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ON THE COMPLEXITY OF CONSTANT ROUND ZKIP OF POSSESSION OF KNOWLEDGE

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1993年第1期E76A卷 31-39页

作者： ITOH, T SAKURAI, K Tokyo Inst of Technology Yosohama-shi Japan

In this paper, we investigate the round complexity of zero-knowledge interactive proof systems of possession of knowledge, and mainly show that if a relation R has a three move blackbox simulation zero-knowledge interactive proof system of possession of knowledge, then there exists a probabilistic polynomial time algorithm that on input x is-an-element-of {0, 1}*, outputs y such that (x, y) is-an-element-of R with overwhelming probability if x is-an-element-of dom R, and outputs ''perpendicular-to'' with probability 1 if x is-not-an-element-of dom R. The result above can not be generalized to zero-knowledge interactive proof systems of possession of knowledge with more than four moves, because it is known that there exists a ''four'' move blackbox simulation perfect zero-knowledge interactive proof system of possession of knowledge for a nontrivial relation R.

关键词： ZERO-KNOWLEDGE INTERACTIVE PROOF SYSTEM POSSESSION OF KNOWLEDGE probabilistic polynomial time algorithm

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A Meeting Point of Probability, Graphs, and algorithms: The Lovasz Local Lemma and Related Results-A Survey

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algorithmS 2021年第12期14卷 355页

作者： Farago, Andras Univ Texas Dallas Dept Comp Sci 800 W Campbell Rd Richardson TX 75080 USA

A classic and fundamental result, known as the Lovasz Local Lemma, is a gem in the probabilistic method of combinatorics. At a high level, its core message can be described by the claim that weakly dependent events behave similarly to independent ones. A fascinating feature of this result is that even though it is a purely probabilistic statement, it provides a valuable and versatile tool for proving completely deterministic theorems. The Lovasz Local Lemma has found many applications;despite being originally published in 1973, it still attracts active novel research. In this survey paper, we review various forms of the Lemma, as well as some related results and applications.

关键词： Lovasz Local Lemma probabilistic method in combinatorics probabilistic polynomial time algorithm

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