Cryptography Reference
In-Depth Information
begin
vertex
1
0
1
0
0
1
1
end
vertex
interpolated vertices
Fig. 6.3.
A simple illustration of Hubers scheme.
In Figure 6.3, the Begin Vertex and the End Vertex represented by two
white circles are two adjacent vertices in the original map. All black filled
points are interpolated new vertices obtained during the embedding proce-
dure. Suppose the distance between the begin vertex and the first interpolated
vertex represents a bit 1 and half of the distance represents a bit 0, the data
embedded in the line segment is then 1010011. The scheme has no distortion
and it is robust to geometric attacks. Embedding the watermark enlarges the
size of the cover data. The scheme is also fragile to map simplification.
Based on Statistical Property
In a scheme proposed by Voigt and Busch [6], the statistical property of the
coordinates is utilized for hiding data. A rectangular region in the original map
is selected as the cover data to embed a watermark bit. Firstly, the region is di-
vided into patches. Then a pseudo-noise sequence is used to divide all patches
into two disjunctive sets A and B. Next, every patch in two sets is further
divided into subpatches. For each subpatch, the coordinates of the vertices
within it are transformed into new relative values by taking the south-west
corner as the origin. If there is no embedded data, the relative coordinates in
set A and B are both uniformly distributed with similar properties such as the
expectation and the variance. If a bit 1 is to be embedded, the modification
of the vertices is done within every subpatch as shown in Fig. 6.4. After the
modification, the sample variance of coordinate values in set A (denoted as
S
A
) is increased and that of set B (denoted as S
B
) is decreased. A random
variable F = S
A
/S
B
which follows F-distribution is then used for detection
based on a threshold.
By utilizing the statistical property of coordinates, the algorithm has
proved to be robust to many attacks such as map shifting, data interpola-
tion, simplification, additive noise, for example.
Correlation Related
Ohbuchi et al. [7] presented a scheme based on correlation detection. A Pseudo
Noise Sequence (PNS) is used to improve the security and the detecting relia-
bility in the scheme. The cover map is first segmented into rectangular blocks
