Research Of Visual Cryptography Scheme Based On Group Structure

Visual cryptography is one kind secret sharing technology aimed at image which takestransparency as share, and can decode concealed images just with visual system of human being.The simple characteristic of secret recovering in visual cryptography can be presented asoperator “OR”. However, the easy operator “OR” has restricted the result of secret recovering,and the fundamental reason is that the algebraic structure is semi-group constructed by “or”. Asthe increasing popularity of all kinds of intelligent equipments and high-speed image processingtechnology, it will be truth or have been truth that transparency will be replaced byelectromagnetic media as the carrier of shares in visual cryptography, which provides superiorexternal environment for group structure being adopted. Group structure not only makes secretimages recovered perfectly to be possible, but also affords theory basics for designing visualcryptography schemes in the new condition.“XOR” operator is the simplest and most typical operation which can construct groupstructure. In this dissertation, the research upon group structure of visual cryptography is carriedout based on “XOR” operator. It is proved from a view of information entropy that the idealvisual cryptography scheme (VCS) can be realized by the operation of “XOR”, and the theoremof existence is proposed, then an ideal VCS which can recover secret image perfectly is designed,which based on the lucubration on the existence of ideal VCS.As the threshold structure does not meet the theorem of existence, a loop operator has beendesigned to construct one kind of basis matrices. Furthermore, a new secret recovery process hasbeen proposed which achieves a threshold structure visual cryptography with low pixelexpansion and perfect recovered secret image without distortion. Based on this, sharingcombined and extraction algorithm has been designed by changing the sharing memory model,then one visual cryptography scheme with same size of shared copies and secret images as wellas no distortion.The storage space consumption can be quite large when participants become more in thetwo kinds of no distortion visual cryptography schemes. According to the problem, byconstructing the optimization model for visual cryptography based on group structure, aXOR-based threshold scheme is designed. In this scheme, the problem of basic matrixconstruction is translated to evaluation of probability, and the shares are generated by choosingencryption rule with probability-matrix. The scheme not only improves the contrast greatly, butalso no pixel expansion. This dissertation lays the foundation for research of perfect recovery.