A complete problem for statistical zero knowledge
Journal of the ACM (JACM)
On Interactive Proofs with a Laconic Prover
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
On interactive proofs with a laconic prover
Computational Complexity
Proceedings of the forty-first annual ACM symposium on Theory of computing
How to achieve perfect simulation and a complete problem for non-interactive perfect zero-knowledge
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Interactive and noninteractive zero knowledge are equivalent in the help model
TCC'08 Proceedings of the 5th conference on Theory of cryptography
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The authors show that if a language has an interactive proof of logarithmic statistical knowledge-complexity, then it belongs to the class A M n co- A M. Thus, if the polynomial time hierarchy does not collapse, then N P-complete languages do not have logarithmic knowledge complexity. Prior to this work, there was no indication that would contradict N P languages being proven with even one bit of knowledge. Next, they consider the relation between the error probability and the knowledge complexity of an interactive proof. They show that if the error probability (n) is less than 2 -3k(n) (where k(n) is the knowledge complexity) then the language proven has to be in the third level of the polynomial time hierarchy. In order to prove their main result, they develop an A M protocol for checking that a samplable distribution has a given entropy. They believe that this protocol is of independent interest.