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 Clifford circuits, where the decryption key can be calculated by Alice with polynomial overhead with respect to the key length.
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 Clifford circuits, where the decryption key can be calculated by Alice with polynomial overhead with respect to the key length.
Homomorphic encryption is a cryptographic primitive that enables information processing on encrypted data. Such primitives are useful in a delegated computing setting in which a client delegates processing to a server, but does not trust the server fully with her information. Here, I discuss a way of performing quantum homomorphic encryption. A homomorphic encryption protocol comprises of four algorithms: random key generation, encryption, evaluation, and decryption. Our technique requires that a pair of commuting operators be used to implement the encryption and evaluation. The client randomly selects the former, while the server implements the latter. Then post-evaluation, if the client decrypts using the inverse of the encryption, he retrieves the input state with the desired computation implemented. The code space has to be chosen carefully so that non-trivial evaluations can be performed on the logical qubits. Since the encryption key is not known to the server, the randomness introduced by key generation hides some information about the encoded data despite it being put into the hands of the server. This framework is powerful because it gives a general description for implementing quantum homomorphic encryption. For example, families of commuting groups of operators are known to exist via the Schur-Weyl duality. However, it is limited by a no-go theorem that states that an exponential overhead is needed if arbitrary computation and perfect security are desired. Nonetheless, our protocols are still interesting as an application for near-term quantum computers, especially when the computational tasks require only low-depth circuits.
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.
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.
Abstract Quantum homomorphic encryption (QHE) can allow directly computation on the encrypted data without need to decrypt it in advance. It is also necessary to provide another property of verifiability that the client should verify whether the evaluation result is correct. However, most existing QHE schemes did not consider it and only assumed servers to be honest. In this paper, we propose a verifiable QHE (vQHE) scheme by using different types of circuits indistinguishable to the server, where the client can detect whether the server is honest or not by verifying the results of test circuits. Furthermore, by designing the gadgets to implement and test T gates and H gates in a non-interactive way for the used circuits, the proposed vQHE scheme does not require interaction during the process of evaluation. Thus the proposed vQHE scheme has the potential to make clients prefer to use it for protecting their private data in future quantum cloud environments.
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.
A fully homomorphic encryption system enables computation on encrypted data without the necessity for prior decryption. This facilitates the seamless establishment of a secure quantum channel, bridging the server and client components, and thereby providing the client with secure access to the server's substantial computational capacity for executing quantum operations. However, traditional homomorphic encryption systems lack scalability, programmability, and stability. In this Letter, we experimentally demonstrate a proof-of-concept implementation of a homomorphic encryption scheme on a compact quantum chip, verifying the feasibility of using photonic chips for quantum homomorphic encryption. Our work not only provides a solution for circuit expansion, addressing the longstanding challenge of scalability while significantly reducing the size of quantum network infrastructure, but also lays the groundwork for the development of highly sophisticated quantum fully homomorphic encryption systems.