Cryptography Reference
In-Depth Information
where s
A
is an elementary block consisting of one white and 2x 1 black
subpixels in which the jth subpixel, denoted as is
A
[j], is defined by
0
if j = x + 1 k;
s
A
[j] =
(3.5)
1
otherwise,
for 1 j 2x and 1 k x.
Figure 3.17 shows the elementary blocks of A for encoding x = 4 secrets.
As an example, we show how the subpixels in s
2
A
are computed by formula
(3.5). Since k = 2 and x+ 1k = 4 + 12 = 3, thus s
A
[3] = 0 and s
A
[j
0
] = 1
for 1 j
0
6= 3 8(= 2x) as shown in Figure 3.17(b).
(a)
(b)
(c)
(d)
FIGURE 3.17
Elementary blocks in E
A
: (a) s
1
A
, (b) s
2
A
, (c) s
3
A
, (d) s
4
A
.
We define the set of the elementary blocks for share B as follows:
E
B
= fs
B
j0 2
x
1g;
where s
B
is also an elementary block containing x white and x black subpixels
in which the jth subpixel, denoted as is
B
[j], is defined by
r
j
1 j x;
r
2x+1j
otherwise,
s
B
[j] =
(3.6)
where = btod(r
x
r
x1
:::r
2
r
1
), r
t
is the tth least signicant bit of is repre-
sent
ed
in binary (x-bit) in which 1 t x and 0 2
x
1 for 1 j 2x
and r
t
is the inverse of r
t
.
Figure 3.18
illustrates the elementary blocks of B for x = 4. Con-
sider s
4
B
. Since = 4 = btod(r
4
r
3
r
2
r
1
) = btod(0100)
2
, we have
(s
4
B
[1];s
4
B
[2];s
4
B
[
3]
;s
4
B
[4])
=
(r
1
;r
2
;
r
3
;r
4
) =
(
0; 0; 1; 0) an
d
(s
4
B
[
5]
;s
4
B
[6];
s
4
B
[7];s
4
B
[8]) = (r
24+15
;r
24+16
;r
24+17
;r
24+18
) = (r
4
;r
3
;r
2
;r
1
)=
(1; 0; 1; 1). Thus, s
4
B
is as shown in Figure 3.18(e).
Formulae (3.1) and (3.4) about the encoding of blocks in A and B, respec-
tively, for x = 3 can now be formulated in a more generalized form as follows.
The blocks in A are encoded by
(a
j
;a
j
;:::;a
j
) = (permute(s
1
A
;
j
);permute(s
2
A
;
j
);:::;permute(s
A
;
j
));
(3.7)
where
j
is a random permutation of f1; 2;:::; 2xg for 1 j .
Given a set of corresponding pixels (p
1
;p
2
;:::;p
x
)
j
in block j of strip k in
(P
1
;P
2
;:::;P
x
), b
j
(i.e., block j of chord k in B) is encoded by
b
j
= permute(s
btod(rotate(p
1
p
2
:::p
x
;k1))
;
j
)
(3.8)
B
Search WWH ::
Custom Search