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Public-coin zero-knowledge and concurrent zero-knowledge (cZK) are two classes of zero knowledge protocols that guarantee some additional desirable properties. Still, to this date no protocol is known that is both public-coin and cZK for a language outside BPP. Furthermore, it is known that no such protocol can be black-box ZK [Pass et.al, Crypto 09]. We present a public-coin concurrent ZK protocol for any NP language. The protocol assumes that all verifiers have access to a globally specified function, drawn from a collision resistant hash function family. (This model, which we call the Global Hash Function, or GHF model, can be seen as a restricted case of the non-programmable reference string model.) We also show that the impossibility of black-box public-coin cZK extends also to the GHF model. Our protocol assumes CRH functions against quasi-polynomial adversaries and takes O(log1+εn) rounds for any ε0, where n is the security parameter. Our techniques combine those for (non-public-coin) black-box cZK with Barak's non-black-box technique for public-coin constant-round ZK. As a corollary we obtain the first simultaneously resettable zero-knowledge protocol with O(log1+εn) rounds, in the GHF model.

Public-Coin Concurrent Zero-Knowledge in the Global Hash Model