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.

Graphical abstract

中文翻译：

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具有可验证功能的量子秘密共享方案

摘要

在（t，n）门限量子秘密共享方案中，很难确保内部参与者是诚实的。本文设计了一种可验证的（t，n）门限量子秘密共享方案，与经典秘密共享方案相结合。首先，分发者使用非对称二进制多项式生成份额并将其发送给每个参与者。其次，分发者将具有机密的初始量子状态发送给第一参与者，并且每个参与者都基于获得的d维单比特量子状态（d是一个大的奇质数）。在此过程中，分发者可以随机检查参与者，并找出内部欺诈者。然后，在所有其他参与者同时公开传播此秘密之后，便会重建该秘密。该方案的分析包括正确性分析，完整性分析和安全性分析。安全性分析表明，该方案可以抵抗内部和外部攻击。

图形概要