Watermarks - Disappearing Cryptography - page 315

and preliminary tests show that rotating an image by 45 degrees be-
fore blurring and sharpening the image will destroy the watermark.
All of the watermarking solutions have some weakness to tricks
like that. Measuring the amount of resistance is hard to do. The
StirMark suite is a collection of basic distortions that bend, fold and
mutilate an image while testing to see if the watermark survives. This
collection is a good beginning, but the range of distortion is almost
infinite and difficult to model or define.
16.2.1 AWatermarking Taxonomy
At this point, watermark creators are still exploring the limits of the
science and trying to define what can and can't be done to resist the
real and somewhat imagined threats. Toward this end, they've cre-
ated a kind of taxonomy of watermarks that describes the different
kinds and their usefulness. Here is a list of the different ways to eval-
uate them:
Fragility Some watermarks disappear if one bit of the image is
changed. Hiding information in the least significant bit (Chap-
ter 9) is usually not a robust watermark because one flipped
bit can make it impossible to recover all of the information.
Even error correction and redundancy can add only so much
strength.
Fragile watermarks, though, are not always useless. Some pro-
pose inserting watermarks that break immediately as a tech-
nique to detect any kind of tampering. If the watermark in-
cludes some digital signature of the document, then it offers
assurance that the file is unaltered.
Continuity Some watermarks resist a wide range of distortions by
disappearing gradually as the changes grow larger. Larger and
larger distortions produce weaker and weaker indications that
a watermark is present.
This continuity is often found in some of the wavelet-encoding
solutions described in Chapter 14. The watermark itself is a
vector of coefficients describing the image. Small changes in
the image produce small changes of the coefficients. A vector
matching algorithm finds the watermark by finding the best
match.
In many cases, the strength of the watermark is a trade off with
the amount of information in the watermark itself. A large