Cryptography Reference
In-Depth Information
0 the weak and the strong contrast property are equivalent. The annihilator
presence = (m1)=m, that is only one out of the m pixels is of the original
color, while the remaining m 1 are annihilated.
As an example, we report the (3; 3)-threshold 3-color scheme. Here are the
three base matrices:
2
3
1
1
1
2
2
2
3
3
3
B
1
=
4
5
1
2
3
1
2
3
1
2
3
1
2
3
2
3
1
3
1
2
2
3
1
1
1
2
2
2
3
3
3
B
2
=
4
5
1
2
3
1
2
3
1
2
3
3
1
2
1
2
3
2
3
1
2
3
1
1
1
2
2
2
3
3
3
4
5
B
3
=
1
2
3
1
2
3
1
2
3
2
3
1
3
1
2
1
2
3
The pixel expansion, that corresponds to the number of columns in the
base matrices, is m = c
k1
= 3
2
= 9. The above base matrices work only in
the vv model. Although the annihilator color is not explicitly used, it appears
because of the special property. Indeed, implementing the special property
using the trick suggested earlier, the base matrices become the following:
2
3
111222333
123 123 123
12323 13 12
4
5
B
1
=
2
3
111222333
123 123 123
3 1212323 1
B
2
=
4
5
2
3
111222333
123 123 123
23 13 12123
B
3
=
4
5
Hence, the real pixel expansion is m = c
k
= 3
3
= 27. In this particular
case superposing 3 shares we get 26 black pixels out of 27 and just 1 colored
pixel. That is, the annihilator presence is = 26=27 (about 96%).
This approach doesn't seem practicable for images, but it can be used for
other applications, like sharing passwords associating, for example, a digit to
each color. For example, as reported in [10], if we use pixels of diameter 0:5
cm with 9 colors we can build a (3; 9)-threshold visual scheme with 9 colors
using 9
2
= 81 pixels for each color of the password; on a standard A4 page
there is room for a 90 digit password.
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