Oded Goldreich, Rafail Ostrovsky, Erez Petrank

We study the computational complexity of languages which have

interactive proofs of logarithmic knowledge complexity. We show that

all such languages can be recognized in ${\cal BPP}^{\cal NP}$. Prior

to this work, for languages with greater-than-zero knowledge

complexity (and specifically, even for knowledge complexity 1) only

trivial computational complexity bounds ...
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Salil Vadhan, Amit Sahai

We present the first complete problem for SZK, the class of (promise)

problems possessing statistical zero-knowledge proofs (against an

honest verifier). The problem, called STATISTICAL DIFFERENCE, is to

decide whether two efficiently samplable distributions are either

statistically close or far apart. This gives a new characterization

of SZK that makes ...
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Shuichi Hirahara, Mikito Nanashima

The fundamental theorem of Goldreich, Micali, and Wigderson (J. ACM 1991) shows that the existence of a one-way function is sufficient for constructing computational zero knowledge ($\mathrm{CZK}$) proofs for all languages in $\mathrm{NP}$. We prove its converse, thereby establishing characterizations of one-way functions based on the worst-case complexities of ... more >>>