Quantum Public Key Encryption for NISQ Devices

Abstract: Quantum public-key encryption (PKE), where public-keys and/or ciphertexts can be quantum states, is an important primitive in quantum cryptography. Unlike classical PKE (e.g., RSA or ECC), quantum PKE can leverage quantum-secure cryptographic assumptions or the principles of quantum mechanics for security. It has great potential in providing for secure cryptographic systems under potentially weaker assumptions than is possible classically. In addition, it is of both practical and theoretical interest, opening the door to novel cryptographic systems not possible with classical information alone. While multiple quantum PKE schemes have been proposed, they require a large number of qubits acting coherently, and are not practical on current noisy quantum devices. In this paper, we design a practical quantum PKE scheme, taking into account the constraints of current NISQ devices. Specifically, we design a PKE scheme with quantum-classical public keys and classical ciphertexts, that is noise-resilient and only requires a small number of qubits acting coherently. In addition, our design provides tradeoffs in terms of efficiency and the number of qubits that are required.