Cryptography Reference
In-Depth Information
by a slight misalignment. We rst give an example, a (2; 2)-VCS, to show
this phenomenon. Denote (d x ;d y ) as the horizontal and vertical misalignment
deviations from the original position of the subpixel.
Example 3 The images (a), (b), and (c) in Figure 11.2 show the recovered
secret image of a (2,2)-VCS for three misalignment deviations, (d x ;d y ) =
(0; 0), (0:5; 0), and (1; 2) (unit: subpixel).
FIGURE 11.2
Recovered secret images of a (2,2)-VCS for three misalignment deviations (a)
(d x ;d y ) = (0; 0), (b) (d x ;d y ) = (0:5; 0), and (c) (d x ;d y ) = (1; 2).
From Figure 11.2, we can observe that, the clearness of Figure 11.2 (b) is
worse than the Figure 11.2 (a), and the secret on Figure 11.2 (c) is completely
invisible.
Figure 11.2 shows the case that only two shares are superimposed. The
misalignment problem will become more complex for stacking k shares for
a (k;n)-VCS. Note that, the recovered image will disappear if any one out
of k shares is not at the correct position. In fact the misalignment problem
critically increases as k grows.
The next two subsections are organized as follows: first, we will investigate
the conditions that the secret image can still be observed when the shares are
slightly misaligned, whereby saying slight misalignment we mean deviation
(d x ;d y ) satisfying 0 d x ;d y 1; and then we will investigate the misalign-
ment tolerance of large and small pixels. To simplify the discussion, we only
consider the case of (2; 2)-VCS.
11.4.1 Shares with Slightly Misalignment Can Still Recover
the Secret Image
We consider a (2; 2)-VCS with deviation (d x ;d y ), where a pixel 1W1B (resp.
1B1W) represents a white pixel that contains a white (resp. black) and a
black (resp. white) subpixel; and a pixel 2B0W represents a black pixel that
contains two black subpixels. All possible four cases, (a1), (a2), (b1), and (b2),
of stacked shares with deviation (d x ;d y ) are shown in Figure 11.3. The stacked
 
 
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