We prove that it is impossible to construct perfect-complete quantum public-key encryption (QPKE) with classical keys from quantumly secure one-way functions (OWFs) in a black-box manner, resolving a long-standing open question in quantum cryptography. Specifically, in the quantum random oracle model (QROM), no perfect-complete QPKE scheme with classical keys, and classical/quantum ciphertext can be secure. This improves the previous works which require either unproven conjectures or imposed restrictions on key generation algorithms. This impossibility extends to QPKE with quantum public key in natural settings, which is tight to all known QPKE constructions with quantum public key.

翻译：我们证明，利用量子安全的单向函数（OWFs）以黑盒方式构造具有经典密钥的完美完全量子公钥加密（QPKE）是不可能的，从而解决了量子密码学中一个长期悬而未决的问题。具体而言，在量子随机预言机模型（QROM）中，任何具有经典密钥以及经典/量子密文的完美完全QPKE方案都无法保证安全性。这一结果改进了先前需依赖未经证明的猜想或对密钥生成算法施加限制的研究工作。该不可能性结论在自然设定下可推广至具有量子公钥的QPKE，这已紧贴所有已知量子公钥QPKE构造的边界。