Cryptography Reference
In-Depth Information
Fig. 5.5.
Example of the clustering technique.
Assume that there are two clusters S
1
and S
2
where the centers are at z
1
=
(r
1
, g
1
, b
1
, )andz
2
=(r
2
, g
2
, b
2
, ). The cluster-ordering relationship between
z
1
and z
2
may be defined as follows,
⎧
⎨
⎩
z
1
>z
2
, if (l
1
> l
2
)or(l
1
= l
2
and r
1
> r
2
)
or (l
1
= l
2
and r
1
= r
2
and g
1
> g
2
),
z
1
= z
2
, if (l
1
= l
2
and r
1
= r
2
and g
1
= g
2
),
z
1
<z
2
, otherwise.
R
cluster−order
:
(5.5)
Here, l
1
and l
2
are computed using the formula for the luminance shown in
Eq. (5.2). To embed 1-bit secret data into the image data X
i,j
belonging
to i-th cluster S
t
, the cluster-mapping function F
cluster−map
defined by the
following is used.
⎧
⎨
0,
if z
t
≥z
′
1
,
′
′
1,
if z
1
>z
t
≥z
2
,
′
′
′
′
if z
′
2
≥z
′
F
cluster−map
(z
t
,z
1
,z
2
,z
3
,z
4
)=
0,
>z
t
3
,
(5.6)
⎩
if z
′
3
≥z
′
1,
>z
t
4
,
0,
otherwise.
Here z
′
1
, z
′
2
, z
′
3
, form the sorting result, z
′
1
is the largest. The output of the
cluster-mapping function F
cluster−map
is the bit to be embedded. We need
to modify image data X(i, j) if the output of the cluster-mapping function
F
cluster−map
is not equal to the embedding bit. Let
RID
denote the image
data that is selected to replace X(i, j). The color c
RID
has to satisfy the three
conditions:
1. The size of the cluster that c
RID
belongs to is one.
2. The cluster includes the replaceable color, together with the four precedent
neighbors of X(i, j). These act together as a complete input to the cluster-
mapping function F
cluster−map
. This gives a binary output value equal to
the secret bit.
