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A multi-valued quantum fully homomorphic encryption scheme

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Abstract

Fully homomorphic encryption enables computation on encrypted data while maintaining secrecy. This leads to an important open question whether quantum computation can be delegated and verified in a non-interactive manner or not. In this paper, we affirmatively answer this question by constructing quantum fully homomorphic encryption (QFHE) schemes with quantum obfuscation. For different scenarios, we propose two QFHE schemes with multi-valued quantum point obfuscation. One is with single-qubit point obfuscation and the other is with multi-qubit point obfuscation. The correctness of two QFHE schemes is proved theoretically. The evaluator does not know the decryption key and does not require a regular interaction with a user. The output state has the property of complete mixture, which guarantees the security. Moreover, the security level of the QFHE schemes depends on quantum obfuscation and encryption operators.

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Acknowledgements

This project was supported by the National Natural Science Foundation of China (Nos. 61971021, 61571024), Aeronautical Science Foundation of China (No.2018ZC51016) and the National Key Research and Development Program of China (No. 2016YFC1000307) for valuable helps.

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Authors and Affiliations

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

    Yuanjing Zhang, Tao Shang & Jianwei Liu

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  1. Yuanjing Zhang
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  2. Tao Shang
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  3. Jianwei Liu
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Correspondence to Tao Shang.

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Zhang, Y., Shang, T. & Liu, J. A multi-valued quantum fully homomorphic encryption scheme. Quantum Inf Process 20, 101 (2021). https://doi.org/10.1007/s11128-021-03051-x

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