Black-box concurrent zero-knowledge requires \tilde {Ω} (logn) rounds

Authors:
Ran Canetti;Joe Kilian;Erez Petrank;Alon Rosen
Affiliations:
IBM T.J. Watson Research Center. P.O. Box 704, Yorktown Heights, NY;Yianilos Labs., Yianilos Labs 707 State Rd., Rt. 206, Suite, 212, Princeton, NJ;Dept. of Computer Science, Technion Israel Institute of Technology, Haifa 32000, Israel;Dept. of Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel
Venue:
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Year:
2001

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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 \tilde&OHgr;(log n) rounds of interaction. This result substantially improves over previous lower bounds, and is the first bound to rule out the possibility of constant-round black-box concurrent zero-knowledge. Furthermore, the bound is polynomially related to the number of rounds in the best known concurrent zero-knowledge protocol for languages in ~$\NP$.