Cryptography Reference
In-Depth Information
blocks are small, then it is entirely possible that the signal will wipe
out the data.
The first part of Figure 14.4, for instance, shows the data between
elements
x
8200
and
x
8300
. Almost all are above
0
. The total is
374
,
684
and the average value is
3746
84
. Subtracting this large amount from
every element would distort the signal dramatically.
Larger blocks are more likely to include enough of the signal to
allow the algorithm to work, but increasing the size of the block re-
duces the amount of information that can be encoded.
In practice, blocks of 1000 elements or
1
.
44
th
of a second seem
to work with a sound file like the one displayed in Figure 14.3. The
following table shows the average values in the blocks. The average
values are about 1% of the largest values in the block. If
/
is set to be
around 3%, then the signal should be encoded without a problem.
x
1
to
S
x
1000
19.865
x
1000
to
x
1999
175.589
x
2000
to
x
2999
-132.675
x
3000
to
x
3999
-354.728
x
4000
to
x
4999
383.372
x
5000
to
x
5999
-111.475
x
6000
to
x
6999
152.809
x
7000
to
x
7999
-154.128
x
8000
to
x
8999
-59.596
x
9000
to
x
9999
153.62
x
10,000
to
x
10999
-215.226
14.3.2 Synchronization
This mechanism is also susceptible to the same synchronization
problem that affects many watermarking and information hiding al-
gorithms, but it is more resilient than many. If a significant number
of elements are lost at the beginning of the file, then the loss of syn-
chronization can destroy the message.
This mechanism does offer a gradual measure of the loss of syn-
chronization. Imagine that the block sizes are 1000 elements. If only
a small number, say 20, are lost from the beginning of the file, then
it is unlikely that the change will destroy the message. Spreading the
message over the block ensures that there will still be 980 elements
carrying the message. Clearly, as the amount of desynchronization
increases, the quality of the message will decrease, reaching a peak
when the gap reaches one half of the block size. It is interesting to
note that the errors will only occur in the blocks where the bits being
encoded change from either a zero to a one or a one to a zero.
