On Concurrent and Resettable Zero-Knowledge Proofs for NP
<|reference_start|>On Concurrent and Resettable Zero-Knowledge Proofs for NP: A proof is concurrent zero-knowledge if it remains zero-knowledge when many copies of the proof are run in an asynchronous environment, such as the Internet. It is known that zero-knowledge is not necessarily preserved in such an environment. Designing concurrent zero-knowledge proofs is a fundamental issue in the study of zero-knowledge since known zero-knowledge protocols cannot be run in a realistic modern computing environment. In this paper we present a concurrent zero-knowledge proof systems for all languages in NP. Currently, the proof system we present is the only known proof system that retains the zero-knowledge property when copies of the proof are allowed to run in an asynchronous environment. Our proof system has $\tilde{O}(\log^2 k)$ rounds (for a security parameter $k$), which is almost optimal, as it is shown by Canetti Kilian Petrank and Rosen that black-box concurrent zero-knowledge requires $\tilde{\Omega}(\log k)$ rounds.   Canetti, Goldreich, Goldwasser and Micali introduced the notion of {\em resettable} zero-knowledge, and modified an earlier version of our proof system to obtain the first resettable zero-knowledge proof system. This protocol requires $k^{\theta(1)}$ rounds. We note that their technique also applies to our current proof system, yielding a resettable zero-knowledge proof for NP with $\tilde{O}(\log^2 k)$ rounds.<|reference_end|>
@article{kilian2001on,
    title={On Concurrent and Resettable Zero-Knowledge Proofs for NP},
    author={Joe Kilian and Erez Petrank and Ransom Richardson},
    journal={arXiv preprint arXiv:cs/0107004},
    year={2001},
    archivePrefix={arXiv},
    eprint={cs/0107004},
    primaryClass={cs.CR}
}