### Abstract

In this paper, we show that without any unproven assumption, there exists a 'four' move blackbox simulation perfect zero-knowledge interactive proof system of computational ability for any random self-reducible relation R whose domain is in B P P, and that without any unproven assumption, there exists a 'four' move blackbox simulation perfect zero-knowledge interactive proof system of knowledge on the prime factorization. These results are optimal in the light of the round complexity, because it is shown that if a relation R has a three move blackbox simulation (perfect) zero-knowledge interactive proof system of computational ability (or of knowledge), then there exists a probabilistic polynomial time algorithm that on input x ε {0, 1}, outputs y such that (x,y) ε R with overwhelming probability if x ε dom R, and outputs '⊥' with probability 1 if x ε dom R.

Original language | English |
---|---|

Pages (from-to) | 1225-1233 |

Number of pages | 9 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E76-A |

Issue number | 7 |

Publication status | Published - Jul 1993 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Hardware and Architecture
- Information Systems
- Electrical and Electronic Engineering

### Cite this

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E76-A*(7), 1225-1233.

**Constant round perfect ZKIP of computational ability.** / Itoh, Toshiya; Sakurai, Kouichi.

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E76-A, no. 7, pp. 1225-1233.

}

TY - JOUR

T1 - Constant round perfect ZKIP of computational ability

AU - Itoh, Toshiya

AU - Sakurai, Kouichi

PY - 1993/7

Y1 - 1993/7

N2 - In this paper, we show that without any unproven assumption, there exists a 'four' move blackbox simulation perfect zero-knowledge interactive proof system of computational ability for any random self-reducible relation R whose domain is in B P P, and that without any unproven assumption, there exists a 'four' move blackbox simulation perfect zero-knowledge interactive proof system of knowledge on the prime factorization. These results are optimal in the light of the round complexity, because it is shown that if a relation R has a three move blackbox simulation (perfect) zero-knowledge interactive proof system of computational ability (or of knowledge), then there exists a probabilistic polynomial time algorithm that on input x ε {0, 1}, outputs y such that (x,y) ε R with overwhelming probability if x ε dom R, and outputs '⊥' with probability 1 if x ε dom R.

AB - In this paper, we show that without any unproven assumption, there exists a 'four' move blackbox simulation perfect zero-knowledge interactive proof system of computational ability for any random self-reducible relation R whose domain is in B P P, and that without any unproven assumption, there exists a 'four' move blackbox simulation perfect zero-knowledge interactive proof system of knowledge on the prime factorization. These results are optimal in the light of the round complexity, because it is shown that if a relation R has a three move blackbox simulation (perfect) zero-knowledge interactive proof system of computational ability (or of knowledge), then there exists a probabilistic polynomial time algorithm that on input x ε {0, 1}, outputs y such that (x,y) ε R with overwhelming probability if x ε dom R, and outputs '⊥' with probability 1 if x ε dom R.

UR - http://www.scopus.com/inward/record.url?scp=0027631850&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027631850&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0027631850

VL - E76-A

SP - 1225

EP - 1233

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 7

ER -