Universal Test for Quantum One-Way Permutations
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, though 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 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.
Cite
@article{arxiv.quant-ph/0401013,
title = {Universal Test for Quantum One-Way Permutations},
author = {Akinori Kawachi and Hirotada Kobayashi and Takeshi Koshiba and Rudy Raymond H. Putra},
journal= {arXiv preprint arXiv:quant-ph/0401013},
year = {2012}
}
Comments
12 pages, 3 figures. The previous version included some error. This is a corrected version. Fortunately, the proof is simplified and results are improved