Cryptography Reference
In-Depth Information
mean that the JPEG algorithm is useless to the person whowould like
to hide information successfully in images.
There are two possible ways that you can use the JPEG algorithm
to store information. The first is to use it as a tool to identify the
complexity of an image. This section discusses that approach. The
second way is to use some hidden parts of the standard to hide infor-
mation. That is described in the next section.
The JPEG algorithm can be a good tool for identifying the level of
detail in a scene. This level of detail can be used to find the noisiest
corners of the image where data can be stored. In the first part of the
chapter, the basic algorithm for hiding information would just use
the
=1
,therewould
only be a small but uniform effect that was randomly distributed
throughout the image. If
n
least significant bits to hide information. If
n
was larger, then more information could
be stored away in the image, but more distortion would also emerge.
In any case, the distortion would be uniformly distributed across the
entire image, even if this wasn't practical.
For instance, imagine a picture of a person sitting on a red-and-
white checked picnic blanket in the middle of a grassy field. It might
make sense to set
n
=4
over a grassy section because it is out of focus
and not particularly filled with important detail. On the other hand,
you would only want to use
n
=1
in the areas of the face because
the detail was so significant to the photo. Naturally, you could go
through the photo by hand and identify the most significant and
fragile sections of the photo, but this would defeat the purpose of
the algorithm. Not only would it be time-consuming, but you would
need to arrange for someone on the other end of the conversation to
construct exactly the same partition. This is the only way that they
would know how to recover the bits.
The JPEG compression algorithm offers an automatic way to seg-
ment the photo and identify the most important or salient portions
of an image. It was designed to do this to increase compression. The
algorithm's creators tweaked the algorithm so it would provide visu-
ally satisfying images even after some of the detail was lost to com-
pression.
The application is basic.
n
be a 24-bit image file wait-
ing to have data hidden in some of its least significant bits. Let
JPEG
−
1
(
Let
f
JPEG
(
f
))
be the result of first compressing
f
with JPEG
and then uncompressing it.
The differences between
f
and
JPEG
−
1
(
))
reveal how much noise is available to hide infor-
mation. For each pixel, you can compare
JPEG
(
f
JPEG
−
1
(
))
and determine how many of the bits are equal. If only the first 4 bits
of the 8 bits encoding the blue intensity are the same, then you can
f
with
JPEG
(
f
