### Abstract

This paper presents a 4-move perfect ZKIP of knowledge with no cryptographic assumption for the random self reducible problems [TW87] whose domain is NP∩BPP. The certified discrete log problem is such an example. (Finding a witness is more difficult than the language membership problem.) A largely simplified 4-move ZKIP for the Hamilton Circuit problem is also shown. In our ZKIP, a trapdoor coin flipping protocol is introduced to generate a challenge bit. P and V cooperatively generate a random bit in a coin flipping protocol. In a trapdoor coin flipping protocol, V who knows the trapdoor can create the view which he can later reveal in two possible ways: both as head and as tail.

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 | 321-330 |

Number of pages | 10 |

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. 321-330). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 739 LNCS). Springer Verlag.

**4 move perfect ZKIP of knowledge with no assumption.** / Saito, Takeshi; Kurosawa, Kaoru; 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. 321-330, 1st International Conference on the Theory and Application of Cryptology, ASIACRYPT 1991, Fujiyoshida, Japan, 11/11/91.

}

TY - GEN

T1 - 4 move perfect ZKIP of knowledge with no assumption

AU - Saito, Takeshi

AU - Kurosawa, Kaoru

AU - Sakurai, Kouichi

PY - 1993/1/1

Y1 - 1993/1/1

N2 - This paper presents a 4-move perfect ZKIP of knowledge with no cryptographic assumption for the random self reducible problems [TW87] whose domain is NP∩BPP. The certified discrete log problem is such an example. (Finding a witness is more difficult than the language membership problem.) A largely simplified 4-move ZKIP for the Hamilton Circuit problem is also shown. In our ZKIP, a trapdoor coin flipping protocol is introduced to generate a challenge bit. P and V cooperatively generate a random bit in a coin flipping protocol. In a trapdoor coin flipping protocol, V who knows the trapdoor can create the view which he can later reveal in two possible ways: both as head and as tail.

AB - This paper presents a 4-move perfect ZKIP of knowledge with no cryptographic assumption for the random self reducible problems [TW87] whose domain is NP∩BPP. The certified discrete log problem is such an example. (Finding a witness is more difficult than the language membership problem.) A largely simplified 4-move ZKIP for the Hamilton Circuit problem is also shown. In our ZKIP, a trapdoor coin flipping protocol is introduced to generate a challenge bit. P and V cooperatively generate a random bit in a coin flipping protocol. In a trapdoor coin flipping protocol, V who knows the trapdoor can create the view which he can later reveal in two possible ways: both as head and as tail.

UR - http://www.scopus.com/inward/record.url?scp=84957804429&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957804429&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84957804429

SN - 9783540573326

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

SP - 321

EP - 330

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 -