Visual Cryptography for Multiple Secrets - Visual Cryptography and Secret Image Sharing - page 61

3.3 Visual Two-Secret Sharing Schemes
3.3.1 Wu and Chen's Scheme
Following the research of Naor and Shamir, Wu and Chen [12] developed a
visual secret sharing scheme that encrypts two secrets into two shares. Given
two N N (square) secret binary images P 1 and P 2 , their scheme produces
two shares, namely S 1 and S 2 , which reveal no information about P 1 or P 2
individually. Yet when stacking S 1 and S 2 , we obtain P 1 visually; moreover,
when stacking S 90
1

and S 2 , we see P 2 .
Consider a pair of pixels p 1 = P 1 [i;j] and p 2 = P 2 [u;v] in P 1 and P 2 ,
respectively. We refer to (p 1 , p 2 ) as the corresponding pixels of P 1 and P 2 if
and only if i = u and j = v. Given a set of corresponding pixels (p 1 , p 2 ),Wu
and Chen's encoding scheme for visual two-secret sharing in two shares is
summarized in Table 3.3.
It is seen from Table 3.3 that each pair of corresponding pixels (p 1 , p 2 ) of
(P 1 , P 2 ) is encoded into extended blocks s 1 (as well as s 9 1

) and s 2 in which

the pixel expansion is m = 4. Note that s 9 1

is exactly the result of rotating
s 1 90 counterclockwise. We explain how Wu and Chen's encoding scheme
works by using a simple example. Assume that the two secret images P 1 and
P 2 are composed in a square of 12 12 pixels. Then, the two encoded shares
S 1 and S 2 are composed in a square of 48 48 (48 = 12 4) pixels. They
rst decompose S 1 into four triangle-like areas with an equal size as shown
in Figure 3.2(a). All of the four areas are composed of an equal amount of
extended blocks (2 2 pixels each), which are indexed as shown in Figure
3.2(b) where each triangle-like area contains 36 blocks. Let block j in area k
be denoted as b j for 1 k 4 and 1 j 36. The extended blocks in area
I, b j , are randomly selected out of those in Figure 3.2(c). Each block, say b j ,
in area II, III, IV is assigned to be the same as b j in area I, that is, b j = b j
for t = 2; 3; 4, and 1 j 36.
Let us pay attention to the four pixels at the top-right, top-left, bottom-
left, and bottom-right corners in sequence (counterclockwise) in P 1 and P 2 .
Assume that those pixels in P 1 (P 2 ) are ;;; (;;;) as shown in
Figure 3.3(a) and (Figure 3.3(b)). Assume that corresponding block b 26 at S 1
is randomly determined as , then as mentioned b 26 is for 2 t 4 (see
Figure 3.3(c)). The above-mentioned pixels in P 1 and P 2 constitute four sets
of corresponding pixels: (;), (;), (;), and (;). Since b 26 in S 1 is
for 1 k 4, according to Table 3.3 the four blocks b 26 , b 26 , b 26 and b 26 ,

in S 2 with respect to the four sets of the corresponding pixels are , ,

and , respectively (see the 2nd, 6th, 10th, and 14th rows in column s 2
of Table 3.3). Figure 3.3(d) illustrates the encoding result of S 2 . As expected,