## Abstract

SUMMARY A trapdoor one-way function is an extended version of a zero-way permutation. A zero-way permutation was first introduced by Niemi-Renvall in Asiacrypt'94 [7]. In this paper we define the class of functions called no-way functions. This is an extended version of a zero-way permutation. Intuitively, a function f is no-way if, without trapdoor, both computing / and computing f^{-1} are hard. Li-Chida-Shizuya [6] defined the notion of a no-way function, which is a provable-security version of a zero-way permutation. They also gave an example of a no-way function such that computing f and f^{-1} is proven to be as hard as breaking the Diffie-Hellman key exchange scheme. We redefine the notion of a trapdoor no-way function more preciously, classify no-way functions by the property of the trapdoor: common, separated and semi-separated trapdoor no-way, give a method for constructing trapdoor no-way functions from trapdoor one-way functions, and also give an example of trapdoor no-way functions.

Original language | English |
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Pages (from-to) | 151-156 |

Number of pages | 6 |

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

Volume | E84-A |

Issue number | 1 |

Publication status | Published - 2001 Jan |

## Keywords

- No-way function
- One-way function
- Trapdoor

## ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics