In this paper we study the round complexity of concurrent zero-knowledge arguments and show that, for any function β(n) = ω(1), there exists an unbounded concurrent zero-knowledge argument system with β(n) rounds. Our result assumes that the same prover is engaged in several concurrent sessions and that the prover has a counter whose value is shared across concurrent executions of the argument. Previous constructions for concurrent zero knowledge required a (almost) logarithmic number of rounds [Prabhakaran et al. - FOCS 2002] in the plain model or seemingly stronger set-up assumptions. Moreover, we construct twoβ(n)-round unbounded concurrent zero-knowledge arguments that are mutually concurrent simulation sound for any β(n) = ω(1). Here we assume that each party has access to a counter and that the two protocols are used by the same two parties to play several concurrent sessions of the two protocols.
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