Cryptography Reference
In-Depth Information
Moving the individual lines up or down by one or two six-hundredths
of an inch is usually sufficient to be detected. They do note that their
results require a well-oriented document where the baselines of the
text are aligned closely with the raster lines. Presumably, a more so-
phisticated algorithm could compensate for the error by modeling
the antialiasing, but it is probably simpler to just line up the paper
correctly in the first place.
15.3.2 MandelSteg and Secrets
Any image is a candidate for hiding information, but some are bet-
ter than others. Ordinarily, images with plenty of variation seem
perfect. If the neighboring pixels are different colors, then the
eye doesn't detect subtle changes in the individual pixels. This
led Henry Hastur to create a program that flips the least signif-
icant bits of a Mandelbrot set. These images are quite popular
and well-known throughout the mathematics community. This pro-
gram, known as MandelSteg, is available with source code from the
Cypherpunks archive (
ftp://ftp.csua.berkeley.edu/pub/cypher-
punks/steganography/
).
Themanual notes that there are several weaknesses in the system.
First, someone can simply run the data recovery program, GifExtract,
to remove the bits. Although there are several different settings, one
will work. For this reason, the author suggests using Stealth, a pro-
gram that will strip away the framing text from a PGP message, leav-
ing only noise.
There are other weaknesses. TheMandelbrot image acts as a one-
time pad for the data. As with any encodingmethod, the information
can be extracted if someone can find a pattern in the key data. The
Mandelbrot set might look very random and chaotic, but there is still
plenty of structure. Each pixel represents the number of iterations
before a simple equation (
)
converges. Adjacent pix-
els often take a different number of pixels, but they are still linked by
their common generating equation. For this reason, I think it may be
quite possible to study themost significant bits of a fractal image and
determine the location from where it came. This would allow some-
one to recalculate the least significant bits and extract the answer.
2
f
(
z
)=
z
2
+
c
2
David Joyce offers a Mandelbrot image generator on the Web (
http://
aleph0.clarku.edu/djoyce/julia/explorer.html
).
