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：寻找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问题。近期研究表明，不经意传输和多方可计算协议可由单向函数构造，而在经典环境下，黑盒方式下这是不可能的。本文研究从单向函数甚至更弱假设出发构建量子公钥加密方案的问题。首先，我们重新审视IND-CPA安全性在此环境下的定义。随后，分别基于单向函数、具有删除证明的伪随机函数态和伪随机函数态，提出了三种量子公钥加密方案。