Cryptography Reference
In-Depth Information
one version and another pixel comes from another, then there's
a good chance that neither watermark will survive. Some
schemes deliberately try to avoid this kind of attack by embed-
ding multiple copies of the signature and creating identifica-
tion codes that can survive this averaging.
Keying Is a key required to read the watermark? Is a key required to
insert it? Some algorithms use keys to control who inserts the
data to prevent unauthorized people from faking documents
or creating faked watermarks. Others use keys to ensure that
only the right people can extract the watermark and glean the
information. Chapter 12 describes some of the approaches.
No algorithm offers the ideal combination of these features, in
part because there's often no way to have one feature without sacri-
ficing the other. The good news is that often watermarks that fail one
task can find use in another form.
16.3 A Basic Watermark
Here is a basic technique for watermarking that blends together
many of the different solutions proposed in recent years. This de-
scription is a bit abstract, which obscures the challenges of actually
producing a working version that implements the technique. Here's
the algorithm:
1. Beginwithadocumentinastandardform.
2. Choose a mechanism for decomposing the document into im-
portant components. One solution is to use the discrete cosine
transform to model the signal as the sum of a collection of co-
sine functions multiplied by some coefficients. Let
{c 0 ,...,c n }
be the set of coefficients.
3. The coefficients measure the size of the different components.
Ideally, the model will guarantee that large coefficients have
a large effect on the document and small coefficients have a
small effect. If this is the case, find a way to exclude the small
coefficients. They're not important and likely to be changed
dramatically by small changes in the document itself.
4. Quantize the coefficents by finding the closest replacement
from a small set of values. One of the simplest quantization
schemes for a value,
c i , is to find the integer
k i such that
k i Q
is
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