Cryptography Reference
In-Depth Information
14.7.2 Removing the Original from the Detection Pro-
cess
Keeping the original unaltered data on hand is often unacceptable
for applications like watermarking. Ideally, an average user will be
able to extract the information from the file without having the orig-
inal available. Many of the watermarking applications assume that
the average person can't be trusted with unwatermarked data be-
cause they'll just pirate it.
A variant of the previous algorithm from Cox et al. does not re-
quire the original data to reveal the watermark. A. Piva, M. Barni,
F. Bartolini, and V. Cappellini produced a similar algorithm that
sorts the coefficients to the transform in a predictable way. Figure
14.13, for instance, shows a zig-zag pattern for ordering the coeffi-
cients from a two dimensional transform according to their rough
frequency. If this solution is used, there is no need to keep the origi-
nal data on hand to look for the
k
most significant coefficients. Many
other variants are emerging.
14.7.3 Tempering the Wake
Inserting information by tweaking the coefficients can sometimes
have a significant effect on the final image. The most fragile sections
of the image are the smooth, constant patches like pictures of a clear,
blue, cloudless summer sky. Listeners can often hear changes in au-
dio files with pure tones or long quiet segments. Data with rapidly
changing values mean there is plenty of texture to hide information.
Smooth, slowly changing data means there's little room. In this most
abstract sense, this follows from information theory. High entropy
data is a high bandwidth channel. Low entropy data is a low band-
width channel.
Some algorithms try to adapt the strength of a watermark to the
underlying data by adjusting the value of
according to the camou-
flaging data. This means the strength of the watermark becomes a
function of location (
α
α
t
)inaudiofiles.
There are numerous ways to calculate this value of
α
i,j
) in images and of time (
,butthesim-
plest usually suffice. Taking a window around the point in space
or time and averaging the deviation from the mean is easy enough.
[PBBC97] More sophisticated studies of the human perception sys-
temmay be able to provide a deeper understanding of how our eyes
and ears react to different frequencies.
α
