Proceedings Article10.1145/237814.238016
On relationships between statistical zero-knowledge proofs
Tatsuaki Okamoto
- 01 Jul 1996
- pp 649-658
63
TL;DR: This paper solves several fundamental open problems about statistical zero-knowledge interactive proofs (SZKIPS) and proves the following:
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Abstract: This paper solves several fundamental open problems about statistical zero-knowledge interactive proofs (SZKIPs). The following two theorems are proven: ?If language L has a statistical zero-knowledge interactive proof against an honest verifier, then L has a statistical zero-knowledge “public-coin” interactive proof against an honest verifier. (Theorem 1) ?If L has a statistical zero-knowledge public-coin interactive proof against an honest verifier then “the complement of L” has a statistical zero-knowledge constant (one) round interactive proof against an honest verifier. (Theorem 2) The following corollaries are obtained directly from these two theorems and the recent result by Goldreich, Sahai, and Vadhan (1998, “Proc. of STOC,” pp. 409?418). ?Public-coin SZKIP=Private-coin SZKIP.Honest verifier SZKIP=Any verifier SZKIP. If L has a statistical zero-knowledge interactive proof against an “honest verifier,” then L has a statistical zero-knowledge public-coin interactive proof against “any verifier.” ?SZKIP=co-SZKIP. If L has a statistical zero-knowledge interactive proof, then the “complement” of L has a statistical zero-knowledge (public-coin) interactive proof. ?Bounded round SZKIP=Unbounded round SZKIP. If L has a statistical zero-knowledge interactive proof, then L has a statistical zero-knowledge “constant (one) round” interactive proof against an honest verifier. ?Black-box simulation SZKIP=Auxiliary-input SZKIP. If L has a statistical “auxiliary-input” zero-knowledge interactive proof, then L has a statistical “black-box simulation” zero-knowledge interactive proof.
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Citations
The knowledge complexity of interactive proof-systems
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- 04 Oct 2019
TL;DR: Permission to copy without fee all or part of this material is granted provided that the copies arc not made or distributed for direct commercial advantage.
From average case complexity to improper learning complexity
Amit Daniely,Nati Linial,Shai Shalev-Shwartz +2 more
- 31 May 2014
TL;DR: In this article, the authors introduce a new technique for proving hardness of improper learning, based on reductions from problems that are hard on average, which is a generalization of Feige's assumption about the complexity of refuting random constraint satisfaction problems.
On interactive proofs with a laconic prover
TL;DR: In this article, Goldreich et al. showed that for NP-complete languages, interactive proofs with bounded communication depend only exponentially on the number of bits sent by the prover to the verifier.
On Relationships between Statistical Zero-Knowledge Proofs
TL;DR: This paper solves several fundamental open problems about statistical zero-knowledge interactive proofs (SZKIPs) and proves that the complement of L has a statisticalzero-knowledge constant (one) round interactive proof against an honest verifier.
111
A complete promise problem for statistical zero-knowledge
Amit Sahai,Salil Vadhan +1 more
- 19 Oct 1997
TL;DR: This paper presents a complete promise problem for SZK, the class of languages possessing statistical zero-knowledge proofs (against an honest verifier), and proves the theorem that two efficiently samplable distributions are either statistically close or far apart.
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The knowledge complexity of interactive proof systems
TL;DR: A computational complexity theory of the “knowledge” contained in a proof is developed and examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity.
The knowledge complexity of interactive proof-systems
Shafi Goldwasser,Silvio Micali,Charles Rackoff +2 more
- 04 Oct 2019
TL;DR: Permission to copy without fee all or part of this material is granted provided that the copies arc not made or distributed for direct commercial advantage.
A hard-core predicate for all one-way functions
Oded Goldreich,Leonid A. Levin +1 more
- 01 Feb 1989
TL;DR: This paper proves a conjecture of [Levin 87, sec. 5.6.2] that the scalar product of Boolean vectors p, g, x is a hard-core of every one-way function ƒ, and extends to multiple (up to the logarithm of security) such bits and to any distribution on the x .
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- 01 Oct 1988
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