Cryptography Reference
In-Depth Information
3. Try all possible values of
)
and choose the maximum
(or minimum). This is the canonical order of
F
(
w, p, q
w
.
If
mn
is a reasonable value, then it might makemore sense to store
versions of each watermark in a database. If it is large, then a
canonical order might make more sense.
It should become clear at this point that all possible
5
16
water-
marks can't be used. Some of them have identical canonical values.
Every watermark has
15
other shifty cousins.
mn
16.4.1 Effects of Distortion
Much of the success of this watermark depends on the way that the
averaging balances out any potential changes. If the noise or distor-
tion in the image is uniformly distributed, then the changes should
balance out. The averages will cancel out the changes.
Not all distortions are equal. Several of the StirMark changes in-
troduce or delete rows or columns of pixels from the middle of the
image. This can throw off the averaging completely and destroy this
kind of watermark. While it may be possible to recover it by sampling
sections of the image, the process is neither easy nor guaranteed.
16.4.2 Birthday Marks
Here is a short, more basic example loosely based on a number of
systems. The phrase
birthday marks
is borrowed from the
birthday
paradox
, the fact that the odds of any two people having the same
birthday in a group of
n
2
)
,asthe
group grows. In a group of 23 people, there's a 50-50 chance that
one pair will share the same birthday and it becomes almost a sure
thing, (
n
people increases quadratically,
O
(
99%
) when there are 57 people. Clearly at 367 people, it's
guaranteed.
>
The birthday paradox
was also an inspiration
for the birthday attacks
using hash collisions.
[Cop85, GCC88]
m
i,j
marks in the content by tweaking
positions in the file. While the notation suggests a grid because there
are two parameters, the marks don't need to be arranged in a grid.
Indeed, there shouldn't be any detectable connection between the
parameters,
Imagine that you can put
i
and
j
,andthelocationsofthemarks. Ifafilehas
k
locations, you might store the marks at a position computed by
encrypting
.
Although there won't be any connection between the locations
and the parameters
i
and
j
, let's write these marks in a matrix for
clarity. For simplicity, let's imagine there are
16
users so we'll assign
16
unique ids. When user
i
and
j
a
buys a document, let's put a mark on
spots
m
a,i
and
m
i,a
for all
0
≤ i<
16
.Forthesakeofexample,
