Quantum homomorphic encryption (QHE), allows a quantum cloud server to compute on private data as uploaded by a client. We provide a proof-of-concept software simulation for QHE, according to the "EPR" scheme of Broadbent and Jeffery, for universal quantum circuits. We demonstrate the near-term viability of this scheme and provide verification that the additional cost of homomorphic circuit evaluation is minor when compared to the simulation cost of the quantum operations. Our simulation toolkit, py−qhe−epr package, is an open-source Python implementation, that serves as a step towards further hardware applications of quantum homomorphic encryption between networked quantum devices.
Quantum homomorphic encryption (QHE), allows a quantum cloud server to compute on private data as uploaded by a client. We provide a proof-of-concept software simulation for QHE, according to the "EPR" scheme of Broadbent and Jeffery, for universal quantum circuits. We demonstrate the near-term viability of this scheme and provide verification that the additional cost of homomorphic circuit evaluation is minor when compared to the simulation cost of the quantum operations. Our simulation toolkit, py−qhe−epr package, is an open-source Python implementation, that serves as a step towards further hardware applications of quantum homomorphic encryption between networked quantum devices.
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.
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.
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.
Quantum homomorphic encryption (QHE) is an encryption method that allows quantum computation to be performed on one party's private data with the program provided by another party, without revealing much information about the data nor the program to the opposite party. We propose a framework for (interactive) QHE based on the universal circuit approach. It contains a subprocedure of calculating a classical linear polynomial, which can be implemented with quantum or classical methods; apart from the subprocedure, the framework has low requirement on the quantum capabilities of the party who provides the circuit. We illustrate the subprocedure using a quite simple classical protocol with some privacy tradeoff. For a special case of such protocol, we obtain a scheme similar to blind quantum computation but with the output on a different party. Another way of implementing the subprocedure is to use a recently studied quantum check-based protocol, which has low requirement on the quantum capabilities of both parties. The subprocedure could also be implemented with a classical additive homomorphic encryption scheme. We demonstrate some key steps of the outer part of the framework in a quantum optics experiment.
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.
Quantum homomorphic encryption (QHE) is an encryption method that allows quantum computation to be performed on one party's private data with the program provided by another party, without revealing much information about the data nor about the program to the opposite party. It is known that information-theoretically-secure QHE for circuits of unrestricted size would require exponential resources, and efficient computationally-secure QHE schemes for polynomial-sized quantum circuits have been constructed. In this paper we first propose a QHE scheme for a type of circuits of polynomial depth, based on the rebit quantum computation formalism. The scheme keeps the restricted type of data perfectly secure. We then propose a QHE scheme for a larger class of polynomial-depth quantum circuits, which has partial data privacy. Both schemes have good circuit privacy. We also propose an interactive QHE scheme with asymptotic data privacy, however, the circuit privacy is not good, in the sense that the party who provides the data could cheat and learn about the circuit. We show that such cheating would generally affect the correctness of the evaluation or cause deviation from the protocol. Hence the cheating can be caught by the opposite party in an interactive scheme with embedded verifications. Such scheme with verification has a minor drawback in data privacy. Finally, we show some methods which achieve some nontrivial level of data privacy and circuit privacy without resorting to allowing early terminations, in both the QHE problem and in secure evaluation of classical functions. The entanglement and classical communication costs in these schemes are polynomial in the circuit size and the security parameter (if any).