Cryptography Reference
In-Depth Information
packed into each element
x
i
. This guarantees that the damage mis-
ordering will not disturb the other packets.
13.4 Invariant Forms
f
One of the biggest challenges in creating the functions
is the fact
f
that the message encoder will use
to choose the order
before
the
f
data is hidden. The receiver will use
after
the data is inserted. If
the hiding process can change the value of
f
, then the order could be
mangled.
There are two basic ways to design
f
does not change when data is hidden. Some simple invariant func-
tions are:
f
. The first is to ensure that
•
If the elements are pixels where data is inserted into the least
significant bit, then the value of
f
should exclude the least sig-
nificant bit from the calculations.
•
If the elements are compressed versions of audio or image data,
then the function
should exclude the coefficients that might
be changed by inserting information. JPEG files, for instance,
can hide data by modifying the least signficant bit of the coeffi-
cients.
f
f
should depend on the other bits.
•
If the data is hidden in the elements with a spread-spectrum
technique that modifies the individual elements by no more
than
±
x
i
be the value
, then the values can be normalized. Let
x
i
− <x
i
≤ x
i
+
of an element. This defines a range
.Letthe
{
0
,
2
,
4
,
6
,...}
set of normalized or canonical points be
.One
and only one of these points is guaranteed to be in each range.
Each value of
x
i
can be replaced by the one canonical point that
lies within
±
of
x
i
.
To comput e
f
use the canonical points instead of the real values
of
x
i
.
13.5 Canonical Forms
Another solution is to create a “canonical form” for each element.
That is, choose one version of the element that is the same. Then,
the data is removed by converting it into the canonical form and the
result is used to compute
.
Here are some basic ones:
f
