Quantum Search on Encrypted Data Based on Quantum Homomorphic Encryption
This work addresses secure data processing in quantum computing for clients with constrained resources, representing an incremental advance in quantum homomorphic encryption protocols.
The paper tackles the problem of enabling a client with limited quantum capabilities to securely outsource search operations on encrypted data to an untrusted quantum server, achieving this through a homomorphic search protocol that allows the client to encrypt data and decrypt results in linear time, while outsourcing key updates to a trusted center.
We propose a homomorphic search protocol based on quantum homomorphic encryption, in which a client Alice with limited quantum ability can give her encrypted data to a powerful but untrusted quantum server and let the server search for her without decryption. By outsourcing the interactive key-update process to a trusted key center, Alice only needs to prepare and encrypt her original data and to decrypt the ciphered search result in linear time. Besides, we also present a compact and perfectly secure quantum homomorphic evaluation protocol for Cliford circuits, where the decryption key can be calculated by Alice with polynomial overhead with respect to the key length.