Cryptography Reference
In-Depth Information
effects of one powerful signal are easy to filter out by placing limits
on the amount of power detected at each frequency.
These algorithms for
spreading information
out over a number of
bits are very similar to
the error-correcting
codes described in
Chapter 3.
If a jammer is actually able to identify the band of frequencies
used for the entire spread-spectrum signal, it is still hard to disrupt
it by injecting random noise everywhere. The noise just cancels out
and the signal shines through after integration. In practice, there are
ways to jam spread-spectrum signals, but they usually require the
jammer to pump out significantly more power. Large amounts of
noise can disrupt the system.
14.3 Going Digital
The spread-spectrum solutions use the analog metaphors of contin-
uous functions measuring “energy” that are evaluated using integra-
tion. In the digital world, integers measuring any quantity define dis-
crete functions. In many cases, they measure energy. The integers
that define the amount of red, blue and green color at any particular
pixel measure the amount of red, green and blue light coming from
that location. The integers in a sound file measure the amount of en-
ergy traveling as a pressure wave. Of course, the same techniques
also work for generic numbers that measure things besides energy.
There's no reason why these techniques couldn't be used with an ac-
counting program counting money.
A “spread-spectrum” digital system uses the following steps:
1.
Choose the Locations
If the information is going to be spread
out over a number of different locations in the document, then
the locations should be chosen with as much care as practical.
The simplest solution is choose a block of pixels, a section of an
audio file, or perhaps a block of numbers. More complicated
solutions may make sense in some cases. There's no reason
why the locations can't be rearranged, reordered, or selected as
directed by some keyed algorithm. This might be done with a
sorting algorithm from Chapter 13 to find the right locations
or a random number generator that hops from pixel to pixel
finding the right ones.
2.
Identify the Signal Strength
Spread spectrum solutions try to
hide the signal in the noise. If the hidden signal is so much
larger than the noise that it competes with and overwhelms the
main signal, then the game is lost.
Choosing the strength for the hidden signal is an art. A strong
signal may withstand the effects of inexact compression algo-
