Cryptography Reference
In-Depth Information
-th permutation spit out by this permutation generation
routine can determine which channel gets which byte in the
The
i
th
i
block. This ensures that no two users will collide.
Another approach can mangle the process even more. Why
should blocks be made up of adjacent bytes? In the most basic ap-
proach, byte
i
from channel
k
in an
n
-channel system is assigned to
in the file. This can be scrambled using exponentiation
modulo the length of the file. So if the file is
byte
in
+
k
p
bytes long and
p
just
)
e
mod
happens to be prime, then
(
in
+
k
p
will scramble the bytes so
they are not adjacent.
Walton imagines that the least significant bits in his randomwalk
can be used to construct a seal for the image. That is, you can “sign”
the image by embedding some digital signature of the image in the
least significant bits. Naturally, this digital signature would only be
computed of the non-least significant bits because those bits are the
only ones that would remain unchanged during the process. This
sealing system could be used by professional photographers to at-
tach their mark to a photograph.
Some have argued that this approach is a waste. Appending the
signature data to the end of the photo made more practical sense.
This type of signature would be able to handle all types of photo
formats including binary images without enough significant bits to
hide data. Also, there would be no need to avoid the least significant
bits while encoding the information and so the signature would be
even better.
Another solution is to
create a random
permutation of the bits.
Tuomas Aura descr ibes
this in [Aur95].
These suggestions are certainly correct. The only advantage that
the surreptitious approach would have is secrecy. Presumably pho-
tographers would sign images to protect their copyright. They could
prove conclusively that the photo was stolen. If the signature is ap-
pended to the file, then someone could remove it or tamper with it.
If it is hidden with a random walk in the least significant bits, then
someone has to find it first. Of course, malicious people could just
write over the least significant bits of a photo as a precaution.
9.4.1 Empty Disk Space
The algorithms for choosing a random subset of an image or sound
file by walking around them at random can be used to hide informa-
tion in other ways.
Earlier versions of S-Tools included a program,
st-fdd.exe
,to
hide information in the unallocated areas of a floppy disk. Each
disk is broken into sectors and the sectors are assigned to individual
files by the file allocation table (FAT). The unused sectors are just
