Cryptography Reference
In-Depth Information
are selected from C
1
. Hence, the first bit of T
1
is 1. The second blocks of a
1
00
11
00
11
and b
1
are
, respectively, which are selected from C
0
. Hence,
the second bit of T
1
is 0. The final reconstructed plane is the same as the
plane demonstrated in Fig. 4.9(b).
and
4.3.5 The Proposed Scheme Extension
The scheme places the sub-shadows in different locations using rotation and
reversion operations on all planes to enhance the security. The legal partici-
pants can restore all of the information from the reconstructed image, since
they own the secret keys to generate the random sequences to rearrange the
rotated and reversed sub-shadows.
If a sender only wants to reveal part of the secret images to some spe-
cific participants, he can arrange part of the sub-shadows, which is available
for the participants, in the fixed locations and randomly disperse the other
sub-shadows to the remaining locations to increase the complexity of the de-
cryption process. The participants are thereby unable to restore the complete
secret images.
4.4 The Proposed (T, N)-VSS Scheme
In this section, the proposed (2, 2)-VSS scheme is extended into a (t, n)-VSS
scheme. Here the gray-scale image is split into n shadows. In addition, any t
legal participants can see the secret images by stacking their shadows together.
4.4.1 The Proposed Scheme Extension
Let T =T
1
,T
2
,,T
2
k
be the set of sub-regions, and each sub-region is
used to paste a secret image. The scheme represents the image by eight bit
planes. Let P =P
1
,P
2
,,P
8
be a set of eight planes. For each sub-
region T
i
, the scheme generates n sub-shadows for the sub-region using the
encryption process. The shadow generation process is shown in Fig. 4.11.
The scheme maps each bit of T
i
into a block from the codebooks C
′
0
or C
′
1
using different shadows. C
′
0
consists of several block patterns of the shadows
generating for the white input bit, and C
′
1
consists several block patterns of
the shadows generating for the black input bit. The probabilities of 0 and 1
appeared in the block are like.
The scheme next rearranges each sub-shadow in different locations on the
plane. The scheme generates n random sequences for P
j
by using the secret key
to relocate the position of the sub-shadow. The right-rotation, left-rotation,
horizontal-reversion, and vertical-reversion operations are used to change the
shape of the sub-shadows so as to be suitable in the new location. The scheme