Cryptography Reference
In-Depth Information
2.6.2 The (2;n)-Threshold AS Schemes
In [1] a constructions of (2;n)-threshold schemes is provided. The construc-
tion uses, as a building block, the base matrix S
for the black color of the
(2;n)-threshold scheme for black and white images dened in [2]. Matrix S
is defined as all the binary column-vector with weight
n
bn=2c
, with the sub-
stitutions 1 $ and 0 $. For example, for n = 4, we have
2
4
3
5
=
2
4
3
5
1 0 0 1 0 1
1 1 0 0 1 0
0 1 1 1 0 0
0 0 1 0 1 1
S
4
=
Then, to obtain the color scheme, the black and white pixels are substituted
with the rows of a specic (2; 2)-threshold color scheme. For example, using
the KY scheme for the set of colors f
C
;
Y
;
G
g with m = 4 provided in the
previous section and substituting with the rst row of the base matrix for
a given color and with the second row of the base matrix we get the base
matrix for that color. For example, to get the base matrix for color
Y
for the
(2; 4)-threshold scheme, we substitute in S
4
the symbol with
Y
C
and the
symbol with
YC
.
The scheme that we obtain is:
2
3
C
YC
Y
C
Y
C
YC
Y
C
Y
C
Y
C
YC
Y
C
Y
CY
C
Y
C
Y
C
Y
C
Y
C
YC
Y
C
Y
C
Y
C
Y
C
YC
Y
C
Y
C
Y
4
5
S
C
=
2
4
3
5
Y
CY
C
Y
C
Y
CY
C
Y
C
Y
C
Y
CY
C
Y
C
YC
Y
C
Y
C
Y
C
Y
C
Y
CY
C
Y
C
Y
C
Y
C
Y
CY
C
Y
C
Y
C
S
Y
=
2
4
3
5
Y
CY
C
Y
C
Y
CY
C
Y
C
Y
C
Y
CY
C
Y
C
YC
Y
C
Y
C
Y
C
Y
C
Y
CY
C
Y
C
Y
C
Y
C
Y
CY
C
Y
C
Y
C
S
Y
=
2.7 Other Schemes
In [9] Shyu proposes a construction that is very similar to the one used in [7,
11]. However, the model, although for many aspects equal to the SC model, has
a crucial difference: the author assumes that the color perceived by the human
eyes is an "average" of the colors present in the subpixels of the reconstructed
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