Cryptography Reference
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repeated 2m + 1 times in the generation phase. In the reconstruction phase,
the voting method is used to recover the best result out of the shared bits in
order to restore the original grayscale value of the pixel.
Let A be the binary matrix representing the secret image.
Distributionphase.
The dealer:
generates a white image (D) and n shares B
1
;:::;B
n
with D as secret
image; compute intermediate matrices C
1
;:::;C
n
where C
i
= B
i
&A,
for i = 1;:::;n;
generates a random matrix R;
distributes the n shares A
1
;:::;A
n
where A
I
= RC
i
for i = 1;:::;n
.
FIGURE 5.2
Ulutas et al. [18] construction for (2,n) Boolean probabilistic VCS.
5.7.2 (n,n) Scheme for Binary Images (Wang)
A construction similar to the one above described, was proposed by Wang also
for a (n,n) probabilistic VCS. The construction is given in Figure 9.6
Let A be the binary matrix representing the secret image.
Distributionphase.
The dealer:
generates n 1 random matrices B
1
;:::;B
n1
;
distributes the n shares A
1
;:::;A
n
where A
1
= B
1
, A
i
= B
i1
B
i
,
and A
n
= B
n1
A.
Reconstructionphase.The n participants reconstruct the secret im-
age as follows:
superimpose their shares executing binary XOR operation to obtain
A
0
= A
1
A
2
A
n
.
FIGURE 5.3
A construction for (n;n) Boolean probabilistic VCS.
In such a scheme it is easy to see that a black pixel in the secret image
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