On Converting Secret Sharing Scheme to Visual Secret Sharing Scheme

Traditional Secret Sharing (SS) schemes reconstruct secret exactly the same as the original one but involve complex computation. Visual Secret Sharing (VSS) schemes decode the secret without computation, but each share is m times as big as the original and the quality of the reconstructed secret image is reduced. Probabilistic visual secret sharing (Prob.VSS) schemes for a binary image use only one subpixel to share the secret image; however the probability of white pixels in a white area is higher than that in a black area in the reconstructed secret image. SS schemes, VSS schemes, and Prob. VSS schemes have various construction methods and advantages. This paper first presents an approach to convert (transform) a (k, k)-SS scheme to a (k, k)-VSS scheme for greyscale images. The generation of the shadow images (shares) is based on Boolean XOR operation. The secret image can be reconstructed directly by performing Boolean OR operation, as in most conventional VSS schemes. Its pixel expansion is significantly smaller than that of VSS schemes. The quality of the reconstructed images, measured by average contrast, is the same as VSS schemes. Then a novel matrix-concatenation approach is used to extend the greyscale (k, k)-SS scheme to a more general case of greyscale (k,n)-VSS scheme.