Visual Cryptography and Random Grids - Visual Cryptography and Secret Image Sharing - page 215

approaches, Algorithm 4 (Algorithm 8 based upon Algorithm 4) is the most
effective scheme in terms of light contrast for binary or gray-level (color) im-
ages.
It is noticed that when we adopt the light contrast to measure the recon-
structed result for a conventional n out of n visual secret sharing scheme [9],
the best result is 1=2 n1 . That means that Algorithm 4 achieves the same
best light contrast. Moreover, it is so appealing that these schemes neither
induce any extra pixel expansion nor require encoding basis matrix. Those
approaches in conventional visual cryptography suffer from the disadvantage
of the inevitable pixel expansion, which increases exponentially as n increases
(and additionally increases as c or dlog 2 ce for the color cases where c is the
number of colors in the secret image), in the basis matrices. Table 7.7 summa-
rizes the pixel expansions needed by some ecient n out of n visual crypto-
graphic schemes in the literature and our (n;n)-VCRG schemes. Owing to the
reason that the size of the encrypted shares and reconstructed image would
not be expanded, our schemes based upon random grids are more attractive
than those in conventional visual cryptography for both theoretical concerns
and practical applications.

TABLE 7.7
Comparison of pixel expansions for conventional (n;n) visual
cryptographic and (n;n)-VCRG schemes.
binary color

Naor and Shyu Blundo et al. Shyu Shyu

Shamir [9] [13] [3] [11] [13]

8
<

(c 1)2 n1 c + 2
if n is odd;
c(c 1)2 n2 c
otherwise

2 n1 dlog 2 ce 2 n1

1 1

:

7.4 Concluding Remarks
In this chapter, we propose novel schemes for visual secret sharing using ran-
dom grids. At first, we give a new definition for the visual cryptograms of
n(> 2) random grids with respect to a binary image. Based upon the defini-
tion, we design effective algorithms, prove their correctness formally, analyze
the light contrast in the reconstructed image, and demonstrate their feasi-
bility by computer simulations. By exploiting the skills of halftone and color
decomposition in Ref. [12], the enhanced algorithms are also developed and
verified to deal with gray-level and color images.