Verifiable Threshold Quantum Secret Sharing with Sequential Communication

Abstract: A ($t$, $n$) threshold quantum secret sharing (QSS) is proposed based on a single $d$-level quantum system. It enables the ($t$, $n$) threshold structure based on Shamir's secret sharing and simply requires sequential communication in $d$-level quantum system to recover secret. Besides, the scheme provides a verification mechanism which employs an additional qudit to detect cheats and eavesdropping during secret reconstruction, and allows a participant to use the share repeatedly. Analyses show that the proposed scheme is resistant to typical attacks. Moreover, the scheme is salable in participant number and easier to realize compared to related schemes. More generally, our scheme also presents a generic method to construct new ($t$, $n$) threshold QSS schemes based on $d$-level quantum system from other classical threshold secret sharing.