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TR01-091 | 27th November 2001 00:00
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#### Concurrent Zero-Knowledge With Timing, Revisited

**Abstract:**
Following Dwork, Naor, and Sahai (30th STOC, 1998),

we consider concurrent execution of protocols in a

semi-synchronized network. Specifically, we assume that each party

holds a local clock such that a constant bound on the relative rates

of these clocks is a-priori known, and consider protocols that

employ time-driven operations

(i.e., time-out in-coming messages and delay out-going messages).

We show that the constant-round zero-knowledge proof for NP

of Goldreich and Kahan (Jour. of Crypto., 1996)

preserves its security when polynomially-many independent copies

are executed concurrently under the above timing model.

We stress that

our main result establishes zero-knowledge of interactive proofs,

whereas the results of Dwork et al. are

either for zero-knowledge arguments

or for a weak notion of zero-knowledge (called $\epsilon$-knowledge) proofs.

Our analysis identifies two extreme schedulings

of concurrent executions under the above timing model:

the first is the case of parallel execution of polynomially-many copies,

and the second is of concurrent execution of polynomially-many

copies such the number of copies that are simultaneously active

at any time is bounded by a constant (i.e., bounded simultaneity).

Dealing with each of these extreme cases is of independent interest,

and the general result (regarding concurrent executions under

the timing model) is obtained by combining the two treatments.