Image Secret Sharing - Visual Cryptography and Secret Image Sharing - page 376

used, then I s cannot be restored. The threshold is indispensable in color image
sharing.
14.2 State of the Art
Applying visual cryptography techniques to color images is a very important
area of research because it allows the use of natural color images to secure
some types of information. Due to the nature of a color image, this again helps
to reduce the risk of alerting someone to the fact that information is hidden
within it. It should also allow high quality sharing of these color images. Color
images are also highly popular and have a wider range of uses when compared
to other image types. Many of the techniques presented within this section
use halftone technologies on the color images in order to make them work
with visual cryptography. That is why color visual cryptography is presented
within this section.
In 1996, Naor and Shamir published a second article on visual cryp-
tography "Visual Cryptography II: Improving the Contrast via the Cover
Base" [23]. The new model contains several important changes from their
previous work; they use two opaque colors and a completely transparent one.
The first difference is the order in which the transparencies are stacked.
There must be an order to correctly recover the secret. Therefore, each of
the shares needs to be predetermined and recorded so recovery is possible.
The second change is that each participant has c sheets, rather than a single
transparency. Each sheet contains red, yellow, and transparent pixels. The
reconstruction is done by merging the sheets of participant I and participant
II, i.e., put the i-th sheet of II on top of the i-th sheet of I and the (i + 1)-th
of I on top of the i-th of II.
The two construction methods are monochromatic construction and
bichromatic construction. In the monochromatic construction, each pixel in
the original image is mapped into c subpixels and each participant holds c
sheets. In each of participant I sheets, one of the subpixels is red and the
remaining c 1 subpixels are transparent. In each of participant II sheets,
one of the subpixels is yellow, the other c 1 subpixels are transparent. The
way the sheets of participant I and II are merged is by starting from the sheet
number 1 of participant I, then putting sheet number 2 of participant II on
top of it, then sheet number 2 of participant I on top of that, and so on.
The order in which subpixels of participant I are colored red constitutes a
permutation on f1; ;cg and the order which the subpixels of participant
II are colored yellow constitutes a permutation . and are generated as
follows: is chosen uniformly at random from the set of all permutations on
c's elements. If the original pixel is yellow, then = , therefore each red
subpixel of the i-th sheet of participant I will be covered by a yellow subpixel