Cryptanalysis of secret sharing with a single d -level quantum system

In this work, we point out that the multiparty secret sharing protocol of Tavakoli et al. (Phys Rev A 92:030302, 2015) based on a single d-level quantum system (where d is a prime number) is insecure and low efficient. In our paper, we show that all the secrets of distributor R1 can be stolen by q dishonest participants with the probability (q/N)ξ. An important improvement is proposed to fix up this security loophole. Besides, another improvement is given to increase the efficiency from 1/d to 1.