We show that any concurrent zero-knowledge protocol for a non-trivial
language (i.e., for a language outside $\BPP$), whose security is proven
via black-box simulation, must use at least $\tilde\Omega(\log n)$
rounds of interaction. This result achieves a substantial improvement
over previous lower bounds, and is the first bound to rule ... more >>>

We consider noninteractive zero-knowledge proofs in the shared random
string model proposed by Blum, Feldman and Micali \cite{bfm}. Until
recently there was a sizable polynomial gap between the most
efficient noninteractive proofs for {\sf NP} based on general
complexity assumptions \cite{fls} versus those based on specific
algebraic assumptions \cite{Da}. ... more >>>