Cryptography Reference
In-Depth Information
mcos
is the
angle.) Many users of the DFT feel that the transform is more
sensitive to changes made in the angles of the coefficient than
changes made in the magnitude of the coefficients.
(
θ
)
and
b
=
msin
(
θ
)
,where
m
is themagnitude and
θ
[RDB96,
LJ00]
This method is naturally adaptive to the size of the coefficients.
Small values are tweaked a small amount if they're rotated
θ
+
ψ
degrees. Large values are tweaked a large amount.
Changing the angle this way requires a bit of attention to sym-
metry. When the input to a DFT are real values, as they almost
are in steganographic examples, then the angles are symmet-
ric. This symmetry must be preserved to guarantee real values
will emerge from the inverse transform.
Let
θ
i,j
stand for the angle of the coefficient
(
i, j
)
.If
ψ
is added
to
θ
i,j
,then
−ψ
must be added to
θ
m−i,n−j
,where
(
m, n
)
are the
dimensions of the image.
14.10 Summary
Spreading the information over a number of pixels or units in a
sound file adds more security and intractability. Splitting each bit
of information into a number of pieces and distributing these pieces
throughout a file reduces the chance of detection and increases re-
sistance to damage. The more the information is spread throughout
the file, the more redundancy blocks attacks.
Many solutions use well-understood software algorithms like the
Fourier transform. These tools are usually quite popular in tech-
niques for adding watermarks because many compression algo-
rithms use the same tools. The watermarks are usually preserved
by compression in these cases because the algorithms use the same
transforms.
The Disguise
Information is spread throughout a file by adding small
changes to a number of data elements in the file. When all of
the small changes are added up, the information emerges.
How Secure Is It?
The changes are small and distributed so they can
be more secure than other solutions. Very distributed informa-
tion is resistant to attack and change because an attacker must
destroy enough of the signal to change it. The more places the
information is hidden, the harder it is for the attacker to locate
it and destroy it.
