Cryptography Reference
In-Depth Information
rithms but it also could be noticeable. A weaker signal may
avoid detection by both a casual user and anyone trying to re-
cover it.
3.
Study the Human Response
Many of the developers of spread-
spectrum solutions for audio files or visual files study the limits
of the human's senses and try to arrange for their signals to stay
beyond these limits. The signal injected into an audio file may
stay in the low levels of the noise or it may hide in the echoes.
Unfortunately, there is a wide range in human perception.
Some people have more sensitive eyes and ears. Everyone can
benefit from training. Many spread-spectrum signal designers
have developed tools that fooled themselves and their friends,
but were easily detected by others.
4.
Inject the Signal
The information is added to the covering data
by making changes simultaneously in all of the locations. If the
file is a picture, then all of the pixels are changed by a small
amount. If it's a sound file, then the sound at each moment
gets either a bit stronger or a bit weaker.
The signal is removed after taking the same steps to find the right
locations in the file.
Many approaches to spread-spectrum signal hiding use a mathe-
matical algorithm known as the Fast Fourier Transform. This uses
a collection of cosine and sine functions to create a model of the
underlying data. The model can be tweaked in small ways to hide
a signal. These approaches might be said to be everything in par-
allel. More modern variations use only the cosine (Discrete Cosine
Transform), the sine (Discrete Sine Transform), or more complicated
waveforms altogether (Discrete Wavelet Transform).
14.3.1 An example
Figure 14.3 shows the graph of .33 seconds from a sound file with
samples taken 44,100 times per second. The sound file records the
sound intensity with a sequence of
14
,
976
integers that vary from
about
30
,
000
to about
−
30
,
000
.Callthese
x
i
,where
i
ranges between
0
and
14975
.
How can information be distributed throughout a file? A spread-
spectrum approach is to grab a block of data and add small parts of
the message to every element in the block. Figure 14.4 shows a graph
of the data at the moments between 8200 and 8600 in the sound file.
A message can be encoded by adding or subtracting a small amount
