Cryptography Reference
In-Depth Information
members is n, then log
2
n secret bits can be embedded. The order of mem-
bers in the sub-cluster is related to the embedded secret message. Therefore,
the member whose order matches the embedded secret message is adopted
to replace the original color index. For example, when there is a 4-member
sub-cluster consisting of four members, ordered as 0, 1, 2, and 3, respectively.
The color indices of these four members are 90, 80, 100 and 110. Since the
number of this 4-member sub-cluster is 4, then 2 secret bits can be embedded.
If the original index is 80, which is ordered as 1 in the sub-cluster, the 2-bit
secret message to be embedded is valued as 3 (11 in binary), an index value of
110, of ordered as 3 in the sub-cluster, will be adopted to replace an original
index 80.
5.2.2 The Color Ordering and Mapping Scheme
The goal of the color ordering and mapping scheme is to improve the perfor-
mance of the scheme [11] proposed by Fridrich and Du in 1999. This embeds
the secret data into the parity bits of closest colors. The flowchart of Tzeng et
al.s data-hiding scheme by color ordering and mapping is shown in Fig. 5.2.
To embed the secret data A =a
1
a
2
into the input color image I
of hw pixels, the image I is first compressed into the palette image with the
color palette C =c
i
a
w
1≤i≤nof n colors to generate the image data X,
where X =X(i, j)0≤i≤h, 0≤j≤w. Before the embedding procedure
is performed, the color palette is first sorted by the color-ordering relationship.
Given two colors c
1
=(r
1
,g
1
,b
1
)andc
2
=(r
2
,g
2
,b
2
), the color-ordering
relationship R
color−order
is defined as follows:
⎧
⎨
⎩
c
1
>c
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
);
c
1
= c
2
, if (l
1
= l
2
and r
1
= r
2
and g
1
= g
2
);
c
1
<c
2
, otherwise.
R
color−order
:
(5.1)
The luminance values are calculated by Eq. (5.2) of the colors.
l =0.3r +0.59g +0.11b.
(5.2)
According to the color-ordering relationship R
color−order
, the sorting result for
all colors in the palette can be obtained. To embed the secret data into the
image I, each pixel with image data X(i, j) is processed in a raster-scanning
manner. In this scheme, the four neighboring pixels are used to determine
whether what the current pixel is embeddable. The four precedent neighbors
of the current pixel are shown in Fig. 5.3.
A pixel is an embeddable pixel if it satisfies the following conditions:
1. The number of distinct colors of X(i, j)s four precedent neighbors is larger
than the threshold value T
α
.
2. The maximum color difference between X(i, j) and its four precedent
neighbors is smaller than the threshold value T
β
.
