Cryptography Reference
In-Depth Information
transmitting the resulting compressed bitstream as a part of the embedding
payload. The CALIC compression algorithm, which uses the unaltered por-
tions of the host signal as side information, improves the compression e
ciency
and, thus, the data-embedding capacity.
Generalized-LSB (G-LSB) Embedding
A generalization of LSB-embedded method, namely G-LSB, is employed by
Celik et al. [8]. If the host signal is represented by a vector, G-LSB embedding
and extraction can be represented as:
s
w
= Q
L
(s)+w,
(13.6)
w = s
w
−Q
L
(s
w
),
(13.7)
where s
w
represents the signal containing the embedded information, w repre-
sents the embedded payload vector of L-ary symbols. That is, w
i
∈0, 1,...,
L−1,and
x
L
Q
L
(x)=L
(13.8)
is an L-level scalar quantization function, and⌊⌋represents the operation of
truncation to the integer part.
In the embedding procedure given in Eq. (13.6), for L-ary watermark sym-
bols w
i
, it is necessary for them to be converted into binary bit-stream and
vice versa in some practical applications. The binary to L-ary conversion algo-
rithm given below, can effectively avoid out-of-range sample values produced
by the embedding procedure. For instance, in an 8 bpp representation where
the range is [0, 255], if operating parameters L =6,Q
L
(s) = 252, w =5are
used, the output s
w
= 257 exceeds the range [0, 255].
The binary to L-ary conversion is presented as follows:
The binary input string h is interpreted as the binary representation of a
number H in the interval R =[0, 1).Thatis,H = .h
0
h
1
h
2
and H∈[0, 1).
The signal is encoded using integer values between zero and s
max
.
1) Given s and s
max
, determine Q
L
(s)andN = min (L, s
max
−Q
L
(s)) the
number of possible levels.
2) Divide R into N equal subintervals, R
0
to R
N−1
.
3) Select the subinterval that satisfies H∈R
n
.
4) The watermark symbol is w = n.
5) Set R = R
n
and then go to Step 1, for the next sample.
The conversion process is illustrated in Fig. 13.5. The inverse conversion
process is performed by the dual of the above algorithm. This process is given
below.
1) Given s and s
max
, determine Q
L
(s)andN = min(L, s
max
−Q
L
(s
w
)) which
is the number of possible levels.
