Size-invariant two-in-one image secret sharing scheme based on gray mixing model

TiOISSS (Two-in-One Image Secret Sharing Scheme) can reconstruct the secret through computation and realize secret preview recovery when the power system is destroyed or the network is paralyzed. However, the visual quality of previewing images obtained by the existing TiOISSS is not satisfactory and usually affected by pixel expansion. To resolve the two problems, this paper introduces multiple gray values in the share image generation stage and establishes an optimization model to obtain the grayscale probabilistic matrix needed in the encoding stage. By using the probability matrix, a secret sharing algorithm is designed to obtain size-invariant shares with multiple gray values. Then, the secret information of another image can be shared and embedded into the multi-level gray shares through Lagrange polynomials over finite fields. In the decryption stage, the electronic shares can be directly superimposed based on a gray mixing model, or they can be printed to transparent films by a multi-level gray printer and then superimposed to obtain the preview image. If computational devices are available, a high-resolution gray image can be obtained by Lagrange interpolation over finite fields. Experimental results indicate that the proposed scheme is effective for generating shares without pixel expansion and improving the preview image quality.