A communication-efficient quantum threshold secret sharing scheme

Abstract

Among quantum secret sharing schemes, communication-efficient quantum secret sharing scheme is an important research issue. Aiming at the quantum threshold secret sharing scheme based on multi-particle entangled states, this paper proposes a new secret share distribution method and constructs a communication-efficient quantum secret sharing scheme. In this paper, we first point out that a unitary operation can be defined by an invertible matrix over a finite field. Based on the secret share distribution method and the unitary operation mentioned above, we give a complete description of our scheme. Then, we systematically analyze the communication cost and communication efficiency of our scheme. The analysis shows that our scheme is a practical and communication-efficient quantum threshold secret sharing scheme. Notably, we creatively use the particles from the mutually unbiased basis to prepare the entangled detection states and decoy particles, which enhances the security of our scheme. Finally, we prove that our scheme is secure under the intercept-and-resend attack, entangle-and-measure attack, collusion attack, and Trojan horse attack.