Cryptography Reference
In-Depth Information
7.1 that the encrypted shares (see
Figure 7.1(b),
(c), (e), (f), (h), and (i)) are
merely random pictures and no information about B can be obtained. Only
when the two shares are superimposed (see Figures (d), (g), and (j)), can we
see B by our visual system. It is worthy of notifying that there is no extra
pixel expansion in Figures 7.1(b){(j).
Figure 7.2
shows the reconstructed results by using Naor and Shamir's
approach for encrypting B in Figure 7.1(a). The pixel expansion of Figure
7.2(a) is 2, while that of Figure 7.2(b) is 4 ( by applying S
0
0
1
0
1
=
0
1
0
1
0
1
0
1
and S
1
=
). The former does not retain the aspect ratio with
1
0
1
0
respect to B, while the latter does. Both sizes of the results in Figure 7.2 are
larger than that of B.
7.3.4 Definition of Light Contrast and Performance Evalua-
tion
To evaluate the relative difference of the light transmissions between the trans-
parent and opaque pixels in reconstructed image S by these random grid-based
algorithms, we define the light contrast of S with respect to B as follows.
Definition 3 The light contrast of a set
of VCRG produced by an encryp-
tion algorithm for a binary image B is defined as
E
) =
T(S[B(0)])
T(S[B(1)])
c(
E
(S[B(1)])
where S is the superimposed result of all visual cryptograms in
1 +
T
E
.
LetE
1
,E
2
, andE
3
denote the three sets of (2, 2)-VCRG produced by Algo-
rithms 1{3, respectively. By Denition 3, the light contrasts ofE
1
,E
2
, andE
3
are c(
E
1
) = 1=2 (= (1=20)=(1 + 0)), c(
E
2
) = 1=5 (= (1=21=4)=(1 + 1=4)),
and c(
E
3
) = 1=4 (= (1=4 0)=(1 + 0)). That is, Algorithm 1 achieves the
highest light contrast among the three. This outcome can also be observed by
comparing the reconstructed images in Figures 7.1(d), (g), and (j) in which (d)
is more recognizable than (g) and (j). Note that 1 +
T
(S[B(1)]) is introduced
as the denominator of c(
E
) in favor of a less
T
(S[B(1)]) (than a larger one)
when two schemes have a same numerator (i.e.,
T
(S[B(0)])
T
(S[B(1)])). For
instance, both of
E
2
and
E
3
have the same result of
T
(S[B(0)])
T
(S[B(1)]),
yet their
T
(S[B(1)])'s are 1/4 and 0, respectively. Thus, c(
E
3
) > c(
E
2
) ac-
cording to Definition 3. As we can see, the reconstructed image by
E
3
(Figure
7.1(j)) is indeed more recognizable than that by
E
2
(Figure 7.1(g)) by our
visual system. In general, we prefer a set of VCRG with a larger light contrast
that helps our visual perception to recognize the result. Thus, Algorithm 1 is
more preferable than the other two.
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