Cryptography Reference
In-Depth Information
2.4.2 The BDD Schemes
Blundo et al. [2] focus on schemes with maximal contrast. They consider the
weak contrast property and dene the contrast as = (h`)=(h + `). The
following results are provided in [2]:
A rst construction of c-color (2;n)-threshold Color-VC schemes with max-
imal contrast. The construction requires c > n.
A proof that the above condition c > n is necessary to have a maximal
contrast scheme. It turns also out that, among the schemes with maximal
contrast, the schemes provided by the first construction are also with optimal
pixel expansion.
A second construction of c-color (2;n)-threshold Color-VC schemes. Such a
construction gives a better pixel expansion with respect to the first one but
the schemes are not with maximal contrast.
A construction of maximal contrast c-color (n;n)-threshold Color-VC
schemes with improved pixel expansion with respect to those provided
in [10].
We refer the interested reader to [2] for details about the constructions
and the lower bound cited in this section.
2.4.3 The KY and YL Schemes
Koga and Yamamoto [7] and independently, Yang and Laih [11] provide (k;n)-
threshold c-color schemes that improve on the pixel expansion of the schemes
in [10, 2]. Here we report the construction provided in [11], but the one in [7]
is equivalent.
Construction 1 The construction exploits as a building block the base ma-
trices B and B of a scheme for black and white images. In order to obtain
the base matrix B i for color i we can concatenate one modified copy of B
with c1 modied copies of B . The required modifications are the following:
in B we substitute with color i while in the c1 copies of B we substitute
with the remaining c 1 colors (one color per copy). The pixel expansion
of the c-color scheme is c times the pixel expansion of the original black and
white scheme.
As an example, consider the following (3; 3)-threshold 3-color scheme. We
start with the base matrices of a (3; 3)-threshold scheme for black and white
images as defined in the paper by Naor and Shamir [8] (however, the con-
struction works with any other choice of the black and white base matrices):
2
3
2
3
4
5
4
5
B =
B =
 
 
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