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A quantum hash function with grouped coarse-grained boson sampling

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Abstract

Boson sampling (BS) is an elegant candidate for the proof of quantum supremacy, and the exploration of its practical cryptographic applications is just at the beginning, including one-way functions, private-key cryptography and quantum signature. In order to investigate improvement methods for the combination of cryptography and BS, we propose a quantum hash function with grouped coarse-grained boson sampling (GCGBS) by making full use of the multi-photon characteristics of BS with undiluted conditions, which can eliminate the uncertain outputs, achieve repeatability and reduce the difficulty of experiment. The theoretical analysis and numerical simulation demonstrate an irreversible, anti-collision, anti-brute force search and uniform-distributed GCGBS-based hash function can be achieved with limited resource-consumption.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61972418, 61872390, 61801522, U1736113), the Natural Science Foundation of Hunan Province (Grant Nos. 2020JJ4750, 2019JJ40352), the Special Foundation for Distinguished Young Scientists of Changsha (Grant No. kq1905058), the CCF-Baidu Open Fund(Grant No. 2021PP15002000), the Outstanding Youth Program of Education Department of Hunan (Grant No. 21B0228).

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Authors and Affiliations

  1. School of Computer Science and Engineering, Central South University, Changsha, 410083, China

    Jinjing Shi, Yuhu Lu, Yanyan Feng, Duan Huang & Ronghua Shi

  2. College of Information Science and Engineering, Hunan Normal University, Changsha, 410006, China

    Xiaoping Lou

  3. School of Computer Science and School of Cyberspace Science, Xiangtan University, Xiangtan, 411301, China

    Qin Li

  4. College of Computer and Information Engineering, Central South University of Forestry and Technology, Changsha, 410004, China

    Yanyan Feng

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  1. Jinjing Shi
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Appendix: the numerical example of Fisher–Yates Shuffle algorithm based post-processing algorithm G

Appendix: the numerical example of Fisher–Yates Shuffle algorithm based post-processing algorithm G

Here, we illustrate the numerical example of algorithm G. The parameters of GCGBS used is \(M=10, N=3, d=8, l=5\), then the MPB of single-photon case \(\mathbb {B}_{\mu }\) belongs to \(\{0,1,\)...\(,d-1\}\) and the MPB of multi-photon case \(\mathbb {B}_{\nu }\) belongs to \(\{0,1,\)...\(,M-1\}\). Assume \(\mathbb {B}_{\mu }\) and \(\mathbb {B}_{\nu }\) obtained before sub-algorithm G are \(\mathbb {B}_{\mu } = \{3, 5, 0, 7, 2\}\) and \(\mathbb {B}_{\nu } = \{4, 6, 2, 0, 5\}\). The process of sub-algorithm G is shown in Table 1. The binary hash value obtained by the sub-algorithm G is y=0b00100000111100110101.

Table 1 Process of sub-algorithm G
Full size table

We introduce the MPB of multi-photon case as the random number of the Fisher–Yates Shuffle algorithm in sub-algorithm G, which is with two advantages. First, the output result is reproducible. Second, the multi-photon resources of dilute BS are not wasted.

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Shi, J., Lu, Y., Feng, Y. et al. A quantum hash function with grouped coarse-grained boson sampling. Quantum Inf Process 21, 73 (2022). https://doi.org/10.1007/s11128-022-03416-w

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