Black-Box Concurrent Zero-Knowledge Requires ~Omega(log n) Rounds

Ran Canetti, Joe Kilian, Erez Petrank and Alon Rosen

Abstract:

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 ~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.

Postscript, gzipped Postscript.

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