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 ... more >>>

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 ... more >>>

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 >>>