Verifiable quantum secret sharing scheme using Bell states for a class of special access structures

Quantum secret sharing (QSS) is a fundamental primitive in quantum cryptography. The existing QSS protocols are either (n,n)-threshold or (t,n)-threshold access structure, where n denotes the number of players and t denotes the threshold number of players. Here, we introduce a novel verifiable QSS scheme that executes a restricted hyperstar access structure by using entangled states. Our method involves encoding selected quantum states and their corresponding measurements to yield outcomes of either + 1 or - 1. Furthermore, we give the validation of the scheme through the system of equations derived from the measurements, which then guarantees the honesty of the participants. At last, we also analyze the security of our scheme in two primary quantum attacks, such as external attacks and internal attacks.