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Quantum homomorphic aggregate signature based on quantum Fourier transform

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Abstract

With the rapid development of computer and internet technology, quantum signature plays an extremely important role in modern secure communication. Quantum homomorphic aggregate signature, as an important guarantee of quantum signature, plays a significant role in reducing storage, communication, and computing costs. This article draws on the idea of quantum multi-party summation and proposes a quantum homomorphic aggregate signature scheme based on quantum Fourier transform. Our scheme uses n-particle entangled states as quantum channels, with different particles of each entangled state sent separately. This ensures secure transmission of signatures and messages with fewer entangled particles during transmission, further improving the efficiency of quantum signatures. Meanwhile, our scheme generates private keys for each participating party by randomly constructing key generation matrixes. Different signers perform quantum Fourier transforms and basis exchange operations on entangled particles based on different messages and private keys to generate signatures. In addition, the aggregator does not need to measure and verify the signature particles after receiving signatures from different signers, and the group addition operation process has additive homomorphism. Security analysis shows that our scheme has unforgeability, non-repudiation, and can resist various attacks such as entanglement measurement attacks, intercept-resend attacks, private key sequence attacks, and internal attacks by aggregator.

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Acknowledgements

We would like to thank the anonymous reviewers for their valuable comments. This work was supported by Special Project for International Cooperation in Science and Technology of Qinghai Province. (No. 202402050039).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qinghai Normal University, Xining, 810008, Qinghai Province, China

    Teng Chen, Dian-Jun Lu & Zhi-Ming Deng

  2. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710119, Shaanxi Province, China

    Dian-Jun Lu

  3. Department of Statistics, University of California, Riverside, Riverside, CA, 92521, USA

    Wei-Xin Yao

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  1. Teng Chen
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [Teng Chen], [Dian-Jun Lu], [Zhi-Ming Deng], [Wei-Xin Yao]. The first draft of the manuscript was written by [Teng Chen], and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Appendix A: The representation of key generation matrixes

Appendix A: The representation of key generation matrixes

The \(B^{1}\) matrix is represented as

$$\begin{aligned} \begin{bmatrix} 40 &{}5 &{} 6 &{} 1 &{} 1 &{} 5 &{} 4 &{} 2 \\ 46 &{} 29 &{} 42 &{} 6 &{} 1 &{} 5 &{} 21 &{} 42 \\ 51 &{} 12 &{} 30 &{} 40 &{} 13 &{} 18 &{} 21 &{} 7 \\ 44 &{} 37 &{} 27 &{} 32 &{} 13 &{} 9 &{} 17 &{} 13 \\ 49 &{} 36 &{} 9 &{} 14 &{} 2 &{} 12 &{} 12 &{} 58 \\ 24 &{} 15 &{} 10 &{} 39 &{} 19 &{} 50 &{} 6 &{} 29 \\ 14 &{} 22 &{} 4 &{} 39 &{} 13 &{} 34 &{} 57 &{} 9 \\ 39 &{} 43 &{} 19 &{} 17 &{} 4 &{} 5 &{} 24 &{} 41 \\ \end{bmatrix} \end{aligned}$$
(A1)

The \(B^{2}\) matrix is represented as:

$$\begin{aligned} \begin{bmatrix} 11 &{} 2 &{} 60 &{} 27 &{} 4 &{} 33 &{} 7 &{} 48 \\ 4 &{} 17 &{} 43 &{} 33 &{} 12 &{} 17 &{} 52 &{} 14 \\ 37 &{} 36 &{} 24 &{} 42 &{} 5 &{} 32 &{} 13 &{} 3 \\ 28 &{} 53 &{} 20 &{} 13 &{} 2 &{} 5 &{} 32 &{} 39 \\ 35 &{} 4 &{} 59 &{} 34 &{} 12 &{} 35 &{} 7 &{} 6 \\ 31 &{} 60 &{} 3 &{} 4 &{} 2 &{} 5 &{} 25 &{} 62 \\ 47 &{} 24 &{} 3 &{} 61 &{} 9 &{} 28 &{} 11 &{} 9 \\ 46 &{} 10 &{} 28 &{} 64 &{} 4 &{} 11 &{} 27 &{} 2 \\ \end{bmatrix} \end{aligned}$$
(A2)

The \(B^{3}\) matrix is represented as:

$$\begin{aligned} \begin{bmatrix} 31 &{} 48 &{} 9 &{} 4 &{} 2 &{} 5 &{} 58 &{} 35 \\ 48 &{} 2 &{} 61 &{} 8 &{} 24 &{} 6 &{} 10 &{} 33 \\ 44 &{} 1 &{} 31 &{} 5 &{} 4 &{} 62 &{} 62 &{} 36 \\ 9 &{} 64 &{} 63 &{} 18 &{} 5 &{} 13 &{} 13 &{} 12 \\ 19 &{} 30 &{} 11 &{} 38 &{} 16 &{} 49 &{} 49 &{} 17 \\ 18 &{} 27 &{} 35 &{} 36 &{} 8 &{} 1 &{} 1 &{} 57 \\ 40 &{} 25 &{} 2 &{} 11 &{} 1 &{} 57 &{} 57 &{} 50 \\ 1 &{} 8 &{} 56 &{} 1 &{} 57 &{} 25 &{} 25 &{} 33 \\ \end{bmatrix} \end{aligned}$$
(A3)

The \(B^{4}\) matrix is represented as:

$$\begin{aligned} \begin{bmatrix} 42 &{} 30 &{} 21 &{} 33 &{} 62 &{} 6 &{} 1 &{} 61 \\ 16 &{} 19 &{} 28 &{} 56 &{} 62 &{} 7 &{} 19 &{} 49 \\ 64 &{} 11 &{} 22 &{} 18 &{} 39 &{} 26 &{} 54 &{} 22 \\ 43 &{} 18 &{} 24 &{} 45 &{} 31 &{} 18 &{} 40 &{} 37 \\ 64 &{} 17 &{} 6 &{} 43 &{} 57 &{} 40 &{} 1 &{} 28 \\ 56 &{} 32 &{} 22 &{} 37 &{} 26 &{} 9 &{} 64 &{} 10 \\ 38 &{} 17 &{} 49 &{} 26 &{} 26 &{} 6 &{} 50 &{} 44 \\ 48 &{} 56 &{} 10 &{} 41 &{} 11 &{} 48 &{} 12 &{} 30 \\ \end{bmatrix} \end{aligned}$$
(A4)

The \(B^{5}\) matrix is represented as:

$$\begin{aligned} \begin{bmatrix} 51 &{} 44 &{} 9 &{} 10 &{} 63 &{} 50 &{} 25 &{} 4 \\ 54 &{} 46 &{} 27 &{} 27 &{} 11 &{} 6 &{} 33 &{} 52 \\ 28 &{} 54 &{} 42 &{} 33 &{} 5 &{} 8 &{} 54 &{} 32 \\ 32 &{} 3 &{} 53 &{} 48 &{} 16 &{} 10 &{} 43 &{} 51 \\ 46 &{} 26 &{} 47 &{} 59 &{} 10 &{} 9 &{} 12 &{} 47 \\ 22 &{} 51 &{} 63 &{} 12 &{} 3 &{} 18 &{} 36 &{} 51 \\ 62 &{} 2 &{} 39 &{} 29 &{} 43 &{} 52 &{} 23 &{} 6 \\ 55 &{} 63 &{} 26 &{} 17 &{} 10 &{} 39 &{} 26 &{} 20 \\ \end{bmatrix} \end{aligned}$$
(A5)

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Chen, T., Lu, DJ., Deng, ZM. et al. Quantum homomorphic aggregate signature based on quantum Fourier transform. Quantum Inf Process 23, 130 (2024). https://doi.org/10.1007/s11128-024-04341-w

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