Cryptography Reference
In-Depth Information
needs to be done. The average value of
102
is already well above
10
.
If the message is
0
, however, the average value needs to be re-
duced by at least 92 and perhaps more if there's going to be any mar-
gin of error. Subtracting
100
from each element does not distort the
signal too much when the values range between
±
7500
.Ofcourse,
some elements have small values like
6
or
190
, and they will be dis-
torted more, but this is well below the threshold of our perception.
A more sophisticated mechanism spreads the distortion propor-
tionately. This can be calculated with this formula:
x
i
=
−
x
i
− x
i
× total change
|x
i
|
If this is reduced to each value,
x
i
, then the summoves by the amount
of total change.
This approach has several advantages over simply encoding the
information in the least signficant bit because the data is spread over
a larger block. Any attacker who just flips a random selection of the
least signficant bits will wipe out the least significant bit message,
but will have no effect on this message. The random changes will
balance out and have no net effect on the sum. If the absolute value
of the average value is over
S
,thenitwillstillbeover
S
.Ifitwas
under, then it will still be under.
Random noise should also have little affect on the message if the
changes balance out. A glitch that adds in one place will probably
be balanced out by a glitch that subtracts in another. Of course, this
depends on the noise behaving as we expect. If the size of the blocks
is big enough, the odds suggest that truly random noise will balance
itself.
The mechanism does have other weaknesses. An attacker might
insert a few random large values in places. Changing several small
elements of
100
to
30
000
is one way to distort the averages. This
random attack is crude and might fail for a number of reasons. The
glitches might be perceptable and thus easily spotted by the parties.
Theycouldalsobeeliminatedwhenthesoundfileisplayedback.
Many electronic systems remove short, random glitches.
Of course, there are also a number of practical limitations. Many
compression algorithms use only a small number of values or quanta
in the hope of removing the complexity of the file. 8-bit
,
-law encod-
ing, for instance, only uses 256 possible values for each data element.
If a file were compressed with this mechanism, anymessage encoded
with this technique could be lost when the value of each element was
compressed by converting it to the closest quantized value.
There are also a great number of practical problems in choosing
the size of the block and the amount of information it can carry. If the
μ
