Visual Cryptography for Multiple Secrets - Visual Cryptography and Secret Image Sharing - page 79

Then the above formula can be simplified as
b j = permute(s btod(rotate(p 1 p 2 p 3 ;k1))

; j ) (3.4)

B

with respect to the set of corresponding pixels (p 1 ;p 2 ;p 3 ) j where 1 j
and 1 k 3.
Since the number of subpixels in both of the elementary blocks of A and B
is 6(= 2x) in the above case, the pixel expansion (i.e., the number of subpixels
in the shares needed to encode a set of corresponding pixels in the secret
images) in this algorithm is 6 for x = 3. The visual x-secret sharing scheme
for any general number x 2 will be formalized in the following section.

3.4.1.4 General Algorithm

The definitions of the elementary blocks for circle shares A (formula (3.1))
and B (formula (3.4)) and the encoding scheme in Tables 3.5, 3.7, and 3.8 for
visual 3-secret sharing can be generalized to accomplish the visual multisecret
sharing for x 1 (including x = 1) secrets. Furthermore, there is no need to
store any codebook like Tables 3.5, 3.7, and 3.8. Thus, this scheme formally
presented in the following is not only general but also ecient for physical
implementation.
Assume that there are x secrets to be shared by two participants. The two
circle shares A and B are evenly decomposed into x chords, respectively. Let
denote the degree expanded in each chord of A and B. It is computed as
= 360 =x:
We refer to the elementary block of the x secrets as a block with 2x ordered
subpixels as shown in Figure 3.16. It is noted that the pixel expansion in
the scheme is 2x when x secrets are shared. The width and height of the
elementary block can be any combination as long as their multiplication is
2x (or even any number larger than 2x for some special purposes, such as
retaining aspect ratios, to ease the production of the circle shares, and so on).
The order of the 2x subpixels in the elementary block can also be arbitrarily
defined. In the following discussions, we follow the shape and order of the
elementary block as shown in Figure 3.16.

...

...

FIGURE 3.16
Elementary block for x secrets.

We define the set of the elementary blocks for share A as follows:
E A = fs A j1 k xg;