Cryptography Reference
In-Depth Information
to rows i
1
;i
2
;K;i
q
are indistinguishable in the sense that they contain the
same matrices with the same frequencies.
Figure 10.2
shows the basic concept of a 2-out-of-2 visual secret sharing
scheme. The secret image is shared through two noise-like transparencies: T
1
and T
2
. In this case, a block consists of 4 subpixels. Each black(white) pixel
of the secret image is turned into two black and two white subpixels of T
1
and
10.2.2 Cheating in VC
In [8], Horng et al. showed that cheating is possible in k-out-of-n VC. Let's
take the 2-out-of-3 visual secret sharing scheme shown in Figure 10.3 as an
example. A secret image is encoded into three distinct transparencies, denoted
T
1
, T
2
, and T
3
. Then, the three transparencies are respectively delivered to
Alice, Bob, and Carol. Without loss of generality, Bob and Carol are assumed
to be collusive cheaters and Alice is the victim. During the cheating activity,
Bob and Carol use S
2
and S
3
to create forged transparency S
0
2
such that su-
10.4.
Precisely, by observing the following collections of 3 3 matrices that
are used to generate transparencies, collusive cheaters can predict the actual
structure of the victim's transparency so as to create S
0
2
.
2
4
3
5
g
1
0
0
C
0
= fall the matrices obtained by permuting the columns of
1
0
0
1
0
0
2
3
1
0
0
4
5
g
C
1
= fall the matrices obtained by permuting the columns of
0
1
0
0
0
1
By observing the above matrices, two rows of above C
0
or C
1
matrix are de-
termined by collusive cheaters. Therefore, the structure of the corresponding
block of S
1
is exact the remaining row. For presenting a white pixel of cheating
image, the block of S
0
2
is set to be the same structure of S
1
. For presenting a
black pixel of cheating image, the block of S
0
2
is set to be the different struc-
ture of S
1
. For example, if the block of S
1
is [010], then S
0
2
is set to be [010]
for a white pixel or it is set to be [001] for a black pixel.
We note that if the forged shares deviate too much from the original shares
then the victim will notice the difference and suspect being cheated. Therefore,
a necessary condition for a cheating activity to be successful is that the forged
shares must be indistinguishable from the original shares. There are different
cheating activities defined in [15].
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