### Abstract

We show that every language in NP has a (black-box) concurrent zero-knowledge proof system using Õ(log n) rounds of interaction. The number of rounds in our protocol is optimal, in the sense that any language outside BPP requires at least Ω̃(log n) rounds of interaction in order to be proved in black-box concurrent zero-knowledge. The zero-knowledge property of our main protocol is proved under the assumption that there exists a collection of claw-free functions. Assuming only the existence of one-way functions, we show the existence of Õ(log n)-round concurrent zero-knowledge arguments for all languages in NP.

Original language | English (US) |
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Pages (from-to) | 366-375 |

Number of pages | 10 |

Journal | Annual Symposium on Foundations of Computer Science - Proceedings |

State | Published - Dec 1 2002 |

Event | The 34rd Annual IEEE Symposium on Foundations of Computer Science - Vancouver, BC, Canada Duration: Nov 16 2002 → Nov 19 2002 |

### ASJC Scopus subject areas

- Hardware and Architecture

## Cite this

Prabhakaran, M. M., Rosen, A., & Sahai, A. (2002). Concurrent zero knowledge with logarithmic round-complexity.

*Annual Symposium on Foundations of Computer Science - Proceedings*, 366-375.