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Fig. 4(c) is a close-up view of the dotted box in 4(b). It is therefore verified that the
LHA technique can effectively resist the χ
2
test.
Resistance Against the RS Analysis.
With the simple LSB replacement technique,
only the mapping
F
1
is applied to the LSBs that differ from the secret bits to be hidden.
Changes of smoothness are different when
F
1
and
F
−
1
, respectively, are
applied to part of
the pixels in a stego-image so that
R
−
M
−
S
−
M
>
R
M
−
S
M
. When the test is carried out on a
clean image, on the other hand, one has
R
M
≈
R
−
M
>
S
M
≈
S
−
M
.
With the LHA approach, on the other hand, both
F
1
and
F
−
1
are applied. Therefore,
changes of smoothness are very close when applying
F
1
and
F
−
1
, respectively,
to the
stego-image so that
R
M
≈
S
−
M
as in a clean image. In other words, the RS test
can no longer distinguish a stego-image from a clean one.
Fig. 5 shows the RS analysis results for a stego-image Baboon. When LSB re-
placement is used, the larger the payload, the greater is the difference between (
R
−
M
−
S
−
M
) and (
R
M
−
S
M
). With LHA, however,
R
M
≈
R
−
M
>
S
M
≈
S
−
M
always holds irrespective of
the increasing payload. Fig.6 shows
R
−
M
−
R
M
from 100 stego-images using the straight
LSB method and LHA techniques respectively, and from 100
clean
images. Clearly,
RS analysis is effective for the straight LSB method, but invalid for LHA.
R
−
M
>
S
M
≈
0.7
0.7
R-
0.6
0.6
R-
0.5
0.5
R+
0.4
0.4
R+
0.3
0.3
0.2
0.2
S+
S-
0.1
0.1
S+
S-
0
0
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
Payload L
Payload L
(a) (b)
Fig. 5.
RS analysis of the stego-image Baboon. (a) Using the simple LSB replacement technique.
(b) Using the LHA technique
Resistance against the GPC Analysis.
Because the mapping
F
−
1
is also used, both
N
O
and
N
E
are increased due to data embedding, and distribution of
R
remains centered
around
R
=1 as shown in Fig.7, where the solid and dashed lines represent the distribu-
tions of
R
of the original and the stego-images generated with the LHA approach,
respectively. Therefore, it is impossible to distinguish a stego-image from a clean
image based on the parameter
R
.
3.3
Application of LHA to Transform Domain Embedding
Digital images are often stored in the JPEG format as quantized DCT coefficients. In
this case, secret data can also be embedded to the LSB of quantized coefficients. But
