Research On The Construction And Related Technology Of A Kind Of Quantum Secret Sharing Scheme

Secret sharing has already become a very important research direction in cryp-tography.It refers to sharing secret shares among many participants.Only autho-rized sets can reconstruct secrets.Unauthorized sets cannot get any secret infor-mation.Owing that the theoretical basis of quantum secret sharing(QSS)scheme is quantum physics,it is more secure than classical secret sharing(CSS)scheme.Referring to the concept of CSS,Hillery et al.proposed the concept of QSS in 1998,and designed the first QSS scheme by using Green-Horne-Zeilinger(GHZ)triplet.Since then,QSS has attracted people's attention,and a series of QSS schemes have been put forward,which has been widely developed and applied.Main research results of this paper are as follows:(1)We study the correlation properties of mutually unbiased bases on CP2.Based on these properties,we construct unitary matrix,and then construct a(N,N)threshold scheme on a p2-dimensional quantum system.This scheme constructs a single-particle quantum protocol involving only one qudit,which shows great advan-tages than other schemes in terms of scalability.For any number of participants N,this method can be used to structure a(N,N)threshold scheme.After analysis,the scheme can resist intercept-and-resend attack,entanglement-and-measure,Trojan horse attack and so on,which shows that the scheme is secure.(2)In d(?)d(d>2)quantum system,we construct 3(d-1)orthogonal product basis quantum states,and prove that the set of quantum states cannot be distin-guished by local operation and classical communication(LOCC).By comparing with other construction methods,the set of product basis quantum states constructed by this method satisfying cannot be distinguished by LOCC and contain the least num-ber of quantum states in d(?)d(d>2)quantum system.