Research On Analysis And Design Of Visual Cryptography Scheme

Due to the characteristics of secret sharing,image encryption,unconditionally security and simple decryption,visual cryptography can be used in the fields of group participation or control,civilian and national security image protection,and economy and military fields,which have the higher requirements on information security,especially has an important application value in the specific scene of lack of complex computing devices.In view of the fact that it has a very broad application prospect,visual cryptography has received considerable attention within the community of information security since its introduction,and its relevent research results are always found in the international high-level journals.In this paper,we give a research on visual cryptography from the following three aspects: scheme analysis,scheme construction and scheme extension.Thereinto,the analysis of visual cryptography scheme is helpful to understand the internal relationship between the various schemes,and has a certain guiding role in constructing visual cryptography schemes.The construction of visual cryptography scheme is mainly based on the optimization of the evaluation parameters(pixel expansion and relative difference)of the scheme.On this basis,we expand the visual cryptography scheme to make the generated shares display meaningful image information,so as to reduce the attacker's suspicion and easy share's management.Specific research contents are as follows:1.Analyze the relationship between schemes from the perspective of access structure in visual cryptography.Two concepts,equivalent participants and participants permutation,are introduced.Then it is pointed out that there may be a simplification or permutation relation between any two access structures,and it is proved that two visual cryptography schemes,constructed for the access structures under the above relation,are equivalent.In this way,the complexity of constructing visual cryptography scheme is reduced to some extent.2.Analyze the relationship between schemes from the perspective of secret sharing method in visual cryptography.For the two secret sharing methods: basis matrix and random grid,it is pointed out that the basis matrix can be represented by the random grid generation algorithm and the random grid generation algorithm can be represented by the basis matrix.Furthermore,the one-to-one correspondence between the basis matrix scheme and the random grid scheme is proved.3.Analyze the relationship between schemes from the perspective of secret recovery method in visual cryptography.For the two secret recovery methods: OR operation and XOR operation,basis matrices are adopted in the secret sharing process.By analyzing the composition of basis matrices,it is proved that the OR-based scheme and the XOR-based scheme are corre-sponding one by one under weak access structures.4.Aiming at the optimization of pixel expansion,the relationship between basis matrix and solution space of linear equations is analyzed,and a method of constructing basis matrices via linear equations is presented.Then by dividing the access structure and deleting the common columns,we construct an OR-based visual cryptography scheme for strong access structures via basis matrices.It reduces the pixel expansion effectively,which means that the storage space and transmission bandwidth are reduced.5.Aiming at the optimization of relative difference,according to the one-to-one correspondence between the basis matrix scheme and the random grid scheme,and by the method of randomly selecting a column from the basis matrices constructed via linear equations,we construct an OR-based visual cryptography scheme for strong access structures via random grids.It increases the relative difference effectively,which means that the visual quality of the recovered image is improved.6.According to the one-to-one correspondences between the basis matrix scheme and the random grid scheme and between the OR-based scheme and the XOR-based scheme,we prove the necessary and sufficient conditions for the XOR-based scheme to recover the secret image perfectly,where the pixel expansion and relative difference are both 1.Then by the partition of access structure,we propose a region-by-region construction of XOR-based visual cryptography scheme for weak access structures.It achieves the relative difference perfectly with smaller pixel expansion.7.To improve the visual quality of meaningful shares,first,the assignment of secret information pixels of the shares is determined by the OR-based visual cryptography scheme for(k,n)threshold access structures,and the distribution of secret information pixels of the shares is realized by the void and cluster algorithm;then,the assignment of non secret information pixels of the shares is determined by the assignment rules,which are designed based on the(k,n)threshold and the complementary cover images;finally,we propose a halftone visual cryptography scheme for(k,n)threshold access structures via error diffusion.The proposed scheme obtains better visual quality of shares,and removes the share's cross interference from other shares,which reduces the attacker's suspicions.Furthermore,the proposed scheme eliminates the burden that each participant may carry multiple shares.