Cryptography Reference
In-Depth Information
FIGURE 4.4
An example of random grid (RG). Two random grids (left and middle) and
reconstructed secret image (right).
and the average opacity
1
of a random grid is 50%:
1
2
:
O(R) =
L
et R(p) denote a pixel value of the random grid R at the position p and
R(p) denote its inverse.
8
<
:
0
if R(p) is transparent (white)
R(p)
=
;
1
if R(p) is opaque (black)
8
<
0
if R(p) = 1
R(p)
=
:
:
1
if R(p) = 0
We must note that
th
e inverse of a random grid is also a random grid and its
opacity is 50 %, O(R) =
1
2
. The superimposition of two random grids, R
1
and
R
2
, pixel by pixel is computed by taking Boolean "OR" operation of their
corresponding pixels, R
1
(p) and R
2
(p), as VSSS and EVCS:
(R
1
+ R
2
)(p) = R
1
(p) + R
2
(p):
It is obvious that the superimposition of the same random grids results in the
original random grid. The superimposition of a random grid and its inverse is
a grid whose pixels are all opaque. Thus, the average opacity will be as below:
1
2
; O(R + R) = 1:
O(R + R) = O(R) =
The encryption algorithm for a binary image B, which generates a pair of
random grids R
1
and R
2
that can achieve the highest contrast is as follows.
1
Originally a concept ofaveragetransmissionwas used both in [17] and [37] instead
of average opacity. However, it is slightly confusing because people usually use 0 for a
transparent (white) pixel and one for an opaque (black) pixel in visual cryptography studies.
Thus, here we use the term average opacity.
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