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<p>Digital signatures are an important class of cryptographic primitives mainly used to verify the integrity and origin of data. In this paper, we propose an efficient and secure quantum (<i>t</i>,&#xa0;<i>n</i>) threshold signature protocol using shift-code operation and Lagrange unitary operation. In the protocol, the signature group encodes the calculated result to the unbiased particle by the shift-code operation. It applies the random numbers, private keys, and secret shares of the signature members to the signature information and decoy particle by the Lagrange unitary operation. On the one hand, it prevents all the participants from embedding private information directly into the transmitted particles, which reduces the risk of information disclosure and improves the security of the protocol. On the other hand, the arbitrator can use the angle value <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4919_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta _c\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>θ</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation> to verify whether the number of participants meets the threshold requirement. Finally, with the help of the arbitrator, the verifier verifies that the number of signing members meets the threshold requirements and that the data is complete and correct. The security analysis shows that the protocol is able to withstand intercept-resend attacks, forgery attacks, and two types of collusion attacks. The performance analysis shows that the protocol can be easily extended due to the low number of transmitted particles and higher computational efficiency. Finally, the correctness of the protocol is verified by simulation experiments.</p>

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Quantum (t, n) threshold signature based on shift-code operation and Lagrange unitary operation

  • 期刊论文

  • 发表日期：

    2025年9月23日

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  • Yaodong Zhang,
  • Feng Liu,
  • Keshun Yang,
  • Ning Liu,
  • Lijian Zhang

摘要

Digital signatures are an important class of cryptographic primitives mainly used to verify the integrity and origin of data. In this paper, we propose an efficient and secure quantum (t, n) threshold signature protocol using shift-code operation and Lagrange unitary operation. In the protocol, the signature group encodes the calculated result to the unbiased particle by the shift-code operation. It applies the random numbers, private keys, and secret shares of the signature members to the signature information and decoy particle by the Lagrange unitary operation. On the one hand, it prevents all the participants from embedding private information directly into the transmitted particles, which reduces the risk of information disclosure and improves the security of the protocol. On the other hand, the arbitrator can use the angle value \(\theta _c\) θ c to verify whether the number of participants meets the threshold requirement. Finally, with the help of the arbitrator, the verifier verifies that the number of signing members meets the threshold requirements and that the data is complete and correct. The security analysis shows that the protocol is able to withstand intercept-resend attacks, forgery attacks, and two types of collusion attacks. The performance analysis shows that the protocol can be easily extended due to the low number of transmitted particles and higher computational efficiency. Finally, the correctness of the protocol is verified by simulation experiments.