Black-Box Concurrent Zero-Knowledge Requires (Almost) Logarithmically Many Rounds

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 ~ (log n) rounds of interaction. This result achieves a substantial improvement over previous lower bounds, and is the rst 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).