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The (True) Complexity of Statistical Zero Knowledge (Extended Abstract)
 Proceedings of the 22nd Annual ACM Symposium on the Theory of Computing, ACM
, 1990
"... ) Mihir Bellare Silvio Micali y Rafail Ostrovsky z MIT Laboratory for Computer Science 545 Technology Square Cambridge, MA 02139 Abstract Statistical zeroknowledge is a very strong privacy constraint which is not dependent on computational limitations. In this paper we show that given a comp ..."
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Cited by 42 (17 self)
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) Mihir Bellare Silvio Micali y Rafail Ostrovsky z MIT Laboratory for Computer Science 545 Technology Square Cambridge, MA 02139 Abstract Statistical zeroknowledge is a very strong privacy constraint which is not dependent on computational limitations. In this paper we show that given a complexity assumption a much weaker condition suffices to attain statistical zeroknowledge. As a result we are able to simplify statistical zeroknowledge and to better characterize, on many counts, the class of languages that possess statistical zeroknowledge proofs. 1 Introduction An interactive proof involves two parties, a prover and a verifier, who talk back and forth. The prover, who is computationally unbounded, tries to convince the probabilistic polynomial time verifier that a given theorem is true. A zeroknowledge proof is an interactive proof with an additional privacy constraint: the verifier does not learn why the theorem is true [11]. That is, whatever the polynomialtime verif...
OneWay Functions are Essential for NonTrivial ZeroKnowledge(Extended Abstract)
 IN PROC. 2ND ISRAEL SYMP. ON THEORY OF COMPUTING AND SYSTEMS (ISTCS93), IEEE COMPUTER
, 1993
"... It was known that if oneway functions exist, then there are zeroknowledge proofs for every language in PSPACE. We prove that unless very weak oneway functions exist, ZeroKnowledge proofs can be given only for languages in BPP. For averagecase definitions of BPP we prove an analogous result und ..."
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Cited by 38 (10 self)
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It was known that if oneway functions exist, then there are zeroknowledge proofs for every language in PSPACE. We prove that unless very weak oneway functions exist, ZeroKnowledge proofs can be given only for languages in BPP. For averagecase definitions of BPP we prove an analogous result under the assumption that uniform oneway functions do not exist. Thus, very loosely speaking, zeroknowledge is either useless (exists only for "easy" languages), or universal (exists for every provable language).
OneWay Functions, Hard on Average Problems, and Statistical ZeroKnowledge Proofs (Extended Abstract)
 IN PROCEEDINGS OF THE 6TH ANNUAL STRUCTURE IN COMPLEXITY THEORY CONFERENCE
, 1991
"... In this paper, we study connections among oneway functions, hard on the average problems, and statistical zeroknowledge proofs. In particular, we show how these three notions are related and how the third notion can be better characterized, assuming the first one. ..."
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Cited by 28 (8 self)
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In this paper, we study connections among oneway functions, hard on the average problems, and statistical zeroknowledge proofs. In particular, we show how these three notions are related and how the third notion can be better characterized, assuming the first one.
Minimum Resource ZeroKnowledge Proofs
 In 30th Annual Symposium on Foundations of Computer Science
, 1989
"... ) Joe Kilian Silvio Micali y Rafail Ostrovsky z Abstract We consider several resources relating to zeroknowledge protocols: The number of envelopes used in the protocol, the number of oblivious transfers protocols executed during the protocol, and the total amount of communication required by ..."
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Cited by 27 (3 self)
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) Joe Kilian Silvio Micali y Rafail Ostrovsky z Abstract We consider several resources relating to zeroknowledge protocols: The number of envelopes used in the protocol, the number of oblivious transfers protocols executed during the protocol, and the total amount of communication required by the protocol. We show that after a preprocessing stage consisting of O(k) executions of Oblivious Transfer, any polynomial number of NPtheorems of any polysize can be proved noninteractively and in zeroknowledge, based on the existence of any oneway function, so that the probability of accepting a false theorem is less then 1 2 k . 1 Minimizing Envelopes 1.1 Envelopes as a resource. [GMR] puts forward the somewhat paradoxical notion of a zeroknowledge proof, and exemplifies it for a few special classes of assertions. The introduction of ideal commitment mechanisms, known as envelopes, allows us to achieve greater generality. Proofs of any NP statements can be accomplished in perfe...