Research On Secret Sharing Schemes On Two Types Of Quantum Systems

Secret sharing is an important,research direction in the field of cryptography.The main idea is that the distributor sends the secret(classical or quantum)to severa.l participants.When enough participants cooperate to recover the secret,one or part of the participants can not recover the secret.In 1979,Shamir and Blake-ly independently proposed the concept of classical secret sharing schemes,which attracted scholars'attention and further research.Quantum secret sharing is a pro-gressive study of classical secret sharing and one of the core contents of quantum cryptography.Hillery et al.proposed quantum secret sharing scheme for the first time in 1999.In the process of quantum secret,sharing,if there are external eaves-dropping or dishonest participants cheating,it will be found,which provides a.new direction for the security management of secure communications.Nowadays more and more quantum secret sharing schemes have been proposed.Main contribut ions of this paper are summarized as follow:(1)We analyze the properties of unbiased bases on odd prime D dimensional quantum systems,and study the(n,n)quantum threshold secret sharing scheme proposed by Tavakoli A et al.Based on this scheme,we study the case of even-dimensional quantum system in this paper.According to the characteristics of standard orthogonal basics on even dimension,obtain the properties satisfied by d group of standard orthogonal bases on even dimension.According to the properties of standard orthogonal basis and unitary transformation on even dinension,a new(n,n)threshold quantum secret sharing scheme is proposed.Finally,we make a security analysis.(2)We analyze the(n,n)threshold quantum secret sharing scheme proposed by Ouyang et al.The number of participants in the scheme is limited to n=4?+1,??Z+.In this paper,we study the case where the number of participants n is arbitrary in the scheme.And a threshold quantum secret sharing,scheme is constructed according to the properties of quantum circuits acting on quantum states,in which the quantum circuit is a provably secure quantum circuit composed of Clifford group gates and Toffoli gates.Finally,we use the property of the quantum circuit to analyze the security against dishonest participant attacks.