Cryptography Reference
In-Depth Information
severalpeopletousethesamechannel. Iftheyuseasmallpart
of the channel chosen at random, then the codes will correct any
occasional collisions.
The field is also blessed with a deep body of literature exploring
many different variations that lie outside of the scope of this intro-
duction. Unfortunately this topic does not have the space to consider
them all nor outline the different ways that they can be more or less
useful for steganography.
Chapter 14 describes spread-spectrum-like applications for hid-
ing information. These techniques also rely on distributing the mes-
sage over a relatively large number of elements in the file. If several of
the elements are disturbed or mangled, these spread-spectrum solu-
tions can still recover the message.
The Disguise
If you want to use these codes to hide information, the
best solution is to tweak a small subset of bits. If each block has
8 bits, for instance, the you can send 3 bits per block. If you
want to send 000, then flip bit 0. If you want to send 011, then
flip bit 3, and so on. When the bits are finally read at the other
end, the error-correcting codes will remove the errors and the
casual reader won't even know they were there. You can use the
error-correcting codes to recover them.
Of course, this solution trades accuracy for steganography. Ac-
cidental or intentional errors will destroy the message. The
error-correcting powers of the equation will be spent on car-
rying the information.
Another simple solution is to encode your message bymaking a
few small changes in a signal that is already protected by some
error correction. Your message might be hide three bits (
0
≤
i<
. This can be repeated for
every error-corrected byte, a pretty good packing ratio. When
someone receives the file, the regular error correction code will
fix the problem effectively hiding your changes. You can strip
the secret bits out by using the error-correcting algorithm to
detect the changes.
8
) by creating a fake error in bit
i
How Secure Is It?
Error-correcting codes are not at all secure against
people who want to read them. The patterns between the bits
are easy to detect. They are quite resistant, however, against
errors.
How To Use Them?
Error-correcting codes are rarely sold to con-
sumers directly, although consumers use them all the time.
Many electronic devices, however, like CD players and cell
