Cryptography Reference
In-Depth Information
for a file. The attackers can rearrange the file as much as they want
but the sender and the receiver will still be able to re-establish the
canonical order and send a message.
Other algorithms exploit the order of the content itself and make
no changes to the underlying information. There are
n
! ways that
n
items can be arranged. That means there are log
2
n
! bits that can
be transmitted in a list with
items. None of the items themselves
change, just their order in a list.
Still other algorithmsmix in false data to act as decoys. They get in
the way until they're eliminated and the canonical order is returned.
All of these algorithms rely on the fact that information does not
need to flow in a preset pattern if the correct order can be found later.
This fact is also be useful if parts of the message travel along different
paths.
n
13.3 Strength Against Scrambling
Many of the attacks on steganographic systems try to destroy the
message with subtle reordering. Image warping is one themost com-
plex and daunting parts of the StirMark benchmarks used tomeasure
the robustness of techniques for hiding data in images.
Here's a very abstract summary of a way to make any stegano-
graphic system resist re-ordering:
•
Break up the data stream into discrete elements:
{x
1
,x
2
,...,x
n
}
.
This may be words, pixels, blocks of pixels, or any subset of the
file. These blocks should be small enough to endure any tweak-
ing or scrambling by an opponent but large enough to be differ-
ent.
•
Choose a function,
, that is independent of the changes that
mightbemadeinthehidingprocess.Iftheleastsignificantbit
is changed to hide a message, then
f
f
should only depend on
the other bits.
Many of the same principles that go into designing a hash func-
tion can be applied to designing this sorting function. This
function,
f
, can also be keyed so that an additional value,
k
,
can change the results.
•
Apply
f
to the elements.
•
Sort the list based on
f
.
•
Hide the information in each element,
x
i
, with appropriate so-
lutions.
