SCIENCE CHINA Information Sciences, Volume 60, Issue 8: 082501(2017) https://doi.org/10.1007/s11432-016-9061-4

## An efficient quantum blind digital signature scheme

• AcceptedMar 9, 2017
• PublishedJul 10, 2017
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### Abstract

Recently, many quantum digital signature (QDS) schemes have been proposed to authenticate the integration ofa message. However, these quantum signature schemes just considerthe situation for bit messages, and the signing-verifying of one-bitmodality. So, their signature efficiency is very low. In this paper,we propose a scheme based on an application of Fibonacci-, Lucas-and Fibonacci-Lucas matrix coding to quantum digital signaturesbased on a recently proposed quantum key distribution (QKD) system.Our scheme can sign a large number of digital messages every time.Moreover, these special matrices provide a method to verify theintegration of information received by the participants, toauthenticate the identity of the participants, and to improve theefficiency for signing-verifying. Therefore, our signature scheme ismore practical than the existing schemes.

### Acknowledgment

Hong LAI was supported by Fundamental Research Funds for the Central Universities (Grant No. XDJK2016C043), 1000-Plan of Chongqing by Southwest University (Grant No. SWU116007), and Doctoral Program of Higher Education (Grant No. SWU115091). Mingxing LUO was supported by Sichuan Youth Science & Technique Foundation (Grant No.2017JQ0048). Josef PIEPRZYK was supported by National Science Centre, Poland (Grant No. UMO-2014/15/B/ST6/05130). Shudong Li was supported by National Natural Science Foundation of China (Grant Nos. 61672020, 61662069, 61472433), Project Funded by China Postdoctoral Science Foundation (Grant Nos. 2013M542560, 2015T81129) and A Project of Shandong Province Higher Educational Science and Technology Program (Grant Nos. J16LN61, 2016ZH054). The paper was also supported by A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology (CICAEET).

• Figure 1

(Color online) The sketch for quantum key distribution of our QDS scheme, where $K_{\rm AB},\; K^{i}_{\rm AB}$, $K_{\rm AC},\;K^{i}_{\rm AC}$, $K_{\rm BC}$, and $K^{i}_{\rm BC}(i=1,2,\ldots,\alpha)$ are key matrices.

• Figure 2

(Color online) The sketch for the process of signature and verification of our QDS scheme, where $K_{\rm AB}=\{K^{1}_{\rm AB},K^{2}_{\rm AB},\ldots,K^{\alpha}_{\rm AB}\}$, $K_{\rm AC}=\{K^{1}_{\rm AC},K^{2}_{\rm AC},\ldots,K^{\alpha}_{\rm AC}\}$, $K_{\rm BC}=\{K^{1}_{\rm BC},K^{2}_{\rm BC},\ldots,K^{\alpha}_{\rm BC}\}$ are all in the form of matrices; $M'=E_{K_{\rm AB}}\{M\}= M\times K_{\rm AB}$, $M''=E_{K_{\rm AC}}\{M'\}=M' \times K_{\rm AC}$, $S=E_{K_{\rm BC}}\{M'\}= M' \times K_{\rm BC}$, ${\rm det}(M')$ is the determinant of $M'$.

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