Cryptography Reference
In-Depth Information
The color difference between c
1
=(r
1
,g
1
,b
1
)andc
2
=(r
2
,g
2
,b
2
) is defined as
c
1
−c
2
=
[(r
1
−r
2
)
2
+(g
1
−g
2
)
2
+(b
1
−b
2
)
2
].
(5.3)
The embedding method uses the color-mapping function F
color−map
to embed
one secret bit into each pixel in the cover image I. The color-mapping function
F
color−map
is defined in Eq. (5.4).
⎧
⎨
≥c
′
0,
if c
X(i,j)
1
,
if c
′
1
≥c
′
1,
>c
X(i,j)
2
,
′
′
′
′
4
if c
′
2
≥c
′
F
color−map
c
X(i,j)
,c
1
,c
2
,c
3
,c
=
0,
>c
X(i,j)
3
,
(5.4)
⎩
if c
′
3
≥c
′
1,
>c
X(i,j)
4
,
0,
otherwise.
In Eq. (5.4), the color c
X(i,j)
is the current pixel that is located at coordinate
(i, j) with an index X(i, j). The four colors c
′
1
, c
′
2
, c
′
3
, c
′
4
are the result of sorting
the colors of the four preceding neighbors c
X(i−1,j−1)
, c
X(i−1,j)
, c
X(i−1,j+1)
,
and c
X(i,j−1)
according to the color-order relationship, size. As a result, the
color c
X(i,j)
and the four colors c
′
′
′
′
4
are the input of the color-mapping
function F
color−map
. The output of the color-mapping function F
color−map
is
a binary value 0 or 1 to represent the embedding bit.
If the pixel is an embeddable pixel, it can be used to embed a secret
bit; otherwise, the pixel is skipped. In the embedding procedure, the current
embeddable pixel and its four preceding neighbors are taken as the input to the
color-mapping function. If the output value is not equal to the current secret
bit, the optimal replacement color selection is adopted to find the closest
color to replace it. Otherwise, the secret bit is embedded into the current
embeddable pixel without modification.
The optimal replacement color selection uses the following steps: First, add
each color C
i
in the color palette C that satisfies the following two replacement
conditions into the replaceable set R. The first condition is that the mapping
value F
color−map
(c
i
,c
′
1
, c
2
, c
3
, c
1
,c
′
2
,c
′
3
,c
′
4
) equals a secret bit. The second replacement
condition is that C
i
is also embeddable. The original color of image data
X(i, j) is replaced by the optimal replacement color, which is the color having
the minimum color difference, in the replaceable set R.
5.3 The Proposed Method
The goal of this data-hiding method is the ability to hide as many secret
bits with the best image quality possible. To achieve the goal, the following
techniques are employed. The cluster ordering-and-mapping technique, the
combination technique are all employed. The proposed method consists of the
following two main procedures, which are: the Embedding Procedure and the
Extraction Procedure.
