Cryptography Reference
In-Depth Information
For F
LSB
the amplitude is 1. The other permutation from the previous para-
graph has A = 2. Larger values of the amplitude A correspond to the action
of adding more noise after applying F .
The main idea for lossless embedding is that the image by groups can be
scanned according to a predefined order and losslessly compress the status
of the image. The bit-stream of R and S groups or the RS-vector with
the U groups may be skipped. This may be considered as overhead needed to
leave room for data embedding. It is not necessary to include the U groups,
because they do not change in the process of message embedding and can be all
unambiguously identified and skipped during embedding and extraction. The
higher a bias between the number of R and S groups, the lower the capacity
consumed by the overheads and the higher the real capacity. By assigning a
1toR anda0toS they embed one message bit in each R or S group. If
the message bit and the group type do not match, the flipping operation F is
applied to the group to obtain a match. The data to be embedded consist of
the overhead and the watermark signal.
The extraction starts by partitioning the watermarked image into disjoint
groups using the same pattern as used in the embedding. They apply the
flipping operation F and discrimination function f to all groups to identify
the R, S and U groups. They then then extract the bit-stream from all R
and S groups (R =1,S = 0) by scanning the image in the same order as
embedding. The extracted bit-stream is separated into the message and the
compressed RS-vector C. The bit-stream C is decompressed to reveal the
original status of all R and S groups. The image is then processed once more
and the status of all groups is adjusted as necessary by flipping the groups back
to their original state. Thus, an exact copy of the original image is obtained.
The block diagram of the embedding and extracting procedure is given in
Fig. 13.4.
Let N
R
, N
S
and N
U
be respectively used to indicate the number of regular,
singular, and unusable groups in the image. The sum of N
R
, N
S
and N
U
is
equal to
MN
n
(the number of all groups). The raw information capacity for
this data embedding method is N
R
+ N
S
=
MN
n
−N
U
bits. However, since
the compressed bit-stream C consumes a large part of the available capacity,
the real capacity C
ap
that can be used for the message is given by
C
ap
= N
R
+ N
S
−C,
(13.4)
whereCis the length of the bit-stream. A theoretical estimate or an upper
bound C
′
ap
for the real capacity is
N
R
N
R
+ N
S
N
S
N
R
+ N
S
′
ap
= N
R
+ N
S
+ N
R
log
C
+ N
S
log
.
(13.5)
An ideal lossless context-free compression scheme (the entropy coder)
would compress the RS-vector consisting of (N
R
+ N
S
) bits using−N
R
N
R
N
R
+N
S
N
S
N
R
+N
S
log
−N
S
log
bits.
