Cryptography Reference
In-Depth Information
FIGURE 4.3
An example of extended visual cryptography scheme (EVCS). Two resulting
shadow images (left and middle) and reconstructed secret image (right).
The reconstructed pixel has 3 or 4 black subpixels if the original secret pixel
is white or black, respectively. In this scheme, the relative contrasts are given
as
R
=
S
=
1
4
. Figure 4.3 shows an example of resulting shadow images
and reconstructed secret image. The size of all images are 128 128 pixels,
because all the original shadow and secret images have 64 64 pixels.
Ateniese et al. also pointed out some of the most important aspects of the
extended capability [2]. One is related to the contrasts of images. A trade-off
between two relative differences exists,
R
and
S
, in any (k;k) EVCS as
below:
2
k1
R
+
k
k 1
S
1:
This means we cannot increase both contrasts of a reconstructed image and
shadow images,
R
m and
S
m, simultaneously. They also specified the lower
bound of the pixel expansion m in (k;k) EVCS as below:
m 2
k1
+ 2:
This means we need more pixels to obtain EVCS. Although people would like
contrasts to be as large as possible and pixel expansion as small as possible,
there exist certain limits of them.
4.2.3 Random Grids
Random Grids (RG) give a very different approach to visual cryptography,
which can keep the size of resulting shadow images to be the same as that
of the original image. In other words, the pixel expansion of this method is
m = 1 and no more expansion problems exist. The method is first introduced
by Kafri and Keren in 1987 [17] and reinvestigated by Shyu in 2007 [37]. A
random grid R is defined as a two-dimensional array of pixels. Each pixel is
either transparent (white) or opaque (black) by a coin-flip procedure. The
numbers of transparent pixels and opaque pixels are probabilistically same
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