Quantum homomorphic encryption integrates quantum computing with homomorphic encryption, which allows calculations to be performed directly on encrypted data without decryption on the server side. In this paper, we explore distributed quantum homomorphic encryption, focusing on the coordination of multiple evaluators to achieve evaluation tasks, which not only ensures security but also boosts computational power. Notably, we propose a $(k, n)$-threshold universal quantum homomorphic encryption scheme based on quantum state sharing. Each server is capable of executing a universal gate set, including the Clifford gates $\{X,Y,Z,H,S,CNOT\}$ and a non-Clifford T gate. The scheme provides that k evaluation servers chosen from $n$ $(0 < k \leq n)$ cooperate to complete the quantum homomorphic encryption so that the client can get the evaluated plaintext after decryption. Several concrete examples are presented to provide clarity to our solution. We also include security analysis, demonstrating its security against eavesdroppers.
Universal quantum homomorphic encryption based on (k,n)-threshold quantum state sharing
Quantum homomorphic encryption integrates quantum computing with homomorphic encryption, which allows calculations to be performed directly on encrypted data without decryption on the server side. In this paper, we explore distributed quantum homomorphic encryption, focusing on the coordination of multiple evaluators to achieve evaluation tasks, which not only ensures security but also boosts computational power. Notably, we propose a (k,n)-threshold universal quantum homomorphic encryption scheme based on quantum state sharing. Each server is capable of executing a universal gate set, including the Clifford gates {X,Y,Z,H,S,CNOT} and a non-Clifford T gate. The scheme provides that k evaluation servers chosen from n(0<k≤n) cooperate to complete the quantum homomorphic encryption so that the client can get the evaluated plaintext after decryption. Several concrete examples are presented to provide clarity to our solution. We also include security analysis, demonstrating its security against eavesdroppers.
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.
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.
Currently, most quantum homomorphic encryption (QHE) schemes only allow a single evaluator (server) to accomplish computation tasks on encrypted data shared by the data owner (user). In addition, the quantum computing capability of the evaluator and the scope of quantum computation it can perform are usually somewhat limited, which significantly reduces the flexibility of the scheme in quantum network environments. In this paper, we propose a novel (t,n)-threshold QHE (TQHE) network scheme based on the Shamir secret sharing protocol, which allows k(t≤k≤n) evaluators to collaboratively perform evaluation computation operations on each qubit within the shared encrypted sequence. Moreover, each evaluator, while possessing the ability to perform all single-qubit unitary operations, is able to perform arbitrary single-qubit gate computation task assigned by the data owner. We give a specific (3, 5)-threshold example, illustrating the scheme's correctness and feasibility, and simulate it on IBM quantum computing cloud platform. Finally, it is shown that the scheme is secure by analyzing encryption/decryption private keys, ciphertext quantum state sequences during transmission, plaintext quantum state sequence, and the result after computations on the plaintext quantum state sequence.
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 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.
Cloud computing allows clients with limited computational resources to offload computations to more powerful remote servers. In this paradigm, homomorphic encryption (HE) schemes enable a server to run any computation on a client's encrypted data. These schemes are widely used in cloud computing protocols such as delegated computing, two-party secure computation, and zero-knowledge proofs. Quantum homomorphic encryption (QHE) aims to achieve the objectives of HE with quantum data and quantum circuits, enabling cloud quantum servers to compute on encrypted quantum data uploaded by clients. In this work, we consider a scenario where a client has access to a quantum “encryption/decryption device”, which allows the encryption, transmission, reception, and decryption of quantum states, but not universal quantum computation. In this setting, we provide a proof-of-concept software simulation of quantum homomorphic encryption. Our code implements the “EPR scheme” of Broadbent and Jeffery, which allows for the execution of universal quantum circuits by the server at the cost of requiring shared EPR pairs between the client and server. Our implementation explores the near-term viability of the EPR scheme. Perhaps unsurprisingly, our experiments indicate that the additional cost of homomorphic circuit evaluation is minor in comparison to the simulation cost of the quantum operations. Our simulation toolkit is implemented in Python and is open-source.