A quantum secret sharing scheme with verifiable function
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THE EUROPEAN PHYSICAL JOURNAL D
Regular Article
A quantum secret sharing scheme with verifiable function Li-Juan Liu, Zhi-Hui Lia , Zhao-Wei Han, and Dan-Li Zhi College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, P.R. China Received 7 January 2020 / Received in final form 14 April 2020 Published online 16 July 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. In the (t, n) threshold quantum secret sharing scheme, it is difficult to ensure that internal participants are honest. In this paper, a verifiable (t, n) threshold quantum secret sharing scheme is designed to combine with classical secret sharing scheme. First of all, the distributor uses the asymmetric binary polynomial to generate the shares and sends them to each participant. Secondly, the distributor sends the initial quantum state with the secret to the first participant, and each participant performs unitary operation that uses the mutually unbiased bases on the obtained d dimension single bit quantum state (d is a large odd prime number). In this process, distributor can randomly check the participants, and find out the internal fraudsters. Then the secret is reconstructed after all other participants publicly transmit it at the same time. The analysis of this scheme includes correctness analysis, completeness analysis and security analysis. And the security analysis shows that the scheme can resist both external and internal attacks.
1 Introduction In 1979, the secret sharing scheme was first proposed by Shamir [1] and Blakely [2], which is an important technology to ensure the security and availability of confidential information. In addition, they are widely used as the components of various cryptographic protocols, such as threshold cryptography, attribute-based encryption and multi-party computing. In the (t, n) threshold secret sharing scheme, the secret is divided into n shares so that it can be only recovered with t or more than t shares, but fewer than t shares cannot reveal any information of the secret. At present, the research of classical secret sharing scheme has become mature [3–5], and the access structure has developed into arbitrary access structures [6,7]. However, most of the schemes have the following potential security hazard: it is impossible to check the honesty of internal participants in the secret sharing phase. Therefore, the verifiable secret sharing (VSS) scheme was proposed by Chor et al. [8]. The purpose of the VSS scheme is to prevent participants from providing wrong shares in the secret sharing phase. So far, more and more theories of VSS [9,10] have been put forward. However, all of the VSS schemes are based on the assumption of computational complexity, namely security is conditional. With the improvement of computing capabilities and algorithms, especially the emergence of quantum algorithms [11], the security of classical cryptography is facing severe challenges. In addition, as the extension of classi
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