It is an important question to find constructions of quantum cryptographic protocols which rely on weaker computational assumptions than classical protocols. Recently, it has been shown that oblivious transfer and multi-party computation can be constructed from one-way functions, whereas this is impossible in the classical setting in a black-box way. In this work, we study the question of building quantum public-key encryption schemes from one-way functions and even weaker assumptions. Firstly, we revisit the definition of IND-CPA security to this setting. Then, we propose three schemes for quantum public-key encryption from one-way functions, pseudorandom function-like states with proof of deletion and pseudorandom function-like states, respectively.

翻译：探索在比经典协议更弱的计算假设下构建量子密码协议是一个重要问题。近期研究表明，不经意传输和多方计算可从单向函数构造，而这在经典背景下以黑盒方式是无法实现的。本工作研究基于单向函数甚至更弱假设构建量子公钥加密方案的问题。首先，我们重新审视IND-CPA安全性在此背景下的定义。随后，我们分别提出三种基于单向函数、带删除证明的类伪随机函数态以及类伪随机函数态的量子公钥加密方案。