Cryptography Reference
In-Depth Information
2
4
3
5
; F
3;4
(i;S
2
) =
2
4
3
5
:
ii ii ii
ii
ii ii ii
ii
F
3;4
(i;S
2
) =
The vertical bars identify the 4 blocks. As can be seen each block is given by
1 black row, and the remaining rows lled, in this order, by one row of i's and
the rows of S
2
(or S
2
), from the first to the last. Using the above F matrices
we can build the following 3-color (3; 4)-threshold scheme.
2
3
1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3
1 1 2 2 3 3
4
5
;
B
1
=
2
3
2 2 2 2 2 2 1 1 1 1 1 1 3 3 3 3 3 3
2 2 1 1 3 3
4
5
;
B
2
=
2
3
3 3 3 3 3 3 1 1 1 1 1 1 2 2 2 2 2 2
3 3 1 1 2 2
4
5
:
B
3
=
Construction 3 builds a c-color (k;n)-threshold scheme with pixel expan-
sion m = c
k
m
0
, where m
0
is the pixel expansion of the black and white
scheme used as building block. The thresholds ` and h depend on the b&w
scheme used as building block, If such a scheme is with perfect reconstruction
of black pixels the resulting scheme has ` = 0, h 1. Notice that the contrast
property satisfied is the weak one.
Using as a building block the best, with respect to the pixel expansion,
b&w (k 1;k 1)-threshold scheme, provided in [8], whose pixel expansion
is m
0
= 2
k2
, the resulting scheme has pixel expansion
n
k
2
k2
:
m = c
For k = n the pixels expansion is m = c2
n2
. The model assumes the weak
contrast property. The parameters h and ` are h = 1 and ` = 0 and the
annihilator presence is = (m 1)=m.
We remark that the schemes of [4] are constructed with the restriction that
the shares have only one colored pixel. This is not a restriction on the model
but just on the kind of schemes that can be constructed. Although this limits
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