### Abstract

In this paper, we show that if a relation R has a three move blackbox simulation zero-knowledge interactive proof system of possession of knowledge, then there exists a probabilistic polynomial time algorithm that on input x ∈ {0,1}*, outputs y such that (x, y) ∈ R with overwhelming probability if x ∈ dom R, and outputs “⊥” with probability 1 if x ∉ dom R. In the present paper, we also show that without any unproven assumption, there exists a four move blackbox simulation perfect zero-knowledge interactive proof system of possession of the prime factorization, which is optimal in the light of the round complexity.

Original language | English |
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Title of host publication | Advances in Cryptology ─ ASIACRYPT 1991 - International Conference on the Theory and Application of Cryptology, Proceedings |

Editors | Hideki Imai, Tsutomu Matsumoto, Ronald L. Rivest |

Publisher | Springer Verlag |

Pages | 331-345 |

Number of pages | 15 |

ISBN (Print) | 9783540573326 |

DOIs | |

Publication status | Published - 1993 |

Externally published | Yes |

Event | 1st International Conference on the Theory and Application of Cryptology, ASIACRYPT 1991 - Fujiyoshida, Japan Duration: Nov 11 1991 → Nov 14 1991 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 739 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 1st International Conference on the Theory and Application of Cryptology, ASIACRYPT 1991 |
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Country | Japan |

City | Fujiyoshida |

Period | 11/11/91 → 11/14/91 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'On the complexity of constant round ZKIP of possession of knowledge'. Together they form a unique fingerprint.

## Cite this

Itoh, T., & Sakurai, K. (1993). On the complexity of constant round ZKIP of possession of knowledge. In H. Imai, T. Matsumoto, & R. L. Rivest (Eds.),

*Advances in Cryptology ─ ASIACRYPT 1991 - International Conference on the Theory and Application of Cryptology, Proceedings*(pp. 331-345). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 739 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-57332-1_28