Cryptomania v.s. Minicrypt in a Quantum World

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 even extends to QPKE with quantum public key if the public key can be uniquely determined by the secret key, and thus is tight to all existing QPKE constructions.

@article{li2025_2504.05710,
  title={ Cryptomania v.s. Minicrypt in a Quantum World },
  author={ Longcheng Li and Qian Li and Xingjian Li and Qipeng Liu },
  journal={arXiv preprint arXiv:2504.05710},
  year={ 2025 }
}