Cryptography Reference
In-Depth Information
Chao and Lin [5] algorithm for (k,n) scheme
Input: the secret image A
Output: the final shadow Si
i
Construction:
Step 1: Generate a random image B
1
with the same size as A.
Step 2: Generate another image B
2
using B
2
= B
1
A.
Step 3: Construct a nm shadows-assignment matrix H, each column
of H have exactly k 1 zeros and nk + 1 ones, so m =
n
k 1
.
Step
4:
Partition B
1
and B
2
into m nonoverlapping
blocks
C
11
;C
21
; ;C
m1
and C
12
;C
22
; ;C
m2
.
Step 5: Let C
= C
11
C
21
C
m1
. Compute C
i3
= C
i2
C
.
Step 6: Construct m temporary shadows C
1
;C
2
; ;C
m
, where the up-
per half of each Ci
i
is the block C
i1
and the lower half of each Ci
i
is the
block C
i3
.
Step 7: Assign the duplicated copies of the m temporary shadows
C
1
;C
2
; ;C
m
to the n persons according to the shadows-assignment ma-
trix H. For each participant i, the final shadow Si
i
is exactly the union of
those copies assigned to him.
Revealing:
Step 1: k participants using their shares Si1
i
1
; ;S
i
k
to reconstruct the
secret image. Referring to H, all m temporary shadows C
1
;C
2
; ;C
m
can
be extracted from these k final shadows.
Step 2: The upper half of each Ci
i
is the block C
i1
and the lower
half of each C
i
is the block C
i3
. So we get all C
11
;C
21
; ;C
m1
and
C
13
;C
23
; ;C
m3
.
Step 3: Compute C
= C
11
C
21
C
m1
, then C
i2
= C
i3
C
.
Step 4: Recombination C
11
;C
21
; ;C
m1
and C
12
;C
22
; ;C
m2
into B
1
and B
2
.
Step 5: Reveal the secret image A
0
by A
0
= B
1
B
2
.
Let the size of secret image A be N
R
N
C
. Since the size of every temporary
shadow C
i
(1 i m) is 2 (N
R
N
C
)=m, the size of every nal shadow
S
i
(1 i n) is
n 1
k 1
h
2(N
R
N
C
)
m
i
2(N
R
N
C
)(nk+1)
n
=
. Notice that
n 1
k 1
each final shadow Si(1
i
(1 i n) contains
temporary shadows. After
we divide by the size of secret image A, we obtain the pixel expansion rate
per = 2
nk+1
n
< 2. Each shadow will be at most two times larger than
secret image A.
Next, we will give an example to analyze the steps of Chao and Lin [5]
(k;n) algorithm scheme.
Example 7 Let k =
3;n =
4,
and
a
grayscale
secret
image A =
235
45
239
.
188
103
234
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