A quantum secret sharing scheme with verifiable function

Abstract: In the $\left( {t,n} \right)$ threshold quantum secret sharing scheme, it is difficult to ensure that internal participants are honest. In this paper, a verifiable $\left( {t,n} \right)$ threshold quantum secret sharing scheme is designed combined with classical secret sharing scheme. First of all, the distributor uses the asymmetric binary polynomials 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 using 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 by unitary inverse operation gradually upward. Then the secret is reconstructed after all other participants simultaneously public transmission. Security analysis show that this scheme can resist both external and internal attacks.