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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