Cryptography Reference
In-Depth Information
(0,10)
(10,10)
(0,10)
(10,10)
referance line
referance line
(0,0)
(10,0)
(0,0)
(10,0)
(a) Subpatch in Set A
(b) Subpatch in Set B
Fig. 6.4.
The modification of vertices in set A and B (algorithm in [6]).
containing like numbers of vertices. One block hides one watermark bit. For
an arbitrary block, a hidden bit can be embedded by Eqn. (6.1),
V
′
i
= V
i
+ b
i
p
i
α,
(6.1)
where V
i
and V
′
i
are the original coordinates and the watermarked coordinates
of the vertices respectively within the ith block. The watermark bit b
i
is
the ith and p
i
is the ith bit of a PNS. The amplitude factor is α.Inthe
watermark extraction procedure, the original map is needed and the same
PNS is used for decoding, which can be seen as a correlation based detecting
procedure. The scheme is robust to kinds of attacks however it is not a blind
scheme. A watermarking scheme with informed detection generally could not
be practically used.
Voigt and Busch [8] proposed an algorithm based on a direct sequence
spread spectrum. Watermark embedding and extraction are restricted to the
specific decimal digital positions of the raw coordinates. Suppose a single bit
is to be embedded. The bit is first replaced by a pseudo noise sequence (PNS)
in order to form the watermark data, which is in essence a procedure of direct
sequence spread spectrum. The PNS is then embedded in the coordinates by
modifying the lower 2 decimal digital values of the coordinates. The ampli-
tudes of the modifications are equal to the tolerance of the map data. In the
data extraction stage, a modified correlation between the PNS and the lower
2 decimal digital values of watermarked coordinates is calculated and used
for judgement. The algorithm is robust to additive noise. Adding or removing
vertices could destroy the synchronization of the detector.
6.2.2 Transform Domain Schemes
A watermark is embedded by modifying the transform coe
cients of the co-
ordinates. The typical schemes are implemented in following domains: DFT
domain, DWT domain, and Mesh-Spectral Domain.
