Cryptography Reference
In-Depth Information
⎧
⎨
d
x
′
2
floor
f
i
=1;
d
i
x
=
(6.12)
d
x
′
2
⎩
2floor
+ L(j),
i
=0.
′
Here d
i
x
and f
i
are respectively the elements of D
′
and F .Forf
i
=1,d
i
x
is
x
′
obtained by discarding the lowest bit of d
i
x
and right shifting it by 1 bit. For
′
f
i
=0,d
i
x
is recovered by directly replacing the LSB of d
i
x
by the original
LSB L(j), where j is the index of L.
Finally, the original x coordinates can be completely recovered by the use
of Eqn. (6.6) and the restored difference sequence D
x
and the integer-mean
sequence M
x
.
Experiments
The performance of the scheme was tested by experiments using a river map
(Fig. 13(a)) with the scale 1:4000000 as the cover data. The total number of
the vertices in the map is 252000. There are 6 digits after the decimal point
of every coordinate value. All coordinates are first converted into integers by
multiplying 10
6
. The precision tolerance of the map is τ =0.5 kilometer.
Fig. 6.12.
Grayscale image (Lena, 130130).
Both the x and y coordinates are used to hide data in order to improve the
capacity. Although the induced distortions of some vertices could exceed the
tolerance τ , the validity of the map data can be ensured as the original map can
be exactly recovered after the hidden data has been extracted. Hidden data
with a max length of 146550 bits can be embedded. Here the max capacity of
the scheme is about 0.58bit/vertex. The MD5 hash of the cover map (128 bits)
and a grayscale image with a size of 130130 (135200 bits, Fig. 6.12) is taken
as the hidden data and is embedded into the cover map. The remaining space
of the payload could also be utilized to hide other user data. For example the
meta data of the cover map. Figure 6.13(b) is the watermarked map which
indicates that the distortions induced by data hiding can be well controlled
