Quantum homomorphic encryption allows computations to be performed directly on encrypted data, ensuring the security of private information. A novel multi-party probabilistic quantum homomorphic encryption scheme based on the Brown state is proposed in this study, which permits multiple clients to simultaneously delegate arbitrary quantum computations to two servers. Firstly, the trusted key center is introduced to collaborate with clients using the B92 protocol for key distribution and updating, as well as to perform operations that eliminate T-gate evaluation errors. Secondly, the proposed scheme employs pre-shared non-maximally entangled states as auxiliary resources to non-interactively address errors occurring during the homomorphic evaluation of T-gate. Lastly, the scheme leverages the properties of Brown state to extend the single-client single-server model to the multi-client multi-server model, making it more suitable for quantum distributed networks and enhancing its practicality. Moreover, this study theoretically proves the correctness, fully homomorphic nature, and information-theoretically security of the scheme. Simulations conducted on the Origin Quantum Cloud platform further validate the scheme’s effectiveness. As the proposed scheme can realize homomorphic computation of any quantum circuit, it is particularly well-suited for delegated computation in quantum cloud networks.
Quantum homomorphic encryption allows computations to be performed directly on encrypted data, ensuring the security of private information. A novel multi-party probabilistic quantum homomorphic encryption scheme based on the Brown state is proposed in this study, which permits multiple clients to simultaneously delegate arbitrary quantum computations to two servers. Firstly, the trusted key center is introduced to collaborate with clients using the B92 protocol for key distribution and updating, as well as to perform operations that eliminate T-gate evaluation errors. Secondly, the proposed scheme employs pre-shared non-maximally entangled states as auxiliary resources to non-interactively address errors occurring during the homomorphic evaluation of T-gate. Lastly, the scheme leverages the properties of Brown state to extend the single-client single-server model to the multi-client multi-server model, making it more suitable for quantum distributed networks and enhancing its practicality. Moreover, this study theoretically proves the correctness, fully homomorphic nature, and information-theoretically security of the scheme. Simulations conducted on the Origin Quantum Cloud platform further validate the scheme’s effectiveness. As the proposed scheme can realize homomorphic computation of any quantum circuit, it is particularly well-suited for delegated computation in quantum cloud networks.
The significant advantage of the quantum homomorphic encryption scheme is to ensure the perfect security of quantum private data. In this paper, a novel secure multiparty quantum homomorphic encryption scheme is proposed, which can complete arbitrary quantum computation on the private data of multiple clients without decryption by an almost dishonest server. Firstly, each client obtains a secure encryption key through the measurement device independent quantum key distribution protocol and encrypts the private data by using the encryption operator and key. Secondly, with the help of the almost dishonest server, the non-maximally entangled states are pre-shared between the client and the server to correct errors in the homomorphic evaluation of T gates, so as to realize universal quantum circuit evaluation on encrypted data. Thirdly, from the perspective of the application scenario of secure multi-party computation, this work is based on the probabilistic quantum homomorphic encryption scheme, allowing multiple parties to delegate the server to perform the secure homomorphic evaluation. The operation and the permission to access the data performed by the client and the server are clearly pointed out. Finally, a concrete security analysis shows that the proposed multiparty quantum homomorphic encryption scheme can securely resist outside and inside attacks.
Abstract Quantum homomorphic encryption is the corresponding technology of classical homomorphic encryption in the quantum field. Due to its ability to ensure the correctness of computation and the security of data, it is particularly suitable for delegated computation in quantum cloud networks. However, previous schemes were unable to simultaneously handle the volatility problem of servers dynamically and eliminate the error caused by homomorphic evaluation of T-gate non-interactively. Therefore, a multi-party dynamic quantum homomorphic encryption scheme based on rotation operators is proposed in this paper. Firstly, the proposed scheme uses the rotation operators to solve the phase gate error that occurs during the homomorphic evaluation of T-gate non-interactively. Secondly, the scheme can dynamically deal with instability of servers, such as adding a server or removing a server. Then, the trusted key center is introduced, which is responsible for key updating and circuit replacement, which lowers the requirements for quantum capabilities on the client. Finally, this scheme extends the single-client multi-server model to the multi-client multi-server model, making it more suitable for quantum distributed networks and enhancing its practicality. In addition, we theoretically prove the correctness and fully homomorphic property of the proposed scheme, and verify it through the simulation conducted on the IBM Quantum Experience. Security analysis and efficiency analysis further demonstrate that the proposed scheme is information-theoretically secure and possesses high qubit efficiency.
Homomorphic encryption has giant advantages in the protection of privacy information. In this paper, we present a new kind of probabilistic quantum homomorphic encryption scheme for the universal quantum circuit evaluation. Firstly, the pre-shared non-maximally entangled states are utilized as auxiliary resources, which lower the requirements of the quantum channel, to correct the errors in non-Clifford gate evaluation. By using the set synthesized by Clifford gates and T gates, it is feasible to perform the arbitrary quantum computation on the encrypted data. Secondly, our scheme is different from the previous scheme described by the quantum homomorphic encryption algorithm. From the perspective of application, a two-party probabilistic quantum homomorphic encryption scheme is proposed. It is clear what the computation and operation that the client and the server need to perform respectively, as well as the permission to access the data. Finally, the security of probabilistic quantum homomorphic encryption scheme is analyzed in detail. It demonstrates that the scheme has favorable security in three aspects, including privacy data, evaluated data and encryption and decryption keys.
Secure multi-party computation has been playing a fundamental role in terms of classical cryptography. Quantum homomorphic encryption (QHE) could compute the encrypted data without decryption. At present, most protocols use a semi-honest third party (TP) to protect participants’ secrets. We use a quantum homomorphic encryption scheme instead of TP to protect the privacy of parties. Based on quantum homomorphic encryption, a secure multi-party quantum summation scheme is proposed in which N participants can delegate a server with strong quantum computing power to assist computation. By delegating the computation and key update processes to a server and a semi-honest key center, participants encrypt their private information data using Pauli operators to get the sum. Besides, the server can design and optimize the summation lines itself, and the correct results can be obtained even if the secret information is negative. The correctness analysis showed that the participants could correctly obtain the results of the calculation. The security analysis proves the scheme is resistant to both outside attack and participant’s attack, and is secure against collusive attack by up to N-2 participants. From the theoretical point of view, our protocol can extend to other secure multi-party computing problems.
Quantum homomorphic encryption (QHE) can allow clients to directly perform quantum computation on encrypted data with the assistance of a remote quantum server. However, existing QHE schemes often overlook the crucial property of verifiability which enables clients to validate the correctness of computation results provided by the server. In this paper, we propose a verifiable QHE scheme based on the universal quantum gate set {H,P,Toffoli}. At first, a specialized gadget is designed to eliminate the errors that may arise during the homomorphic evaluation of non-Clifford Toffoli gates in a non-interactive manner. Furthermore, the designed gadget is versatile and can be seamlessly integrated into an existing QHE scheme that implements quantum gates in another universal quantum gate set {H,T,CNOT} to homomorphically evaluate more quantum gates. Subsequently, a verifiable method is introduced to the QHE scheme based on {H,P,Toffoli} for the client to detect whether the server is honest during the homomorphic computation by employing three types of indistinguishable quantum circuits.
Quantum fully homomorphic encryption (QFHE) is a kind of secure method which allows random evaluation computations performed by each server on the cipher states and do not decrypt them. In order to extend the QFHE scheme for three-participant, an extend QFHE scheme based on brown state is proposed in this paper. Firstly, the conception of extend means we use a state which are familiar in quantum secret sharing procedure to extend the former QFHE scheme with three-part. Secondly, universal quantum circuit (UQC) enables random quantum transformations on the cipher states which promise the security, and the key-updating algorithms are also secure because of the former UQC. Finally, due to the property of QFHE, we do not need any security check to make it efficient for the secret sharing procedure.