Cryptography Reference
In-Depth Information
M
i=1
S
i
;
(2)∀i, j, 1≤i, j≤M, if i = j, then S
i
∩S
j
=∅;
(3)∀i, 1≤i≤M ,ifc
l
∈S
i
and c
j
∈S
i
(0≤l, j≤N−1), then d (c
l
, c
j
)≤
D;
(4)S
i
=2
n(i)
. WhereS
i
denotes the number of codewords in S
i
and n(i)
is a natural number.
(1) S =
Before the embedding process, the original image is first divided into blocks.
For each block, the index of the best match codeword is found. The water-
marked codeword index is then obtained by modifying the original codeword
index according to the corresponding watermark bits. The modification is un-
der the constraint that the modified index and the original are in the same
partition. A further condition is that the introduced extra distortion is less
than the given distortion threshold. In the decoding phase, not the original but
the watermarked codeword is used to represent the input image block. There-
fore, the VQ-based digital image watermarking will introduce some additional
distortion. Whether the original image is required or not during the water-
mark extraction is dependent on the embedding method. In these algorithms,
the codebook is open for users but the partition is the secret key. Experi-
mental results show that these algorithms are robust to VQ compression with
high-performance codebooks, JPEG compression and some to spatial image
processing operations. These algorithms are fragile to rotation operations and
to VQ compression with low-performance codebooks.
Watermarking Algorithms Based on Index Properties
To enhance the robustness to rotation operations and VQ compression oper-
ations, some image watermarking algorithms [20, 21] based on the properties
of neighboring indices have been proposed. In [20], the original watermark W
of size A
w
B
w
is first permuted by a predetermined key, key
1
, to generate
the permuted watermark W
P
for embedding. The original image X with size
AB is then divided into vectors x(m, n) with a size (A/A
w
)(B/B
w
),
where x(m, n) denotes the image block at the position of (m, n). After that,
each vector x(m, n) finds its best codeword c
i
in the codebook C and the
index i is assigned to x(m, n). We can then obtain the indices matrix Y with
elements y(m, n), which can be represented by:
A
A
w
B
B
w
A
A
w
B
B
w
−1
−1
−1
−1
Y =VQ(X)=
VQ (x(m, n)) =
y(m, n).
(11.3)
m=0
n=0
m=0
n=0
For natural images, the VQ indices among neighboring blocks tend to be very
similar. We can make use of this property to generate the
polarities
P. After
calculating the variances of y(m, n) and the indices of its surrounding blocks
using
