Cryptography Reference
In-Depth Information
all zeros. Indeed, the matrix corresponding to the i-th subtransparency of U
0
is the same as the i-th subtransparency of T, which from the property of
the XOR operator and the composition of the Naor-Shamir basis matrices
corresponds to the original image. Moreover, the matrices corresponding to
the subtransparency of U but the i-th one contains all ones. Hence, from the
property of the XOR operator such subtransparencies contains all zeros in U
0
.
The reconstruction phase requires a qualified set of p participants to per-
form exactly 4p reversing operations and 4p1 stacking operations, since, as
seen in
Section 9.4.1,
the XOR operation can be implemented by means of 3
ORs and 4 NOTs operations.
n
o
n
f1; 4g;f2; 3; 4gg
o
Example 6 Let P = f1; 2; 3; 4g,
0
=
. Let
S
1
and S
1
be the basis matrices associated to the XOR-(2,2)-VCS for X
1
and
let S
2
and S
2
be the basis matrices associated with the XOR-(3,3)-VCS for
X
2
defined as follows:
X
1
;X
2
=
2
3
2
3
1
0
1
0
4
5
4
5
;
1
1
1
1
S
1
=
S
1
=
1
1
1
1
1
0
0
1
2
4
3
5
2
4
3
5
:
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
S
2
=
S
2
=
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
Let I =
be the original image. The transparencies are computed
0
1
0
as follows:
1
0
1
0
1
1
1
0
0
1
1
1
t
0
1
=
t
1
=
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
t
0
2
=
t
2
=
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
t
0
3
=
t
3
=
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
t
0
4
=
t
4
=
0
0
1
1
0
1
0
0
0
0
0
0
Participants in X
2
= f2; 3; 4g reconstruct the original image by computing
1
0
0
1
0
1
1
0
0
1
1
1
T
0
=
T =
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
0
U
0
=
U =
:
0
1
0
1
1
1
0
1
0
0
0
0
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