### Abstract

A notion of “divertible” zero-knowledge interactive proof systems was introduced by Okamoto and Ohta, and they showed that for any commutative random self-reducible relation, there exists a divertible (perfect) zero-knowledge interactive proof system of possession of information. In addition, Burmester and Desmedt proved that for any language L ∈ NP, there exists a divertible zero-knowledge interactive proof system for the language L under the assumption that probabilistic encryption homomorphisms exist. In this paper, we classify the notion of divertible into three types, i.e., perfectly divertible, almost perfectly divertible, and computationally divertible, and investigate which complexity class of languages has a perfectly (almost perfectly) (computationally) divertible zero-knowledge interactive proof system. The main results in this paper are: (1) there exists a perfectly divertible perfect zero-knowledge interactive proof system for graph non-isomorphism (GNI) without any unproven assumption; and (2) for any language L having an interactive proof system, there exists a computationally divertible computational zero-knowledge interactive proof system for the language L under the assumption that probabilistic encryption homomorphisms exist.

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 | 382-396 |

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. 382-396). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 739 LNCS). Springer Verlag.

**Any language in IP has a divertible ZKIP.** / Itoh, Toshiya; Sakurai, Kouichi; Shizuya, Hiroki.

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. 382-396, 1st International Conference on the Theory and Application of Cryptology, ASIACRYPT 1991, Fujiyoshida, Japan, 11/11/91.

}

TY - GEN

T1 - Any language in IP has a divertible ZKIP

AU - Itoh, Toshiya

AU - Sakurai, Kouichi

AU - Shizuya, Hiroki

PY - 1993/1/1

Y1 - 1993/1/1

N2 - A notion of “divertible” zero-knowledge interactive proof systems was introduced by Okamoto and Ohta, and they showed that for any commutative random self-reducible relation, there exists a divertible (perfect) zero-knowledge interactive proof system of possession of information. In addition, Burmester and Desmedt proved that for any language L ∈ NP, there exists a divertible zero-knowledge interactive proof system for the language L under the assumption that probabilistic encryption homomorphisms exist. In this paper, we classify the notion of divertible into three types, i.e., perfectly divertible, almost perfectly divertible, and computationally divertible, and investigate which complexity class of languages has a perfectly (almost perfectly) (computationally) divertible zero-knowledge interactive proof system. The main results in this paper are: (1) there exists a perfectly divertible perfect zero-knowledge interactive proof system for graph non-isomorphism (GNI) without any unproven assumption; and (2) for any language L having an interactive proof system, there exists a computationally divertible computational zero-knowledge interactive proof system for the language L under the assumption that probabilistic encryption homomorphisms exist.

AB - A notion of “divertible” zero-knowledge interactive proof systems was introduced by Okamoto and Ohta, and they showed that for any commutative random self-reducible relation, there exists a divertible (perfect) zero-knowledge interactive proof system of possession of information. In addition, Burmester and Desmedt proved that for any language L ∈ NP, there exists a divertible zero-knowledge interactive proof system for the language L under the assumption that probabilistic encryption homomorphisms exist. In this paper, we classify the notion of divertible into three types, i.e., perfectly divertible, almost perfectly divertible, and computationally divertible, and investigate which complexity class of languages has a perfectly (almost perfectly) (computationally) divertible zero-knowledge interactive proof system. The main results in this paper are: (1) there exists a perfectly divertible perfect zero-knowledge interactive proof system for graph non-isomorphism (GNI) without any unproven assumption; and (2) for any language L having an interactive proof system, there exists a computationally divertible computational zero-knowledge interactive proof system for the language L under the assumption that probabilistic encryption homomorphisms exist.

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M3 - Conference contribution

AN - SCOPUS:0003056823

SN - 9783540573326

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

SP - 382

EP - 396

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 -