Cryptography Reference
In-Depth Information
The same argument also holds for RSA. The loop contains a num-
ber for each of all possible messages and these numbers are dis-
tributed around the loop in a way that we can't invert. Therefore,
each output value has practically the same probability of emerging
from the function.
Although these two arguments don't prove that the output from
an encryption function is random, they do suggest that DES and RSA
will pass any test that you can throw at them. If a test is good enough
to detect a pattern, then it would be a good lever for breaking the
code. In practice, the simple tests support these results. The out-
put of DES is quite random.
3
Many tests show that it is a good way
to “whiten” a random number source to make it more intractable.
For instance, some people experiment with using a random physical
process like counting cosmic rays to create random numbers. How-
ever, there might be a pattern caused by the physics of the detector.
A good way to remove this possibility is to use DES to encrypt the
random data and produce the whitest noise possible.
2.3 Measuring and Encrypting Information
Information is a slippery notion. Just how big is a fact? How much
data must be accumulated before you have a full-fledged concept?
None of these questions are easy to answer, but there are approxima-
tions that help with digital data. Shannon's measure of information is
closely tied to probability and randomness. In a sense, information
is defined by how much randomness it can remove. Our goal is to
harness randomness and replace it with a hidden message. Knowing
the size, length, depth or breadth of our target is a good beginning.
Let an information stream be composed of
n
characters between
x
i
)
. Shan-
non's measure of the
entropy
in the information stream, that is the
number bits per character, can be written:
x
0
and
x
n
−
1
that occur in the stream with probability
ρ
(
x
i
)log
1
ρ
n
−
1
ρ
(
.
(
x
i
)
i=0
The
log
is taken base two.
3
The level of randomness depends on the input file if there is no key feedback
mechanism being used. In some versions of DES, the results of one block are XORed
with the inputs for the next block so that there will be diffusion across the blocks. If
this is not used, someone could input a file with a pattern and get out a file with a
pattern as long as the pattern repeats in an even multiple of 8 bytes.
