Cryptography Reference
In-Depth Information
are superimposed can we see P, while any group of less than n shares obtains
nothing but a color random grid.
Let Encrypt cVCRG (P
x
,x, n) denote the procedure of encrypting P
x
into n sharesR
1
;R
2
;:::;R
n
in terms of binary color set fx; 0g where
x2 fc; m; yg. It is easy to implement Encrypt cVCRG (P
x
by using Al-
gorithms 4, 5, or 6 as long as we take 0 andxas the inverse to each other and
modify random pixel() to return 0 orxrandomly. Algorithm 8 summarizes
the whole idea of producing color (n;n)-VCRG for a color image.
Algorithm 8. Encrypting a color image into a set of (n;n)-VCRG
Input: an hw color image P and an integer n
Output: a set of n color random grids
E
= fR
1
;R
2
;:::;R
n
g constituting a
(n;n)-VCRG of P
1. Decompose P into (P
c
;P
m
;P
y
)
2. for (x2fc; m; yg) do P
x
=
(P
x
)
H
(P
x
) is an x -colored halftone function so that for eachp
x
2 P
x
,
p
x
=xor 0
//
H
3. for (x2fc; m; yg) do (R
1
;R
2
;:::;R
n
)=Encrypt cVCRG (P
x
,x, n)
4. for (1 6 i 6 n) doR
i
= (R
c
i
;R
m
i
;R
y
i
)
// color composition ofR
c
i
,R
m
i
, andR
y
i
5. output(R
1
;R
2
;:::;R
n
)
Based upon the statements in the proofs of Theorems 2 and 3 as well as
those for color (2, 2)-VCRG in Ref. [12], we have the following consequence.
Theorem 4 Given a color image P,E= fR
1
;R
2
;:::;R
n
g produced by Al-
gorithm 8 with respect to P is a set of color (n;n)-VCRG of P.
7.3.7 Experiments for (n;n)-VCRG
We designed four experiments by computer simulations to verify the feasibility
and applicability of the VCRG algorithms. Experiment 1 was designed to test
Algorithms 4, 5, and 6 to obtain sets of VCRG-3 for a binary image. Experi-
ments 2 and 3 focused on producing sets of VCRG-3 for gray-level and color
images, respectively. The sets of VCRG-4 were tested in Experiment 4. All
computer programs in these experiments were coded in Borland C++ Builder
and run in a PC with Windows.
Experiment 1: Encrypting a binary image to obtain VCRG-3.
In this experiment, we adopted Algorithms 4, 5, and 6 to produce three sets
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