Comparing entropies in statistical zero knowledge with applications to the structure of SZK

Goldreich, Oded; Vadhan, Salil

doi:10.1109/ccc.1999.766262

Cited by 53 publications

(63 citation statements)

References 26 publications

(62 reference statements)

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“…On the other hand, it is contained in the class AM ∩ co-AM [5,6] and hence is unlikely to contain NP-hard problems. More recently, it was discovered that SZK is closed under complement [7] and has natural complete problems [8,9]. Moreover, a number of useful transformations of statistical zero-knowledge proof systems have been given, for example showing that every proof system which is statistical zero knowledge for the honest verifier can be transformed into one which is statistical zero knowledge even for cheating verifiers [7,10].…”

Section: Statistical Zero Knowledgementioning

confidence: 99%

“…Since these problems are in NP, we can hope to construct statistical zero-knowledge proofs with efficient provers for them. However, the SZK proofs obtained by applying the general result of [7] (or even later simplifications [8,9,27]) do not guarantee efficient provers, and in addition would be extremely cumbersome and impractical.…”

Section: Lattice Problemsmentioning

confidence: 99%

“…All previous proof systems for variants of Statistical Difference e.g. [8,9,43], used the input circuits as "black boxes." That is, the use of the circuits by the verifier and prover consisted solely of evaluating the circuits on various inputs, and never referred to the internal structure of the circuits.…”

Section: Efficient Provers For All Of Szk?mentioning

confidence: 99%

See 2 more Smart Citations

Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More

Micciancio

Vadhan

2003

Lecture Notes in Computer Science

115

119

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Abstract. We construct several new statistical zero-knowledge proofs with efficient provers, i.e. ones where the prover strategy runs in probabilistic polynomial time given an NP witness for the input string. Our first proof systems are for approximate versions of the Shortest Vector Problem (SVP) and Closest Vector Problem (CVP), where the witness is simply a short vector in the lattice or a lattice vector close to the target, respectively. Our proof systems are in fact proofs of knowledge, and as a result, we immediately obtain efficient lattice-based identification schemes which can be implemented with arbitrary families of lattices in which the approximate SVP or CVP are hard. We then turn to the general question of whether all problems in SZK ∩ NP admit statistical zero-knowledge proofs with efficient provers. Towards this end, we give a statistical zero-knowledge proof system with an efficient prover for a natural restriction of Statistical Difference, a complete problem for SZK. We also suggest a plausible approach to resolving the general question in the positive.

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Section: Statistical Zero Knowledgementioning

confidence: 99%

Section: Lattice Problemsmentioning

confidence: 99%

See 1 more Smart Citation

Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More

Micciancio

Vadhan

2003

Lecture Notes in Computer Science

115

119

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“…Entropy Difference (ED) is a promise problem that is complete for SZK [GV99]. Entropy Difference is a promise problem defined as …”

Section: Entropy Differencementioning

confidence: 99%

On Basing Private Information Retrieval on NP-Hardness

Liu¹,

Vaikuntanathan²

2015

Lecture Notes in Computer Science

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The possibility of basing the security of cryptographic objects on the (minimal) assumption that NP Z BPP is at the very heart of complexity-theoretic cryptography. Most known results along these lines are negative, showing that assuming widely believed complexity-theoretic conjectures, there are no reductions from an NP-hard problem to the task of breaking certain cryptographic schemes. We make progress along this line of inquiry by showing that the security of single-server single-round private information retrieval schemes cannot be based on NP-hardness, unless the polynomial hierarchy collapses. Our main technical contribution is in showing how to break the security of a PIR protocol given an SZK oracle. Our result is tight in terms of both the correctness and the privacy parameter of the PIR scheme.

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“…Okamoto's transformation provided a crucial starting point for a number of subsequent works on statistical zero knowledge (cf., [SV97,GSV98,Vad99]). Like the Goldwasser-Sipser transformation, neither Okamoto's transformation nor its later simplifications [GV99,Vad99] preserve the complexity of the prover.…”

Section: Theorem 1 If One-way Functions Exist Then There Is No Blackmentioning

confidence: 99%

On transformation of interactive proofs that preserve the prover's complexity

Vadhan

2000

Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing

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The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. AbstractGoldwasser and Sipser [GS89] proved that every interactive proof system can be transformed into a public-coin one (a.k.a., an Arthur-Merlin game). Their transformation has the drawback that the computational complexity of the prover's strategy is not preserved. We show that this is inherent, by proving that the same must be true of any transformation which only uses the original prover and verifier strategies as "black boxes." Our negative result holds even if the original proof system is restricted to be honest-verifier perfect zero knowledge and the transformation can also use the simulator as a black box.We also examine a similar deficiency in a transformation of Fürer et al. [FGM · 89] from interactive proofs to ones with perfect completeness. We argue that the increase in prover complexity incurred by their transformation is necessary, given that their construction is a black-box transformation which works regardless of the verifier's computational complexity.

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Comparing entropies in statistical zero knowledge with applications to the structure of SZK

Cited by 53 publications

References 26 publications

Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More

Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More

On Basing Private Information Retrieval on NP-Hardness

On transformation of interactive proofs that preserve the prover's complexity

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