Cryptography Reference
In-Depth Information
In the following, we discuss all these issues. We start by defining the secret
and the shares palettes as follows:
Secret palette: this is the set of colors used in the secret image. This is a
finite set of c colors (we can have at most one color per pixel). To make
notation easier we will denote these colors simply with the set of integers
f1; 2;:::;cg. For the colors white, black, red, green, blue, cyan, magenta,
and yellow we will also use the corresponding symbol (;; R ; G ; B ; C ; M ; Y )
instead of the palette index.
Shares palette: this is the set of colors that we can print on the shares or
obtain by superposing printed shares. The shares palette might be the same
as the original palette, or it might be augmented with some (or even many)
other colors. Most of the schemes used in the literature augment the shares
palette with the colors and . We denote the colors in the shares palette
with the set of integers f1; 2;:::;dg. When the shares palette is a superset
of the secret palette (this is the case in almost all of the scheme presented
in this chapter) we have that d c and to simplify the notation we assume,
without loss of generality, that the first c colors of the shares palette are
exactly those in the secret palette.
The secret image consists of a collection of pixels, each one with a color of
the secret palette. As for B&W-VC, each pixel of the secret image is encoded
in the shares into a certain number m of subpixels. Such an integer m is the
pixel expansion of the scheme.
In order to define a scheme we need to specify the qualified and the non-
qualified set of participants. There are n participants. For simplicity we con-
sider only the case of threshold schemes: Any set of at least k participants is
a qualified set, while any set with less than k participant is a nonqualified set
of participants.
In order to share each pixel of the secret image a trusted third party has to
create and distribute shares to the n participants. The creation of the shares
is defined using distribution matrices. These are c collections (multisets) of
nm matrices C 1 ;C 2 ;:::;C c , whose elements are in the shares palette.
To share a secret pixel of color i, the dealer randomly chooses one of the
matrices in Ci i and distributes row j to participant j. Thus, the chosen matrix
defines the m subpixels in each of the n transparencies.
An example of distribution matrix is the following:
2
3
11 M 1
R 1 12
2 1 13
M 1 GB
4
5
D =
In this case, there are n = 4 participants (number of rows in the distri-
bution matrices) and the pixel expansion of the scheme is m = 5 (number of
 
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