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Two-round quantum homomorphic encryption scheme based on matrix decomposition

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Abstract

As a promising emerging technology, quantum homomorphic encryption (QHE) attracts considerable attention in the domain of cloud computing. However, as the homomorphic evaluation for non-Clifford gate generates an undesired error, efficient QHE scheme for any quantum circuit still faces a serious challenge. In this paper, we propose a two-round QHE scheme based on matrix decomposition, which can be used to eliminate the error and obtain the decryption matrix non-interactively. Through the circuit synthesis method, the decryption matrix can be decomposed into a quantum circuit to complete the decryption. In order to reduce the decryption overhead for Client, an extra round of evaluation is used to perform the decryption circuit by Server. We prove that the scheme is compact and information-theoretically secure. In addition, we apply the QHE scheme to ciphertext retrieval and complete a ciphertext retrieval experiment on IBM Qiskit. The retrieval scheme is efficient even if the evaluated circuit contains any number of non-Clifford gates.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This project was supported by the National Natural Science Foundation of China(No. 61971021), the Key Research and Development Project of Hebei Province (No. 22340701D) and the Universities Innovation Foundation of China-Beichuang Teaching Assistant Project (No. 2021BCA0200) for valuable helps.

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Authors and Affiliations

  1. School of Cyber Science and Technology, Beihang University, Beijing, 100083, China

    Tao Shang, Shuolin Wang, Yazhuo Jiang & Jianwei Liu

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  1. Tao Shang
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  2. Shuolin Wang
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  4. Jianwei Liu
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Correspondence to Tao Shang.

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Shang, T., Wang, S., Jiang, Y. et al. Two-round quantum homomorphic encryption scheme based on matrix decomposition. Quantum Inf Process 22, 422 (2023). https://doi.org/10.1007/s11128-023-04173-0

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