A quantum secret sharing scheme with verifiable function

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 obtainedddimension single bit quantum state (dis 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.