Cryptography Reference
In-Depth Information
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(a)
(b)
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(c)
FIGURE 3.2
Encoding S 1 in Wu and Chen's scheme: (a) Four triangle-like areas. (b) In-
dexing the blocks in each of the four areas. (c) Blocks to be assigned.
the four corners in the above-mentioned order in S 1 S 2 reveal ;;;,
respectively (see Figure 3.3(e)) to our visual system. When S 1 is rotated as
S 90
1
as indicated in Figure 3.3(f), where all blocks are in the form of s 9 1
, the
S 2 recover ;;;, respectively (see
Figure 3.3(g)). It is not hard to see that by encoding all pixels in S 1 and S 2
with respect to the corresponding pixels in P 1 and P 2 according to Table 3.3,
P 1 and P 2 can be recovered by S 1 S 2 and S 90
four corresponding corners in S 90
1
S 2 , respectively.
Note that S 1 and S 2 are in the shape of squares of the same size. S 1 S 2
reveals P 1 , while S 1 S 2 reveals P 2 . Wu and Chen set to be 90 . It is easy
to extend their idea to design as one of 90 ; 180 , or 270 , but the other
degrees are infeasible. This is because the rotated S 1 (S 1 ) cannot be aligned to
S 2 pixel by pixel when 6= 0 ; 90 ; 180 , or 270 . Except for the fact that it is
restricted, there is another pitfall in their scheme: since the encoded pixels in
each of areas I, II, III, and IV in S 1 are exactly the same, S 1 is not a random
picture. In fact, only 1/4 shares of S 1 are purely random pictures.
1
3.3.2 Wu and Chang's Scheme
Based upon the idea of Wu and Chen [12], Wu and Chang [13] devised an-
other visual two-secret sharing scheme that allows the rotation angle to be an
arbitrary one between 0 and 360 by adopting circle shares. Given an angle
and two secret images P 1 and P 2 , their approach produces two circle shares A
and B such that any single A or B is a seemingly random picture that leaks
 
 
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