In this paper, three impossible results for one-way permutations in the quantum world are obtained. The first one is the impossibility of fully black-box reduction from one-way permutations to one-way functions in a quantum setting. The two-oracle method is the main technique adopted in our proof that was originally proposed by Hsiao and Reyzin, and extended later to a quantum setting by Hosoyamada and Yamakawa. Informally this technique involves a pair of oracles, and in our proof, one oracle is chosen as a random function, and the other one is devised for breaking the security of quantum one-way permutation. We show, according to the first oracle, that there is an oracle-aided circuit that is a quantum-secure one-way function. However, we also show, according to the second oracle, that there is no one-way permutation relative to those oracles. It hence claims the impossibility in the quantum setting to construct one-way permutations from one-way functions (even if both input and output are classical).

The rest two impossibilities are essential enhancements of the first impossibility: We successfully obtain that it is impossible, in the quantum world, to obtain one-way permutations in a black-box manner from injective adaptive one-way functions, and (respectively) even from injective adaptive trapdoor functions.

In order to reach the latter two results, we manage to get over the obstacle of finding the inverse of random injective functions even given the partial invert oracle in the quantum setting. As a result, we get a quantum lower bound of inverting random injective functions in random case. That should be of independent interest in this paper, which might, to authors' knowledge, be the first quantum lower bound of inverting random injective functions given the partial invert oracle.

在本文中，获得了量子世界中单向排列的三个不可能的结果。第一个是不可能在量子环境中将黑匣子从单向置换完全转换为单向函数。二预言法是我们的​​证明中采用的主要技术，该技术最初是由Hsiao和Reyzin提出的，后来又扩展到了Hosoyamada和Yamakawa的量子设定。非正式地，该技术涉及一对预言，在我们的证明中，选择了一个预言作为随机函数，而设计了另一个预言以打破量子单向置换的安全性。根据第一个预言，我们表明存在一个预言辅助电路，该电路是量子安全的单向函数。但是，根据第二个预言，我们也表明相对于那些预言没有单向排列。

剩下的两种可能性是对第一种可能性的本质增强：我们成功地获得了在量子世界中不可能从内射自适应单向函数以黑盒方式获得单向置换的功能，并且（甚至）来自内射自适应活板门功能。

为了获得后两个结果，即使在量子环境中给出了部分逆预言，我们也设法克服了寻找随机注入函数逆的障碍。结果，我们得到了在随机情况下求逆随机注入函数的量子下界。在作者中，这应该是独立关注的问题，据作者所知，在给出部分反向预言的前提下，这可能是对随机内射函数进行求逆的第一个量子下限。