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：找到相比经典协议依赖更弱计算假设的量子密码协议构造是一个重要课题。最近研究表明，不经意传输和多方计算可由单向函数构造，而这在经典环境下以黑盒方式是不可能的。本文研究如何基于单向函数甚至更弱假设构建量子公钥加密方案。首先，我们重新审视IND-CPA安全性定义在此场景中的应用。随后，分别基于单向函数、带删除证明的类伪随机函数态以及类伪随机函数态，提出三种量子公钥加密方案。