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 out the
possibility of constant-round concurrent zero-knowledge when proven via
black-box simulation. Furthermore, the bound is polynomially related to
the number of rounds in the best known concurrent zero-knowledge
protocol for languages in $\NP$.