We present the first leveled fully homomorphic encryption scheme for quantum circuits with classical keys. The scheme allows a classical client to blindly delegate a quantum computation to a quantum server: an honest server is able to run the computation while a malicious server is unable to learn any information about the computation. We show that it is possible to construct such a scheme directly from a quantum secure classical homomorphic encryption scheme with certain properties. Finally, we show that a classical homomorphic encryption scheme with the required properties can be constructed from the learning with errors problem.
We present the first leveled fully homomorphic encryption scheme for quantum circuits with classical keys. The scheme allows a classical client to blindly delegate a quantum computation to a quantum server: an honest server is able to run the computation while a malicious server is unable to learn any information about the computation. We show that it is possible to construct such a scheme directly from a quantum secure classical homomorphic encryption scheme with certain properties. Finally, we show that a classical homomorphic encryption scheme with the required properties can be constructed from the learning with errors problem.
We present a new scheme for quantum homomorphic encryption which is compact and allows for efficient evaluation of arbitrary quantum circuits, as long as those circuits are of size, polynomial in the security parameter. Building on the framework of Broadbent and Jeffery (CRYPTO'15) and recent results in the area of instantaneous non-local quantum computation by Speelman (TQC'16), we show how to construct quantum gadgets that allow perfect correction of the errors which occur during the homomorphic evaluation of T gates on encrypted quantum data. Our scheme can be based on any classical (leveled) fully homomorphic encryption (FHE) scheme and requires no computational assumptions besides those already used by the classical scheme. The size of our quantum gadget depends on the space complexity of the classical decryption function -- which aligns well with the current efforts to minimize the complexity of the decryption function. Our scheme (or slight variants of it) offers a number of additional advantages such as ideal compactness, the ability to supply gadgets “on demand,” circuit privacy for the evaluator against passive adversaries, and a three-round scheme for blind delegated quantum computation which puts only very limited demands on the quantum abilities of the client. A conference version of this paper appeared in Advances in Cryptology: Proceedings of the 36th International Cryptology Conference (CRYPTO 2016).
Fully homomorphic encryption is a kind of encryption scheme, which enables arbitrary computation on encrypted data without accessing the data. We present the quantum version of fully homomorphic encryption scheme, which is constructed based on quantum fault-tolerant construction. Two schemes are constructed. The first is a symmetric scheme, and the secret key is the quantum CSS code. In the scheme, when Server performs quantum computation on the encrypted plaintext, some ancillary quantum states should be provided by Client. The second is an asymmetric scheme, which contains the periodical interaction between Client and Server.
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 computers promise not only to outperform classical machines for certain important tasks, but also to preserve privacy of computation. For example, the blind quantum computing protocol enables secure delegated quantum computation, where a client can protect the privacy of their data and algorithms from a quantum server assigned to run the computation. However, this security comes with the practical limitation that the client and server must communicate after each step of computation. A practical alternative is homomorphic encryption, which does not require any interactions, while providing quantum-enhanced data security for a variety of computations. In this scenario, the server specifies the computation to be performed, and the client provides only the input data, thus enabling secure noninteractive computation. Here, we demonstrate homomorphic-encrypted quantum computing with unitary transformations of individual qubits, as well as multi-qubit quantum walk computations using single-photon states and non-birefringent integrated optics. The client encrypts their input in the photons’ polarization state, while the server performs the computation using the path degree of freedom. Our demonstration using integrated quantum photonics underlines the applicability of homomorphic-encrypted quantum computations, and shows the potential for delegated quantum computing using photons.
Suppose a large scale quantum computer becomes available over the Internet. Could we delegate universal quantum computations to this server, using only classical communication between client and server, in a way that is information-theoretically blind (i.e., the server learns nothing about the input apart from its size, with no cryptographic assumptions required)? In this paper we give strong indications that the answer is no. This contrasts with the situation where quantum communication between client and server is allowed --- where we know that such information-theoretically blind quantum computation is possible. It also contrasts with the case where cryptographic assumptions are allowed: there again, it is now known that there are quantum analogues of fully homomorphic encryption. In more detail, we observe that, if there exist information-theoretically secure classical schemes for performing universal quantum computations on encrypted data, then we get unlikely containments between complexity classes, such as BQP⊂NP/poly. Moreover, we prove that having such schemes for delegating quantum sampling problems, such as Boson Sampling, would lead to a collapse of the polynomial hierarchy. We then consider encryption schemes which allow one round of quantum communication and polynomially many rounds of classical communication, yielding a generalization of blind quantum computation. We give a complexity theoretic upper bound, namely QCMA/qpoly∩coQCMA/qpoly, on the types of functions that admit such a scheme. This upper bound then lets us show that, under plausible complexity assumptions, such a protocol is no more useful than classical schemes for delegating NP-hard problems to the server. Lastly, we comment on the implications of these results for the prospect of verifying a quantum computation through classical interaction with the server.
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.