Visual Cryptography and Random Grids - Visual Cryptography and Secret Image Sharing - page 209

(a) (b)

FIGURE 7.8
Reconstructed results of VCRG-3 with respect to G: (a) R 1 R 2 R 3 ; (b)
R 1 R 2 R 3 .

components of P, respectively; (e), (f), and (g) are P c , P m , and P y which are
the c-, m-, and y-colored halftone images (by error diffusion) of P c , P m and
P y , respectively.
By Step 3 of Algorithm 8, P x would be encrypted into fR 1 ;R 2 ;R 3 g by
Eycrypt cVCRG (P x ,x, 3) forx2 fc; m; yg. When Eycrypt cVCRG (P m ,
m, 3) was based upon Algorithm 4, Figure 7.10 evidences the effectiveness of
fR 1 ;R 2 ;R 3 g for being a set of m-colored VCRG-3 with respect to P m in
which (a){(f) are the results ofR m 1 ,R m 2 ,R m 3 ,R m 1 R m 2 ,R m 1 R m 3 , and
R m 2 R m 3 , respectively; and (g) is that ofR m 1 R m 2 R m 3 . Regarding P c
and P y , the corresponding results are similar to Figure 7.10 so that we simply
omit them.
The encrypted monochromatic-colored shares P c i , P m i and P y i were further
composed to obtain color random gridR i = fP c i ;P m i ;P y i g for 1 6 i 6 3 in
Step 4 of Algorithm 8. We show the corresponding results in Figure 7.11 where
(a){(c) are color random gridsR 1 ,R 2 ,R 3 ; (d){(f) give results ofR 1 R 2 ,
R 1 R 3 ,R 2 R 3 , respectively; and (g) shows that ofR 1 R 2 R 3 . When
we implemented Eycrypt cVCRG (P x ,x, 3) is based upon Algorithm 4, 5, or
6. The correctness of Theorem 4 holds in a visual sense from the results of
Figures 7.8{10.

Experiment 4: Obtaining VCRG-4.
From the above analytic and experimental results, we know that Algorithm
4 achieves the higher light contrast as compared to Algorithms 5 and 6 for
binary and gray-level images, so does Algorithm 8 based upon Algorithm 4 as
compared to those based upon Algorithms 5 and 6 for a color image. We only
tested Algorithm 4 for binary VCRG-4 and Algorithm 8 based upon Algo-
rithm 4 for color VCRG-4 here. Figure 7.12 summarizes the results of binary
VCRG-4 where (a) is the binary image B encrypted; (b){(e) are R 1 , R 2 , R 3 ,
R 4 produced by Algorithm 4; (f) presents the result of R 1 R 2 ; (g) shows that
of R 1 R 2 R 3 ; and (h) gives that of R 1 R 2 R 3 R 4 . Even though the
superimposed results from other groups of less than four shares are not shown
here, they are really random grids as expected. It is seen from Figure 7.12
that only when all four shares are superimposed can we see B, while no group