Cryptography Reference
In-Depth Information
vide plenty of practical cover. Better computer graphics technology
is evolving faster than any algorithm for detecting the flaws. More
complicated models are coming faster than we can suss them out.
If the practical limitations aren't good enough, themodels for syn-
thesizing worlds can be deputized to carry additional information.
Instead of hiding the extra information of the final image or sound
file, the information can be encoded during the synthesis.
There are many opportunities to hide information. Many com-
puter graphics algorithms use random number generators to add a
few bits of imperfection and the realism that comes along with them.
Any of these random number streams can be hijacked to carry data.
The program
MandelSteg, developed
by Henry Hastur, hides
information in the least
significant bit of an
image of the
Mandelbrot Set. This
synthetic image is
computed to seven bits
of accuracy and then the
message is hidden in the
eighth. See page 319.
Another source can be found in tweaking the data used to drive
the synthesis, perhaps by changing the least significant bits of the
data. One version of an image may put the ball at coordinates
(1414
220)
.Awater-
marked version of a movie may encode the true owner's name in the
position of one of the characters and the moment they start talk-
ing. Each version of the film will have slightly different values for
these items. The rightful owner could be extracted from these subtle
changes.
Wolfgang Funk worked through some of the details for perturbing
three-dimensional models described with polynomial curves in the
NURBS standard. [Fun06] The polynomials describing the objects
are specified by points along the surface known as
control points
.
New control points can be added without significantly changing the
description of the surface if they're placed in the right spots. Old
control points can usually be moved a slight amount so the shape
changes a bit. Hao-Tian Wu and Yiu-ming Cheung suggest using a
secret key to traverse the points describing the object and thenmod-
ifying their position relative to the centroid of other points. Moving
one direction by a small amount encodes a 0 andmoving in the other
direction encodes a 1.[WmC06]
An even more complicated location to hide the information can
be found by changing the physics of the model. The acoustical char-
acteristics of the room are easy to change slightly. The music may
sound exactly the same. The musicians may start playing at exactly
the same time. But the size and characteristics of the echos may
change just a bit.
There are many ways that the parameters used to model the
physics can be changed throughout a file. The most important chal-
lenge is guaranteeing that the changes will be detectable in the image
or sound file. This is not as much of a problem as it can be for other
,
221)
and another version may put it at
(1413
,
