Black-box concurrent zero-knowledge requires (almost) logarithmically many rounds

We show that any concurrent zero-knowledge protocol for a nontrivial language (i.e., for a language outside BPP), whose security is proven via black-box simulation, must use at least Ω̃(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 (which is established via black-box simulation).