Cryptography Reference
In-Depth Information
⎛
⎞
⎛
⎞
2
m+1
n+1
m+1
n+1
1
9
1
9
⎝
⎠
⎝
⎠
σ
2
(m, n)=
y
2
(i, j)
−
y(i, j)
.
(11.4)
i=m−1
j=n−1
i=m−1
j=n−1
We can obtain the polarities P as follows
A
A
w
−1
B
B
w
−1
P =
p(m, n),
(11.5)
m=0
n=0
where
1,
if σ
2
(m, n)≥T ;
p(m, n)=
(11.6)
0,
otherwise.
For convenience, we set the threshold T to be half of the codebook size, N/2.
We are then able to generate the final embedded watermark or the secret key,
key
2
, with the exclusive-or operation as follows
key
2
= W
P
⊕P.
(11.7)
After the inverse-VQ operation, both the reconstructed image X
′
and the
secret key, key
2
, work together to protect the ownership of the original image.
In the extraction process, we first calculate the estimated polarities P
′
from X
′
. We then obtain an estimate of the permuted watermark by
′
P
′
W
= key
2
⊕P
.
(11.8)
Finally, we can do the inverse permutation operation with key
1
to obtain the
extracted watermark W
′
.
In order to embed multiple watermarks, reference [21] also uses the mean
of the indices to generate another kind of polarities P
1
for embedding. Experi-
mental results show that these algorithms are robust to many kinds of attacks,
including JPEG, VQ, filtering, blurring and rotation. These algorithms have
the following two problems:
(1) We can also extract the watermark from the original image that has no
embedded watermark.
(2) The codebook should be used as a key, because if the user possesses the
same codebook, he can also embed his own watermark in the watermarked
image without modification.
In fact, unlike traditional watermarking methods, these watermarking al-
gorithms do not modify the VQ compressed cover work. The term finger-
print or secure fingerprint may be more appropriate. Sometimes we can
call this kind of watermark zero-watermark. In view of unification, we use
the term robust watermark instead of secure fingerprint although we
dont modify the VQ compressed cover work during the robust watermarking
process.
