Research On Secret Sharing Schemes For Two Typical Access Structures

Secret sharing scheme(SSS)is an important technology in cryptography,which is mainly used for key management and information protection.SSS encrypts a secret into several shares or subsecrets and distributes them to the participants among a group who have conflict interests but must cooperate.Only designated sets of participants can cooperate to recover the secret.SSS can establish a relationship of trust among the participants of a group.It has been widely used in secure multiparty computing,privacy protection,e-commerce and other areas of distributed cryptography.First of all,the concept of hierarchical secret sharing scheme is introduced.Based on the Chinese Remainder Theorem over polynomial rings,the disjunctive and conjunctive multilevel weighted threshold schemes are constructed,and the con-cepts of disjunctive multilevel weighted access structure and conjunctive multilevel weighted access structure are proposed.In this paper,integer linear programming is used to construct suitable modular polynomials with the sum of the orders of modular polynomials as the objective function and the corresponding multilevel ac-cess structure conditions as the constraint conditions.Compared with the previous schemes,the two schemes not only make the participants carry only a share,but also reflect their different privileges of participants in different security levels.Through experiments and theoretical analysis,it is proved that the scheme has perfect secu-rity.The multilevel access structures are suitable for key management systems with multiple security levels.Secondly,this paper introduces visual secret sharing scheme,who is also known as visual cryptography scheme(VCS).This paper puts forward two new ideas to realize the VC schemes for the general access structure.The first scheme is to design a suitable(k,l)-VCS to realize the general access structure by using the optimal multiple assignments mapping,and use the integer linear programming to find the optimal l and k.The second scheme is to use the integer linear programming to find the optimal(k,l)-VCS based on the idea of weighted distribution,and shares are distributed to participants by weight.It is proved that the visual secret sharing for general access structure can be realized by share sets of(k,l)-VCS,and the pixel expansion of two schemes are less than or equal to the pixel expansion logl·2O(klogk)of(k,l)-VCS.Experimental results show that schemes have perfect security and can recover secret images correctly.This paper proposes secret sharing schemes for two typical access structures,which provides theoretical support for the access strategy in current cloud storage environment,and have important application values in access control.The schemes proposed in this paper improve the previous results,extend the theory of secret shar-ing schemes,and have important theoretical significance in cryptography research.