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This paper shows how to efficiently transform any 3-round public-coin honest verifier zero knowledge argument system for any language in NP into a 4 round (round-optimal) concurrent zero knowledge argument for the same language in the bare public-key model. The transformation has the following properties: 1) incurs only O(1) (small constant, about 20) additional modular exponentiations. Compared to the concurrent zero knowledge protocol proposed by Di Crescenzo and Visconti in ICALP 2005, in which their transformation requires an overhead of Θ(n), the protocol is significantly more efficient under the same intractability assumptions; 2) yields a perfect zero knowledge argument under DL assumption. Note that the Di Crescenzo, et al.’s argument system enjoys only computational zero knowledge property. The transformation relies on a specific 3-round honest verifier zero knowledge proof of knowledge for committed discrete log. Such protocols that require only O(1) modular exponentiations based on different kinds of commitment scheme are developed and they may be of independent interest.

Efficient Concurrent Zero Knowledge Arguments for NP in the Bare Public-Key Model