Cryptography Reference
In-Depth Information
The process also restricts the ability of an attacker to add random
glitches in the hope of destroying the message. In the first example,
the attacker might always use either positive or negative glitches and
drive the total to be either very positive or very negative. If the values
of
α
are equally distributed, then the heavy glitches should balance
out. If the attacker adds more and more glitches in the hope of ob-
scuring any message, they become more and more likely to cancel
each other out.
Clearly, the complexity can be increased by choosing different
values of
10
or
1000
, but there do not seem to be many
obviousadvantagestothissolution.
α
such as
2
,
14.3.4 Packing Multiple Messages
Random number sources like this can also be used to select strange
or discontinuous blocks of data. There's no reason why the elements
x
1
through
x
1000
need towork together to hide the first bit of themes-
sage. Any
1000
elements chosen at random from the file can be used.
If both the message sender and the receiver have access to the same
cryptographically secure random number stream generated by the
same key, then they can both extract the right elements and group
them together in blocks to hide the message.
This approach has some advantages. If the elements are chosen
at random, then the block sizes can be significantly smaller. As noted
above, the values between
are largely positive with a
large average. It's not possible to adjust the average up or down to be
larger or smaller than a value,
x
8200
and
x
8300
, without signficantly distorting the
values in the block. If the elements are contiguous, then the block
sizes need to be big to ensure that they'll include enough variation
to have a small average. Choosing the elements at random from the
entire file reduces this problem significantly.
The approach also allows multiple messages to be packed to-
gether. Imagine that Alice encodes one bit of a message by choosing
100 elements from the sound file and tweaking the average to be ei-
ther above or below
S
. Now, imagine that Bob also encodes one bit by
choosing his own set of 100 elements. The two may choose the same
element several times, but the odds are quite low that there will be
any significant overlap between the two. Even if Alice is encoding a 1
by raising the average of her block and Bob is encoding a 0 by lower-
ing the average of his block, the work won't be distorted too much if
very few elements are in both blocks. The averages will still be close
to the same.
Engineering a system depends on calculating the odds and this
S
