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**2000/013**

**Title:**

Concurrent Zero-Knowledge in Poly-logarithmic Rounds

**Authors:**
Joe Kilian, Erez Petrank

**Abstract:**

A proof is concurrent zero-knowledge if it remains zero-knowledge when run in an asynchronous environment, such as

the Internet. It is known that zero-knowledge is not necessarily preserved in such an environment; Kilian, Petrank and Rackoff have

shown that any {\bf 4} rounds zero-knowledge interactive proof (for a non-trivial language) is not concurrent zero-knowledge. On the

other hand, Richardson and Kilian have shown that there exists a concurrent zero-knowledge argument for all languages in NP, but it

requires a {\bf polynomial} number of rounds. In this paper, we present a concurrent zero-knowledge proof for all languages in NP

with a drastically improved complexity: our proof requires only a poly-logarithmic, specifically, \omega(\log^2 k) number of rounds.

Thus, we narrow the huge gap between the known upper and lower bounds on the number of rounds required for a zero-knowledge

proof that is robust for asynchronous composition.

**ePrint:**
https://eprint.iacr.org/2000/013

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