Visual Cryptography for Multiple Secrets - Visual Cryptography and Secret Image Sharing - page 86

is 85 counterclockwise away from that in AB.
Experiment 3: Figure 3.22 gives the implementation results of the pro-
posed scheme for sharing four secrets. Figures 3.22(a){(d) are the four secrets
to be shared, namely P 1 , P 2 , P 3 , and P 4 , respectively. Figures 3.22(e) and (f)
are the encoded circle shares A and B. Figures 3.22(g){(j) show the superim-
posed results of AB, A 90 B, A 180 B, and A 270 B that recover P 1 ,
P 2 , P 3 , and P 4 in our visual system, respectively.
Experiment 4: One disadvantage in applying circle shares is that the
reconstructed secrets might be distorted. This shortcoming could be easily
refined by introducing cylinder shares.
Suppose that we encode each set of x pixels into square blocks (instead
of chord blocks) in Shyu et al.'s scheme. The encoded shares evolve into the
shape of rectangles. Each of the two rectangle shares can be easily rolled
up into a cylinder by aligning the rightmost column next to the leftmost
one. Figure 3.23 shows an example of applying cylinder shares to reveal the
corresponding distorted secrets where (a) and (b) are distorted reconstructed
secrets (which are the same as those in Figure 3.22(g) and (j), respectively)
using circular shares, while (c) and (d) are the corresponding counterparts
using cylinder shares which avoid any distortion when exposing the secrets.
The results in Experiments 1{4, as expected, demonstrate the feasibility
and applicability of Shyu et al.'s visual multisecret sharing scheme. We com-
pare the performances of the aformentioned schemes in terms of the capability
of sharing secrets, pixel expansion, contrast, and shape of shares in the next
subsection.
3.4.4 Comparison and Discussions
When we deal with x secrets, the pixel expansion of Shyu et al.'s scheme [8]
is 2x and the contrast (i.e., the relative difference between the reconstructed
white and black pixels in the superimposed image) of the scheme is 1=(2x)
since all 2x subpixels in a reconstructed black pixel are black, while those
in a reconstructed white pixel are 2x. Suppose that Feng et al.'s scheme is
applied. The pixel expansion becomes 3x and the contrast is 1=(3x). Note
that when x = 2, the pixel expansions (contrasts) in Wu and Chen's [12], Wu
and Chang's [13], and Shyu et al's schemes are all 4 (1=4); while in Feng et
al.'s scheme is 6 (1=6).
Table 3.10 summarizes the numbers of secrets shared (denoted as x), pixel
expansions(denoted as m), contrasts, and the shapes of shares in these visual
multiple-secret sharing schemes for the comparison purpose.
The pixel expansion of Shyu et al.'s scheme [8] is 2x when x secrets are
shared. It would be challenging to prove whether or not it is optimal. Is there
any algorithm that improves the contrast in the scheme? It is surely worthy of
further study. How to extend Shyu et al.'s scheme such that multiple secrets