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arXiv:2305.15978

Efficient and secure quantum network coding based on quantum full homomorphic encryption

Ning Wang, Gao, Fei, Song Lin

Published May 25, 2023• 1 citation
arXivHTMLPDF

Abstract

Based on $d$-dimensional quantum full homomorphic encryption, an efficient and secure quantum network coding protocol is proposed in this paper. First, a quantum full homomorphic encryption protocol is constructed utilizing $d$-dimensional universal quantum gates. On this basis, an efficient quantum network coding protocol is proposed. In the protocol, two source nodes encrypt their respective prepared quantum states with the quantum full homomorphic encryption protocol. The two intermediate nodes successively perform homomorphic evaluation of the received quantum states. Finally, the two sink nodes recover the quantum states transmitted by the two source nodes in the butterfly network depending on their measurement results. The performance analysis shows that the proposed quantum network coding protocol is correct and resistant to attacks launched by dishonest intermediate nodes and external eavesdroppers. Compared to related protocols, the proposed protocol not only enables to transfer information in $d$-dimensional quantum system, but also requires only 1 quantum gate and a key of length 2 in the encryption phase, which makes the protocol has higher efficiency.

DOI
10.48550/arxiv.2305.15978

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Abstract In order to solve the information leakage caused by dishonest intermediate nodes in quantum network coding, we apply quantum homomorphic encryption to the butterfly network, and propose a secure protocol for crossing two qubits. Firstly, in the communication process between two senders and the first intermediate node, two senders encrypt their measured particles and send them to the first intermediate node for encoding. If two intermediate nodes are dishonest and know the encryption rules between two senders and two receivers, or there is an external eavesdropper, none of them can recover the transmitted qubits of two senders from the encrypted transmitted particles. In this way, our protocol can transmit two qubits safely and crossly in the butterfly network. Secondly, by analyzing the internal participant attack and the external eavesdropper attack launched by dishonest intermediate nodes and an external eavesdropper respectively, it is confirmed that our protocol is secure. Finally, the experimental simulation results based on the Qiskit framework prove that our protocol is feasible.
Quantum homomorphic encryption hides quantum information from unauthorized participants while still allowing them to perform calculations on encrypted quantum information. In this paper, we propose a cross quantum homomorphic encryption scheme based on the butterfly network, in which every receiver can receive the evaluated quantum state with perfect fidelity. The entangled states between senders of the butterfly network are preshared, and the Bell basis measurements are used to encrypt the quantum plaintext. With both classical and quantum channels, the homomorphic evaluation of quantum plaintext can be completed on the butterfly network perfectly and crossly. Our scheme solves a bottleneck problem of cross evaluation at the bottleneck nodes, and improves the evaluation efficiency and total network throughput. In addition, we have designed quantum circuits according to different quantum evaluations with a butterfly network, which provide a basic blueprint for experimental implementation. The security of the scheme is also analyzed.
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.
Quantum network coding is vulnerable to pollution attacks, especially when using classical channel as auxiliary resource. On this basis, this letter proposes a secure quantum network coding scheme against pollution attacks. The scheme uses quantum homomorphic signature for the efficient authentication of different data sources so as to detect pollution attacks in the butterfly network. Furthermore, with the help of trusted intermediate nodes, it can locate a corrupt data source. Analysis results show that the proposed quantum network coding scheme can defend against pollution attacks with high fidelity, fewer resource consumption, and lower rate region.
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.
As a specific example of network coding, the butterfly network often represents the networks with bottlenecks. In this paper, we propose a typical butterfly quantum network coding scheme based on remote state preparation of arbitrary two-qubit states with the assistance of GHZ channels. Firstly, in a butterfly network, each source node simultaneously performs two appropriate projective measurements under suitable measurement basis on their own qubits. Next, their measurement results would be distributed to mid-side nodes. In the following, midside nodes perform encoded operations and send their encoded information to destination nodes. Finally, two destination nodes obtain the target state according to all information they receive with the success probability 1.