Cryptography Reference
In-Depth Information
in functions means that the compression can be further tuned to
extract the best performance. There are many different wavelets
available and some are better at compressing some files than others.
Choosing the best one is often as much an art as a science.
In some cases, steganographers suggest that the choice of the
function can also act like a key if only the sender and the receiver
know the particular wavelet.
Are highly tuned
wavelets more or less
stable for information
encoding? That is, can a
small change in a
coefficient be reliably
reassembled later, even
after printing and
scanning? In other
words, how large must
the
It is not possible to go into the wavelet field in much depth here
because it is more complex and not much of this complexity affects
the ability to hide information.
Most of the same techniques for hiding information with DCTs
and DFTs work well with DWTs. In some cases, they outperform the
basic solutions. It is not uncommon to find that information hidden
withDWTs does a better job of surviving wavelet-based compression
algorithms than information hidden with DCTs or DFTs. [XBA97] Us-
ing the same model for compression and information hiding works
well. Of course, this means that an attacker can just choose a dif-
ferent compression scheme or compress the file with a number of
schemes in the hope of foiling one.
α
term be?
14.9 Modifications
The basic approach to hiding information with sines, cosines or
other wavelets is to transform the underlying data, tweak the coef-
ficients, and then invert the transformation. If the choice of coef-
ficientsisgoodandthesizeofthechangeismanageable,thenthe
result is pretty close to the original.
There are a number of variations on the way to choose the coeffi-
cients and encode some data in the ones that are selected. Here are
some of the more notable:
Identify the Best Areas
Many algorithms attempt to break up an im-
age or sound file and identify the best parts for hiding the infor-
mation. Smooth, stable regions turn mottled or noisy if coeffi-
cients are changed even a small amount.
Multi-resolution wavelet transforms are a good tool for identi-
fying these regions because they recursively break up an image
until a good enough model is found. Smooth, stable sections
are often modeled on a large scale, while noisy, detailed sec-
tions get broken up multiple times. The natural solution is to
hide the information in the coefficients that model the small-
est, most detailed regions. This confines the changes to the
