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Homomorphic encryption of linear optics quantum computation on almost arbitrary states of light with asymptotically perfect security

Ouyang, Y., Tan, S.-H., Fitzsimons, J., Peter P. Rohde

Published Feb 28, 2019• 15 citations
OpenAlex

Abstract

Future quantum computers are likely to be expensive and affordable outright\nby few, motivating client/server models for outsourced computation. However,\nthe applications for quantum computing will often involve sensitive data, and\nthe client would like to keep her data secret, both from eavesdroppers and the\nserver itself. Homomorphic encryption is an approach for encrypted, outsourced\nquantum computation, where the client's data remains secret, even during\nexecution of the computation. We present a scheme for the homomorphic\nencryption of arbitrary quantum states of light with no more than a fixed\nnumber of photons, under the evolution of both passive and adaptive linear\noptics, the latter of which is universal for quantum computation. The scheme\nuses random coherent displacements in phase-space to obfuscate client data. In\nthe limit of large coherent displacements, the protocol exhibits asymptotically\nperfect information-theoretic secrecy. The experimental requirements are\nmodest, and easily implementable using present-day technology.

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Future quantum computers are likely to be expensive and affordable outright\nby few, motivating client/server models for outsourced computation. However,\nthe applications for quantum computing will often involve sensitive data, and\nthe client would like to keep her data secret, both from eavesdroppers and the\nserver itself. Homomorphic encryption is an approach for encrypted, outsourced\nquantum computation, where the client's data remains secret, even during\nexecution of the computation. We present a scheme for the homomorphic\nencryption of arbitrary quantum states of light with no more than a fixed\nnumber of photons, under the evolution of both passive and adaptive linear\noptics, the latter of which is universal for quantum computation. The scheme\nuses random coherent displacements in phase-space to obfuscate client data. In\nthe limit of large coherent displacements, the protocol exhibits asymptotically\nperfect information-theoretic secrecy. The experimental requirements are\nmodest, and easily implementable using present-day technology.
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.
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.
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.
We present a scheme for implementing homomorphic encryption on coherent states encoded using phase-shift keys. The encryption operations require only rotations in phase space, which commute with computations in the code space performed via passive linear optics, and with generalized nonlinear phase operations that are polynomials of the photon-number operator in the code space. This encoding scheme can thus be applied to any computation with coherent-state inputs, and the computation proceeds via a combination of passive linear optics and generalized nonlinear phase operations. An example of such a computation is matrix multiplication, whereby a vector representing coherent-state amplitudes is multiplied by a matrix representing a linear optics network, yielding a new vector of coherent-state amplitudes. By finding an orthogonal partitioning of the support of our encoded states, we quantify the security of our scheme via the indistinguishability of the encrypted code words. While we focus on coherent-state encodings, we expect that this phase-key encoding technique could apply to any continuous-variable computation scheme where the phase-shift operator commutes with the computation.