Research On Visual Image Sharing Scheme With Essential Participants

Visual cryptography scheme(VCS)can share a binary secret image as multiple shadow images.Superposing shadows printed on transparencies of qualified sets,the secret can be directly observed visually by human visual system without computational resources.In particular,a(k,n)threshold VCS((k,n)-VCS)encrypts a secret image into n shadows.Superimposing any k shadow images and the human visual system can identify the secret information,while any set which contains less than k shadows cannot reconstruct the secret information.In practice,some participants(essentials)play more important roles t han others(non-essentials)when making decisions.To solve these problems,scholars have proposed visual cryptography scheme with essential participants((t,s,k,n)-EPVCS)which is of great significance since it provides different levels of importance to shadows.In order to reduce the size expansion of shadow images and reconstructed images,this paper proposes a new pattern of EPVCS which is constructed from a monotonic(K,N)-VCS based on integer programming.Primarily,for a(t,s,k,n)-EPVCS whose parameters is given,an integer programming model is constructed based on the quantitative relationship between the parameters in the two types of schemes and the essentiality and threshold conditions of(t,s,k,n)-EPVCS.By solving the integer programming model,the optimal parameters of(K,N)-VCS and allocation parameters are obtained.Then,according to the actual needs,the construction scheme of(K,N)-VCS is selected and the shadow images are generated by sharing the secret image.Finally,the shadow image of(K,N)-VCS is transformed into the shadow image of(t,s,k,n)-EPVCS according to the allocation parameters.The proposed scheme achieves size invariable if we adopt random grid-based VCS(RGVCS) to generate shadows.In order to improve the visual quality of restored images,a n EPVCS based on XOR operation is proposed in this paper((t,s,k,n)-XEPVCS).Firstly,we give a pre-scheme,XOR-based compound scheme(<(k₁,n₁),(k₂,n₂)>-XVCS)whose qualified sets are partitioned into v parts and we generate v pairs of basis matrices for pre-scheme.For a(t,s,k,n)-XEPVCS,it is decomposed into a combination of several<(k₁,n₁),(k₂,n₂)>-XVCS whose union of qualified sets is qualified set of(t,s,k,n)-XEPVCS.Definitively,we generate the final basis matrices for(t,s,k,n)-XEPVCS by concatenating basis matrices of<(k₁,n₁),(k₂,n₂)>-XVCS.In the procedure of reconstruction,implementing XOR operation on the shadows of qualified set,the secret image can be reconstructed completely and the size expansion is relatively small.To sum up,this paper focuses on two aspects of how to reduce size expansion and improve the visual quality of EPVCS.Theoretical analysis and experimental results verify the feasibility and practicability of the proposed scheme.