Cryptography Reference
In-Depth Information
4.3.2 An Encryption Example
Assume that we have a gray-scale image with four secret images as shown in
Fig. 4.9(a). The image is represented by eight bit planes. The first plane P
1
is shown in Fig. 4.9(b). The scheme uses the encryption function to generate
two shadows for P
1
. The shadows are shown in Fig. 4.9(c) and Fig. 4.9(d).
The random sequences used to rearrange the sub-shadows be RA
1
=(321
4) and RB
1
= (1 4 3 2). The element ra
1
= 3 means a
1
should be rearranged
to the third location of the plane. The shape of a
1
is an inverted triangle.
However, the shape of the third location of the plane is an equiangular triangle.
In order to match the shape of a
1
with that of a
3
, we use the vertical-reversion
operation to reverse a
1
. In addition, the element rb
2
= 4 means that b
2
should
be put in the fourth location of the plane. For b
2
, we use the horizontal-
reversion operation to reverse b
2
. The shadows α
1
and β
1
of P
1
are shown
in Fig. 4.9(e) and Fig. 4.9(f), respectively. Following the same encryption
process, we can obtain the final shadows S
1
and S
2
shown in Fig. 4.9(g) and
Fig. 4.9(h), respectively.
4.3.3 The Decryption Process
Before starting the decryption process, the scheme decomposes each shadow
into eight planes. For example, the first shadow S
1
is decomposed into eight
bit planes, α
1
, α
2
,, α
8
. Next, the scheme performs the bit plane recon-
struction process to reconstruct the original binary plane P
j
. The diagram of
the reconstruction process for P
j
is shown in Fig. 4.10.
The first step of the reconstruction process is to separate the sub-region
from the shadows α
j
and β
j
. The second step is to move the sub-shadows, a
i
and b
i
, back to their original locations, a
i
and b
i
. The scheme uses the random
sequences, RA
j
ra
2
k
)andRB
j
rb
2
k
), to restore
the original sub-shadows. Only legal participants own the secret keys used
to generate the sequences RA
j
and RB
j
to rearrange the locations of the
sub-shadows. In this step, right-rotation, left-rotation, horizontal-reversion,
and vertical-reversion operations are also used to change the shape of the
sub-shadows so as to fit in with the original locations.
In the third step, the decryption function is used to decrypt the secret
information in the restored a
i
and b
i
. The scheme stacks the sub-shadows,
a
i
and b
i
, using the decryption function f
d CLF
to reconstruct the original
sub-region T
i
, which is defined as follows,
=(ra
1
ra
2
=(rb
1
rb
2
if a
iγ
∩b
iγ
1,
∈C
1
∈C
1
;
f
d CLF
(a
i
,b
i
)=
(4.7)
0,
otherwise,
where a
iγ
is the γ-th block of a
i
,andb
iγ
is the γ-th block of b
i
.LetT
iγ
=
f
d CLF
(a
i
,b
i
), where T
iγ
is the γ-th bit of T
i
.
