A Note on the Round-Complexity of Concurrent Zero-Knowledge

Abstract

We present a lower bound on the number of rounds required by Concurrent Zero-Knowledge proofs for languages in NP. It is shown that in the context of Concurrent Zero-Knowledge, at least eight rounds of interaction are essential for black-box simulation of non-trivial proof systems (i.e., systems for languages that are not in BPP). This improves previously known lower bounds, and rules out several candidates for constant-round Concurrent Zero-Knowledge. In particular, we investigate the Richardson-Kilian protocol [20] (which is the only protocol known to be Concurrent Zero-Knowledge in the vanilla model), and show that for an apparently natural choice of its main parameter (which yields a 9-round protocol), the protocol is not likely to be Concurrent Zero-Knowledge.KeywordsProof SystemRecursive ConstructionInteractive ProofConcurrent ExecutionOracle AccessThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.