Dynamic quantum fully homomorphic encryption scheme based on universal quantum circuit

Quantum fully homomorphic encryption (QFHE) allows arbitrary computations which is performed by each server on encrypted quantum states without decrypting them. However, the existing QFHE schemes are not capable to handle the volatility problem with the servers: once a dynamic server wants to leave or join the protocol, it must be updated. Consequently, a dynamic quantum fully homomorphic encryption (DQFHE) scheme based on universal quantum circuit (UQC) is proposed in this paper. Firstly, our scheme could extend the two-part QFHE scheme to m-part. Secondly, the dynamic property means the completed protocol could be retained when involved servers changed which means we allow new servers to join our scheme and the absence of elder servers. Thirdly, UQC enables arbitrary quantum transformations on the encrypted quantum states and could be proved to be perfectly secure, and the key-updating algorithms are also based on the UQC so that the keys could not be revealed. Finally, due to the property of QFHE, compared with the quantum secret sharing, we could finish the sharing procedure efficiently because we cancel the security check procedure.