Cryptography Reference
In-Depth Information
a number of tests for primality that work quite well. The solu-
tion is to choose a large, odd number at random and test it to
see if it is prime. If it isn't, choose another. The length of time
it takes to find a prime number close to an integer
x
is roughly
x
proportional to the number of bits in
.
The Lehman test [Leh82] is a good way to determine if
n
is
prime. To do so, choose a random number
a
and compute
a
(n
−
1)/2
mod
n
.Ifthisvalueisnot1or
−
1
,then
n
is not prime.
Each value of
has at least a 50% chance of showing up a non-
prime number. If we repeat this test
a
m
times, then we're sure
that we have a 1 in
2
m
chance that
n
is not prime, but we haven't
= 100
is a good
starting point. It is not absolute proof, but it is good enough.
a
m
found an
that would prove it yet. Making
RSA encryption is a very popular algorithm used for public-key
encryption. There are also a large number of other algorithms that
are available. The discussion of these variants is beyond the scope of
this topic. Both Bruce Schneier's book, [Sch94], and Gus Simmons'
book [ed.92] offer good surveys.
2.4 Summary
Pure encryption algorithms are the best way to convert data into
white noise. This alone is a good way to hide the information in the
data. Some scientists, for instance, encrypt random data to make it
even more random. Encryption is also the basis for all of the other
algorithms used in steganography. The algorithms that take a block
of data and hide it in the noise of an image or sound file need data
that is as close to random as possible. This lowers the chance that it
can be detected.
Of course, nothing is perfect. Sometimes data that is too random
can stick out too. Chapter 17 describes how to find hidden informa-
tion by looking for values that are more random than they should be.
The Disguise
Good encryption turns data into white noise that ap-
pears random. This is a good beginning for many algorithms
that use the data as a random source to imitate the world.
How Secure Is It?
The best new encryption algorithms like Rijndael
and the other four AES finalists have no practical attack known
to the public. These algorithms are designed and evaluated on
their ability to resist attack. DES is no longer very secure for
serious applications.
