Cryptography Reference
In-Depth Information
4. Use the appropriate formula to extract the values of
αb
i
.
5. Use the knowledge of the distribution of the random elements,
b
i
, to normalize this vector. That is, if the values of
b
i
are real
numbers chosen from a normal distribution around .5, then
determine which value of
α
moves the average to
.
5
.Remove
α
from the vector through division.
6. Compare the vector of
{b
0
,b
1
,b
2
,...b
k−1
}
to the other known
vectors and choose the best match.
The last step for identifying the “watermark” is one of the most
limiting for this particular algorithm. Anyone searching for it must
have a database of all watermarks in existence. The algorithmusually
doesn't identify a perfect match because roundoff errors add impre-
cision evenwhen the image file is not distorted. The process of com-
puting the DCTs and FFTs introduces some roundoff errors and en-
capsulating the image in a standard 8-bit or 24-bit format adds some
more. For this reason, the best we get is the most probable match.
This makes the algorithm good for some kinds of watermarks but
less than perfect for hidden communication. The sender and re-
ceiver must agree on both the cover image and some code book of
messages or watermarks that will be embedded in the data.
If these restrictions don't affect your needs, the algorithm does
offer a number of desirable features. Cox and colleagues tested the
algorithm with a number of experiments that proved its robustness.
They began with several
256
256
pixel images, distorted the images
and then tested for the correct watermark. They tried shrinking the
size by a factor of
×
1
2
, using heavy JPEG compression, deleting a re-
gion around the outside border, and dithering it. They even printed
the image, photocopied it, and scanned it back in without removing
the watermark. In all of their reported experiments, the algorithm
identified the correct watermark, although the distortions reduced
the strength.
The group also tested several good attacks that might bemounted
by an attacker determined to erase the information. First, they tried
watermarking the image with four new watermarks. The final test
pulled out all five, although it could not be determined which were
the first and the last. Second, they tried to average together five im-
ages created with different watermarks and found that all five could
still be identified. They indicate, however, that the algorithm may
not be as robust if the attacker were to push this a bit further, say by
using
100
or
1000
different watermarks.
