Cryptography Reference
In-Depth Information
> 1 on the first round. As a result, we obtain a bit stream with
D
om
bits and the product Q. The embedding capacity D
cb
is then calculated
using Eq. (5.9).
On the second round, we use Du et al.s method to calculate the series
number of combination Y from the image data X(i, j) that are embeddable
pixels
f (c
X(i,j)
)
> 1. Then, we transfer the series number to a secret bit
stream by Eq. (5.10). Finally, the total secret data is obtained by connecting
the secret bit stream on the first round with the secret bit stream on the
second round:
f (c
X(i,j)
)
a
i
=(Y/2
D
cb
−i
)mod2.
(5.10)
An example of the extraction procedure using Fig. 5.9(b) is now described.
The image data X(2, 2), X(2, 4), X(3, 1), and X(4, 4) are embeddable and the
size of the cluster they belong to is one, four secret bits are extracted from
the image data.
The other image data, D
cb
is calculated by Eq. (5.8) and Eq. (5.9). D
cb
is
20. A bit stream with 20 secret bits can be extracted from this Stego-Image.
We use Du et al.s method to calculate the series number Y of combination.
Equation (5.10) is used to transfer the decimal number Y
to a secret bit
stream. The secret data has now been correctly extracted.
5.3.3 Binary Search Embedding Algorithm
1. Input: A stego-image composed of the collection of colors on the palette
P and the image data X(i, j). The clustering result with m clusters
S
1
,S
2
,,S
m
, and the threshold values T
α
and T
β
are also given.
2. Output: The secret data A.
Step 1. Assume X(i, j) is the image data used to start the extraction
procedure.
Step 2. Check whether all pixels have been processed. When this is com-
plete, the first round of the extraction procedure is done, go to
Step 6. Otherwise, go to the next step.
Step 3. Check whether the color c
X(i,j)
corresponding to X(i, j)isem-
beddable. If c
X(i,j)
is not embeddable, X(i, j) is skipped. Go to
Step 2. Otherwise, go to the next step.
Step 4. Iff (c
X(i,j)
)= 1, go to the next step. Otherwise, calculate the
product Q. Here Q = Qf (c
X(i,j)
).
Step 5. Take the color c
X(i,j)
of X(i, j) and the sorted centers of the
clusters z
′
1
, z
′
2
, z
′
3
,andz
′
4
of X(i, j)s four preceding neighbors as
the input to the cluster mapping function F
cluster−map
to obtain
an extracted secret bit a. Then, go to Step 2.
Step 6. Calculate the embedding capacity D
cb
with Q. Then, go to next
step.
