Cryptography Reference
In-Depth Information
it results that
min
M2M b
H(M i ) max
M2M w
H(M i ) S m;
where
M b = C c 1 c i1 bc i+1 c n
[C c 1 c i1 bc i+1 c n
w
;
b
M w = C c 1 c i1 wc i+1 c n
[C c 1 c i1 wc i+1 c n
w
;
b
and H(M i ) denotes the Hamming weight of the i-th row vector Mi i
of a matrix M.
The values R > 0 and S > 0 are referred to as the relative difference of
the reconstructed image and relative difference of shadow images, respectively.
The number R m 1 and S m 1 are contrasts of the reconstructed image
and the shadow images. People would like both R and S to be as large as
possible.
The first condition is the contrast condition that indicates any qualified
set X 2 Qual can recover the secret image. The secret image can be re-
covered by stacking the transparencies of a qualified set, belonging to Qual .
The second condition is the security condition that states any forbidden set
X = fi 1 ;;i q g2 Forb has no information on the secret image. People can-
not get any information on the secret image by inspecting the shadow images
of a forbidden set. The third condition is the extended condition that im-
plies that the shadows images are still meaningful after the original images
are encoded. Any participant can recognize the shadow image on one's trans-
parency. Although the collection M b is obtained by combining two collections
C c 1 c i1 bc i+1 c n
b
and C c 1 c i1 bc i+1 c w , we have the same set of fM i g only with
one of the collections, because fM i : M 2C c1c n
w gfM i : M 2C c1c b g for
any c 1 ;;c n 2fb;wg and any i 2f1;;ng due to the second condition.
Here we show how to accomplish a 2 out of 2 EVCS. Each share consists
of 4 subpixels like (2; 2) VSSS. However, it contains either two 1's or three
1's depending on the colors of pixels of the corresponding original image,
white or black, respectively. The scheme is given by the 4 pairs of collections
(C c 1 c w ;C c 1 c b ), namely 8 collections C c 1 c c , where c;c 1 ;c 2 2 fb;wg. The collec-
tions are obtained by permuting the columns of the following 8 basic matrices,
S c 1 c 2
c
:
0
0
0
1
1
0
1
1
S ww
w
; S ww
b
=
=
;
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
S wb w =
; S wb
b
=
;
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
S b w =
; S bw
b
=
;
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
S b w =
; S bb b =
:
0
1
1
1
1
1
1
0
 
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