Cryptography Reference
In-Depth Information
Class 1: A difference value h is classified as belonging to the first class un-
der the integer average value l if for all values of b
1
∈0, 1, given by
Eq. (13.14), h
′
does not satisfy the condition in Eq. (13.15).
Class 2: A difference value h is classified into the second class under the
integer average value l if for all values of b
1
∈0, 1, given by Eq. (13.14),
h
′
does satisfy the condition in Eq. (13.15). For all values of b
2
∈0, 1,
′′
h
, given by Eq. (13.25), does not satisfy the condition in Eq. (13.15),
′′
′
h
=2h
+ b
2
.
(13.25)
Class 3: A difference value h is classified into the third class under the integer
average value l if for all values of b
1
∈0, 1, given by Eq. (13.14). The
value h
′
does satisfy the condition in Eq. (13.15), and for all values of
′′
b
2
∈0, 1. The value h
, given by Eq. (13.25), satisfies the condition in
Eq. (13.15).
After we embed watermark bits w into some pixel pairs of class 2, these
watermarked pixel pairs can be classified as Class 2 or Class 3 in the decoding
process. Those especial pixel pairs are called as the Flipping Class 2. We take
an example in order to introduce the Flipping Class 2.
A pair of pixel values (x = 194,y = 219) is selected from Class 2, and
(l, h) = (206,−25) is then obtained according to Eq. (13.12). Owing to the
embedded bit b
1
∈0, 1,theh
′
via Eq. (13.14) is equal to−49 or−50. On
the decoding side, the average value l and watermarked difference value h
′
′
′′
are obtained via the integer transform Eq. (13.12). If h
according
to Eq. (13.25) does not satisfy the condition in Eq. (13.15). However, if h
is−50, h
′
is−49, the value h
′′
via Eq. (13.25) does satisfy the condition Eq. (13.15).
Therefore, h
′
may be classified as Class 3 or Class 2 in the decoding process.
Fig. 13.10.
General framework of watermark embedding scheme.
Those flipping pixel pairs are classified into the Flipping Class 2. The
values h and l have certain relationships for those pixel pairs. That is,
2(2h + b
1
)+b
2
=
min (2(255−l), 2l−1) for all values of b
1
∈
0, 1and b
2
∈0, 1.
