Research On A New Quantum Secret Sharing Scheme

Secret sharing is an important subject of modern cryptography,which is a protocol that a group of participants share the secret together.The dealer splits the secret into a number of sub-secrets and distributes the shared secret into participants through the channel.In this way,each participant can get some information about it,where only certain authorized subsets can collaboratively recover the secret,the participants of unauthorized subsets can not get any information about it.Since Hillery et al.proposed the first quantum secret sharing scheme in 1999,many scholars home and abroad have invested in this research and have gained a lot of scientific achievements to make it rapid development and application.However,the construction of the quantum secret sharing schemes which can realize more quantum access structures is one of the most important problems in the field of modern quantum cryptography,it needs to be further studied and analyzed.This paper is aimed to study the construction and the security of quantum secret sharing schemes,and it focuses on the advantages and disadvantages of the existing quantum secret sharing schemes.And we do some improvements based on these schemes.Thus,a new quantum secret sharing scheme is constructed.Then the security of the scheme is analyzed quantitatively and qualitatively.Main contributions of this paper are summarized as follow:(1)Analyzing the limitations of an improved quantum secret sharing scheme proposed by Nascimento et al.in implementing the quantum access structure.When the number of participants is large,it is difficult to construct a perfect quantum secret sharing scheme which can realize some quantum access structures.Therefore,a new improvable quantum secret sharing scheme which is based on this scheme is proposed.The new scheme can realize all hyperstar,threshold and hypercycle quantum access structures abstractly.Finally,the security of the scheme is analyzed.(2)The paper focuses on a(n,n)-threshold quantum scheme which is proposed by Rahaman et al.based on local distinguishability.It is clear that the special X and Y basis are used for local measurements in check phase of this scheme to detect the eavesdropping.But X?Y basis have a lack of generality.So the special basis is extended to a general one in this paper.For this reason,this paper uses the gen-eral basis to construct a new(n,n)-threshold quantum secret sharing scheme based on local distinguishability.Finally,this paper comprehensively and systematically analyzes the security of the new scheme in four aspects.