### 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 |

Publication status | Published - Jan 1 1993 |

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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

**On the complexity of constant round ZKIP of possession of knowledge.** / Itoh, Toshiya; Sakurai, Kouichi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Advances in Cryptology ─ ASIACRYPT 1991 - International Conference on the Theory and Application of Cryptology, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 739 LNCS, Springer Verlag, pp. 331-345, 1st International Conference on the Theory and Application of Cryptology, ASIACRYPT 1991, Fujiyoshida, Japan, 11/11/91.

}

TY - GEN

T1 - On the complexity of constant round ZKIP of possession of knowledge

AU - Itoh, Toshiya

AU - Sakurai, Kouichi

PY - 1993/1/1

Y1 - 1993/1/1

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:84879820140

SN - 9783540573326

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 331

EP - 345

BT - Advances in Cryptology ─ ASIACRYPT 1991 - International Conference on the Theory and Application of Cryptology, Proceedings

A2 - Imai, Hideki

A2 - Matsumoto, Tsutomu

A2 - Rivest, Ronald L.

PB - Springer Verlag

ER -