial‐timh d ti it b i f [IMS’12he non‐adaptivity barrier of [IMS’12

th efficient ZK PCPs.to make compiler of [GOVW] efficie

r 3 or 4) needed in addition to anr 3 or 4) needed in addition to an o get statistical zero‐knowledge for N

Th kThank Y !You !