How (not) to Build Quantum PKE in Minicrypt

The seminal work by Impagliazzo and Rudich (STOC'89) demonstrated the impossibility of constructing classical public key encryption (PKE) from one-way functions (OWF) in a blackbox manner. Quantum information has the potential to bypass classical limitations, enabling the realization of seemingly impossible tasks such as quantum money, copy protection for software, and commitment without one-way functions. However, the question remains: can quantum PKE (QPKE) be constructed from quantumly secure OWF?

A recent line of work has shown that it is indeed possible to build QPKE from OWF, but with one caveat. These constructions necessitate public keys being quantum and unclonable, diminishing the practicality of such "public" encryption schemes -public keys cannot be authenticated and reused. In this work, we re-examine the possibility of perfect complete QPKE in the quantum random oracle model (QROM), where OWF exists.