Cryptography Reference
In-Depth Information
of VCRG-3, respectively, for binary image B as in Figure 7.3.
Figure 7.4
illus-
trates the implementation results of Algorithm 4 where (a), (b), and (c) are
the three random grids produced, namely R
1
, R
2
, and R
3
, respectively; (d),
(e) and (f) are the superimposed results of R
1
R
2
, R
1
R
3
, and R
2
R
3
,
respectively; and (g) is the result of R
1
R
2
R
3
.
FIGURE 7.3
Binary image B in Experiment 1.
We see from Figure 7.4 that (a){(f), including R
1
, R
2
, R
3
and the super-
imposed results of all groups of two out of the three shares, are merely random
grids from which no secret can be obtained, whereas (g) R
1
R
2
R
3
, the
superimpositiion of the three random grids, reveals B to our visual system.
As a result, fR
1
;R
2
;R
3
g produced by Algorithm 4 is indeed a set of VCRG-3
of B. It is lucid that Figure 7.4 provides some visualized evidence to Theorem
2.
Figures 7.5
and
7.6
show the corresponding results of Algorithms 5 and 6
for VCRG-3 with respect to B where fR
1
;R
2
;R
3
g and fR
1
;R
2
;R
3
g are the
two sets of random grids produced by Algorithms 5 and 6, respectively. It is
seen from Figure 7.5 and 7.6, fR
1
;R
2
;R
3
g and fR
1
;R
2
;R
3
g are surely two
sets of VCRG-3 of B. The correctness of Theorem 3 is visually shown here.
In summary, based upon Figures 7.4{6, R
i
and R
i
R
i
are random grids
withT(R
i
) = 1=2 (see Figures 7.4(a){(c), 7.5(a){(c), and 7.6(a){(c)) and
T(R
i
(R
j
) = 1=4 (see Figures 7.4(d){(f), 7.5(d){(f), and 7.6(d){(f)) for
1 6 i 6= j 6 3 and a 2f4; 5; 6g. By comparing the reconstructed images, i.e.,
R
1
R
2
R
3
, R
1
R
2
R
3
and R
1
R
2
R
3
(see Figures 7.3(g), 7.4(g), and
7.5(g), respectively), we realize that R
1
R
2
R
3
(by Algorithm 4) attains
the highest light contrast, while R
1
R
2
R
3
(by Algorithm 5) the lowest.
In fact, these results are foretold by
Table 7.6:
c(
E
4
) = 1=4, c(
E
5
) = 1=9,
E
a
= fR
1
;R
2
;R
3
g for a 2f4; 5; 6g:
c(
E
6
) = 1=8 for n = 3 where
Experiment 2: Encrypting a gray-level image to obtain VCRG-3.
Figure 7.7
illustrates the experimental results of applying Algorithm 7 to pro-
duce a set of VCRG-3 for a gray-level image. Figure 7.7(a) is the gray-level
image G to be encrypted; (b) shows the halftone version H of G by using
the error diffusion technology; (c), (d), and (e) present the outcomes of Al-
gorithm 7 where Encryption VCRG (H, 3) was implemented by Algorithm 4,
namely R
1
, R
2
and R
3
, respectively; (f), (g), and (h) give the superimposed
results of R
1
R
2
, R
1
R
3
and R
2
R
3
, respectively; and (i) depicts that of
R
1
R
2
R
3
. As seen from Figure 7.7, R
1
, R
2
, and R
3
and the superimposed
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