Low Communication 2-Prover Zero-Knowledge Proofs for NP
Cynthia Dwork,Uriel Feige,Joe Kilian,Moni Naor,Muli Safra +4 more
- pp 215-227
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TLDR
For any language in NP a protocol is constructed with the property that any nonmember of the language be rejected with constant probability, and this protocol is exhibited for 3-SAT.Abstract:
We exhibit a two-prover perfect zero-knowledge proof system for 3-SAT. In this protocol, the verifier asks a single message to each prover, whose size grows logarithmically in the size of the 3-SAT formula. Each prover's answer consists of only a constant number of bits. The verifier will always accept correct proofs. Given an unsatisfiable formula S the verifier will reject with probability at least ?((|S| - max-sat(S))/|S|, where max-sat(S) denotes the maximum number of clauses of S that may be simultaneously satisfied, and |S| denotes the total number of clauses of S. Using a recent result by Arora et al [2], we can construct for any language in NP a protocol with the property that any nonmember of the language be rejected with constant probability.read more
Citations
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Journal ArticleDOI
A Parallel Repetition Theorem
TL;DR: It is shown that a parallel repetition of any two-prover one-round proof system (MIP(2,1) decreases the probability of error at an exponential rate, and no constructive bound was previously known.
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A parallel repetition theorem
TL;DR: It is shown that a parallel repetition of any two-prover one-round proof system (MIP(2; 1) decreases the probability of error at an exponential rate, and no constructive bound was previously known.
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Zero Knowledge and the Chromatic Number
Uriel Feige,Joe Kilian +1 more
TL;DR: This work presents a new technique, inspired by zero-knowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph, and matches (up to low order terms) the known gap for approximation the size of the largest independent set.
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Scalable, transparent, and post-quantum secure computational integrity.
TL;DR: The first realization of a transparent ZK system (ZK-STARK) in which verification scales exponentially faster than database size is reported, and this exponential speedup in verification is observed concretely for meaningful and sequential computations, described next.
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On the (In) security of the Fiat-Shamir Paradigm
TL;DR: Barak and Shamir as mentioned in this paper showed that there exist secure 3-round public-coin identiflcation schemes for which the Fiat-Shamir transformation yields insecure digital signature schemes for any hash function used by the transformation.
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