Quantum Search on Encrypted Data Based on Quantum Homomorphic Encryption
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Here we propose a quantum search protocols on ciphered superposition state based on quantum homomorphic encryption where a client Alice with limited quantum ability can deliver her encrypted quantum data to a powerful but untrusted quantum search server and let the server search for her without decryption. By outsourcing the key-updating and interaction work to a trusted key center, the client only needs to take linear steps to encrypt her original data and decrypt the returned result, and the intermediate process does not bother her at all. In our search protocol, the computational complexity of searching or key-updating on the search server or key center is the same as the Grover search, and the information-theoretic security holds as well. We also present a succinct quantum homomorphic encryption protocol for Clifford circuits with perfect security where the key-updating procedure is quantumly performed by the evaluating party. In contrast with the CL scheme proposed by Broadbent, this protocol does not need any help from classical homomorphic encryption to maintain compactness.
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