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arXiv:1503.04061

Quantum fully homomorphic encryption scheme based on quantum fault-tolerant construction

Min Liang, Li Yang

Published Mar 13, 2015• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1503.04061

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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.
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.
Suppose some data have been encrypted, can you compute with the data without decrypting them? This problem has been studied as homomorphic encryption and blind computing. We consider this problem in the context of quantum information processing, and present the definitions of quantum homomorphic encryption (QHE) and quantum fully homomorphic encryption (QFHE). Then, based on quantum one-time pad (QOTP), we construct a symmetric QFHE scheme, where the evaluate algorithm depends on the secret key. This scheme permits any unitary transformation on any nnn-qubit state that has been encrypted. Compared with classical homomorphic encryption, the QFHE scheme has perfect security. Finally, we also construct a QOTP-based symmetric QHE scheme, where the evaluate algorithm is independent of the secret key.
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.
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.
Quantum fully homomorphic encryption (QFHE) is a kind of secure method which allows random evaluation computations performed by each server on the cipher states and do not decrypt them. In order to extend the QFHE scheme for three-participant, an extend QFHE scheme based on brown state is proposed in this paper. Firstly, the conception of extend means we use a state which are familiar in quantum secret sharing procedure to extend the former QFHE scheme with three-part. Secondly, universal quantum circuit (UQC) enables random quantum transformations on the cipher states which promise the security, and the key-updating algorithms are also secure because of the former UQC. Finally, due to the property of QFHE, we do not need any security check to make it efficient for the secret sharing procedure.