Cryptography Reference
In-Depth Information
ences: every
m
i,j
,where
i
or
j
is either
3
or
7
except
for
m
3,3
,m
3,7
,m
7,3
and
m
7,7
.
If
3
and
7
are able to blur away the marks at every place where
there's a difference, they'll still leave four marks that identify the pair.
The content owners will be able to track the document to these two
people.
If
3
and
7
decide to use an attack and flip a coin at every difference
they find in their document and keep one or the other version, they'll
still leave plenty of marks with their unique identity.
This naive solution does not have the best performance as the
number of unique Ids grows larger because it requires
n
2
)
marks
O
(
for
unique Ids. This can be avoided to some extent by repeating the
process a number of times. Imagine, for instance, that a unique Id
number consists of six hexadecimal digits. The previous matrix with
16
2
= 256
marks could be repeated six times, once to encode each
digit. Instead of requiring
2
24
2
=2
48
marks, it would only require
6
n
×
256
, a much smaller number.
16.5 Summary
Watermarking is not an easy challenge for steganography. Many of
the researchers exploring it have high ideals and want their water-
marks to remain intact even after a fairly daunting array of distor-
tions and changes.
This chapter offers two basic algorithms that resist some basic
distortions. The discussion avoids much of the complexity involved
in determining when a watermark may or may not be present. Find-
ing it is easy if the image is not changed. Finding it afterwards be-
comesanexerciseininformedguessing. Justwhenisonevectorof
numbers close enough to another? Which is the best match for a
watermark? These are questions of engineering and design not an-
swered in this chapter. Finding the best solution requires building a
system and testing it with a collection of sample images and sound
files. Much of the real challenge is tweaking the coefficents.
The Disguise
Watermarks are steganographic solutions designed to
withstand more general attacks from a savvy set of users and
potential pirates. The ideal watermark will embed information
in such a way that the only way to destroy it is to introduce so
much noise and distortion that the original image is unusable
and perhaps unrecognizable.
How Secure Is It?
None of the watermarks come close to this ideal,
but some are quite useful. Systems like Digimarc's are in wide
