Cryptography Reference
In-Depth Information
FIGURE 10.10
TCH.
gorithm. Therefore, the dealer should control the quality of all reconstructed
secret images before delivering all transparencies. That is, all transparencies
should be indistinguishable.
10.3.4 PS1 and PS2
In 2009, De Prisco and De Santis [20] proposed 2-out-of-n and n-out-of-n
cheating prevention schemes, as shown in
Figure 10.11.
They are obtained by
simply adding an extra column with all 0s to the base matrices of the schemes
of Naor and Shamir.
In the following, we describe another 2-out-of-n cheating prevention
scheme, as shown in
Figure 10.12
a
nd proposed in the same paper. This scheme
does not require the use of a complementary image. The base matrices of the
scheme have dimension n (2
n
+ n + 1). The white base matrix C
0
has the
following columns: all the possible 2
n
binary column vectors of length n, one
additional column with all 1s and n additional columns with all 0s. Whereas,
the black base matrix C
1
has the following columns: all the possible 2
n
binary
column-vectors of length n, one additional column with all 0s in the n columns
of the identity matrix of dimension nn.
The base matrices of a 2-out-of-3 PS2 scheme are shown as follows:
2
3
0
0
0
0
1
1
1
1
0
1
0
0
4
5
C
0
=
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
2
3
0
0
0
0
1
1
1
1
0
1
0
0
4
5
C
1
=
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
We refer the readers to [20] for more details.
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