### Abstract

The next bit test was introduced by Blum and Micali and proved by Yao to be a universal test for cryptographic pseudorandom generators. On the other hand, no universal test for the cryptographic one-wayness of functions (or permutations) is known, although the existence of cryptographic pseudorandom generators is equivalent to that of cryptographic one-way functions. In the quantum computation model, Kashefi, Nishimura and Vedral gave a sufficient condition of (cryptographic) quantum one-way permutations and conjectured that the condition would be necessary. In this paper, we affirmatively settle their conjecture and complete a necessary and sufficient condition for quantum one-way permutations. The necessary and sufficient condition can be regarded as a universal test for quantum one-way permutations, since the condition is described as a collection of stepwise tests similar to the next bit test for pseudorandom generators.

Original language | English |
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Pages (from-to) | 370-385 |

Number of pages | 16 |

Journal | Theoretical Computer Science |

Volume | 345 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 2005 Nov 22 |

### Keywords

- Computational cryptography
- One-way function
- One-way permutation
- Quantum computation
- Universal test

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Theoretical Computer Science*,

*345*(2-3), 370-385. https://doi.org/10.1016/j.tcs.2005.07.036