Cryptography Reference
In-Depth Information
M
reg
A regular mask of size (x=) (y=). This mask is only designed
for p
B
= p
S
= 50%.
Fig
ure
11.7
(a) shows the r
egu
lar mask with
the alternate blocks,
B
and
S
, where a block
B
contains large
subpixels and a block
S
contains small subpixels.
M
ran
A random mask of size (
x=
)(y
=
). This mask is designed for any
p
B
and p
S
. At this time,
B
and
S
are randomly chosen according
p
B
and p
S
, as shown in Figure 11.7(b).
D
B
()
Let A = [a
i;j
] , where a
i;j
is the element of the i-th row and j-th
column in A, be a matrix in C
1
or C
0
. The function D
B
() divides
a secret pixel s into m large subpixels (bp)
j
( (bp)
j
= 0 denotes
white and (bp)
j
= 1 denotes black) in the i-th share, 1 i n and
1 j m, dened as follows:
(bp)
j
= a
i;j
in A 2 C
0
for s is the white secret pixel.
(bp)
j
= a
i;j
in A 2 C
1
for s is the black secret pixel.
D
S
() Similar to D
B
(), it divides a secret pixel into m small subpixels
(sp)
j
in the i-th share, 1 i n and 1 j m.
A
m
x
;m
y
() Arrangement function that randomly arranges m large (or small)
subpixels into an (m
x
m
y
)-sized rectangle where m = m
x
m
y
.
O
(i)
n output shares, i 2 [1;n], of size (xm
x
) (ym
y
).
I
0
The recovered secret image of size (xm
x
) (ym
y
).
D
B
(s) =
FIGURE 11.7
Regular and random masks for arranging the large and small subpixels: (a)
regular mask and (b) random mask.
Even though the shares use a regular mask, an attacker could not gain any
information from the mask and the secrecy is not compromised.
Encrypting Algorithm:
Input: I,
2
, p
B
, p
S
, C
0
and C
1
of a (k;n)-threshold VCS.
Output: O
(i)
, i 2 [1;n].
Step 1:
Obtain the large-scaled and small-scaled secret images I
B
and I
S
from a secret image I.
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