Cryptography Reference
In-Depth Information
in the interval i−0.5 <x<i+0.5 are used for embedding zero and their
quantized coe
cients are unchanged after embedding. However, the other half,
(h
−
i
/2
coe
cients are quantized to i−1andh
i
/2 coe
cients to i + 1. Alternatively,
h
i−1
/2 coe
cients from the bin i−1andh
−
i
+ h
i
)/2 coe
cients are used for embedding one, resulting in that h
−
i+1
/2 coe
cients from the bin i +1
are quantized to i for embedding zero. With similar consideration, it is easily
understood that the change shown in Eq. (8.19) holds true for odd number i.
A typical example of before- and after-embedding histograms is shown in
Fig. 8.14. These histograms are those of (2, 2) frequency component among
64 components (k, l), 1≤k, l≤8 for Lena image (512512 pixels in size,
8 bit per pixel (bpp)) compressed with quality factor 80. It is seen that the
numbers of quantized coe
cients for low absolute values around zero change
significantly after embedding. Eq. (8.19) indicates that if h
i
= h
i−1
+ h
−
i+1
,
then the number in the bin i does not change. In particular for i =0,1, how-
ever, much difference between h
i
and h
i−1
+ h
−
i+1
causes the significant change
on h
′
i
after embedding. Therefore a straightforward application of QIM in the
DCT domain cannot be allowed for secure steganography against histogram-
based attacks.
2000
Before embedding
After embedding
by direct QIM
1800
1600
1400
1200
1000
800
600
400
200
0
-8
-6
-4
-2
0
2
4
6
8
Quantized DCT coefficient
Fig. 8.14.
Before- and after-embedding histograms of (2, 2) frequency component.
Direct application of QIM causes a significant histogram change.
8.6.2 Histogram Quasi-Preserving QIM-JPEG Steganography
As shown in Fig. 8.14, the most significant changes caused by direct appli-
cation of QIM are decrease of h
0
and increase of h
1
and h
−1
. Let us try to
preserve h
0
, h
1
and h
−1
after embedding. We introduce a dead zone for DCT
coe
cients x, t
d
< 0 <t
d
< 0.5) where DCT coe
-
cients are not used for embedding. The number of positive DCT coe
cients
−
d
<x<t
d
−
(−0.5 <t
