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There has been a recent interest in proposing quantum protocols whosesecurity relies on weaker computational assumptions than their classicalcounterparts. Importantly to our work, it has been recently shown thatpublic-key encryption (PKE) from one-way functions (OWF) is possible if weconsider quantum public keys. Notice that we do not expect classical PKE fromOWF given the impossibility results of Impagliazzo and Rudich (STOC'89).However, the distribution of quantum public keys is a challenging task.Therefore, the main question that motivates our work is if quantum PKE from OWFis possible if we have classical public keys. Such protocols are impossible ifciphertexts are also classical, given the impossibility result of Austrin etal. (CRYPTO'22) of quantum enhanced key-agreement (KA) with classicalcommunication. In this paper, we focus on black-box separation for PKE withclassical public key and quantum ciphertext from OWF under the polynomialcompatibility conjecture, first introduced in Austrin et al.. More precisely,we show the separation when the decryption algorithm of the PKE does not querythe OWF. We prove our result by extending the techniques of Austrin et al. andwe show an attack for KA in an extended classical communication model where thelast message in the protocol can be a quantum state.

Towards the Impossibility of Quantum Public Key Encryption with Classical Keys from One-Way Functions