Cryptography Reference
In-Depth Information
comp(L): Lossless Compressed L. To recover the original data when the hid-
den bit is embedded by LSB replacing, the original LSB of d
i
x
must be
known. This is recorded in L.
P : The payload of the scheme. It could be the hash for example either MD5in
the cover map for data authentication, the meta data of the cover map,
or where the secret message is transmitted by users (Hidden Communica-
tion).
Comp(F ) and comp(L) are both used for lossless data recovering. P is the
real payload which is referred to as the capacity of the scheme. The final W
is a N -length binary sequence which can be denoted as W =w
1
,,w
N
.
2. Data Embedding
We will use the method of hiding data in the x coordinates as an example.
The method is exactly the same for the y coordinates. Until now, three N -
length sequences could be obtained by former methods. That is the difference
sequence D
x
, the flag F , and the hidden data W . The embedding task is to
hide W in the x coordinates by modifying the difference sequence D
x
.Each
element d
i
x
of D
x
is modified as shown in Eqn. (6.11) according to the flag f
i
:
2d
i
x
+ w
i
,f
i
=1;
′
d
i
x
=
i =1,,N.
(6.11)
d
x
2
2floor
+ w
i
,f
i
=0;
For d
i
x
when f
i
= 1, the value w
i
is embedded by difference expansion. That
is left shift d
i
x
by 1 bit and place w
i
at the lowest bit of the shifted d
i
x
. Other-
wise for d
i
x
where f
i
= 0, the value w
i
is embedded by directly replacing the
LSB of d
i
x
. Denoting the modified difference sequence as D
′
′
,
′
x
=d
x
,,d
x
′
the watermarked x coordinates could be calculated with D
x
and M
x
by the
inverse transform as shown in Eqn. (6.6).
3. Data Extraction and Original Map Recovering
Given the watermarked map containing hidden data in its x coordinates,
the same methods used in the embedding procedure are used to group the
map data and to calculate both the difference sequence D
x
and the integer-
mean sequence M
x
. The hidden data W can be obtained by extracting the
lowest bits of all elements of D
′
′
x
. The payload P and two compressed sequence
comp(F ) and comp(L) may be separated from W with the help of the header
information H.
In order to recover the original x coordinates, it is necessary to obtain
the original difference sequence D
x
. Two sequences comp(F ) and comp(L)
are uncompressed, obtaining the flag F and the original LSB L. Then D
x
is
obtained by using D
′
x
, F and L.Fori =1,,N, each element d
i
x
of D
x
is
calculated using Eqn. (6.12),
