The Construction Of Two Secret Sharing Schemes

Secret sharing is an important key management technology in the field of information security,which can establish trustworthy relationship among a group of mutual suspicious and cooperative participants.So it is widely used in the fields of privacy protection,public key cryptography,online transactions,e-commerce,confidential communication and so on.In this thesis,I designed two secret sharing schemes.The first one is a secret sharing scheme for the general access structure,which is different from the previous schemes built on the integer ring but is built on the polynomial ring.This scheme avoids the shortcomings of previous schemes which are difficult to find primes and difficult to solve nonlinear integer programming problems.In this scheme,each participant only needs to take a share.This scheme can grant different participants with different privileges.The second scheme is a(k,n)visual cryptography(VC)scheme and it keeps two advantages of high contrast and low pixel expansion.A(k,n)-VC scheme can encode a secret image into n shadows printed on transparencies and then distributed among a group of n participants secretly,and it reveals the secret image by stacking no less than k of them.Its decryption requires no computation and attracts much attention in image security applications.The pixel expansion and contrast are two important characteristics to evaluate the visual quality of the revealed secret image for a(k,n)-VC scheme.A(k,n)XOR-based VC(XVC)schemes can greatly improve the visual quality.Previous methods required complex computation and resulted high pixel expansion when they were used to construct such schemes.In this thesis,a pixel expansion adjustable(k,n)-XVC scheme is proposed,which allows pixel expansion to be changed among 2k-1-1 different values.It ensures each pixel being exactly recovered with the same average contrast no matter it takes any pixel expansion value The least pixel expansion is much smaller than the previous schemes.The proposed scheme can be easily implemented on any conventional OR-based(k,n)-VC(OVC)scheme.