Cryptography Reference
In-Depth Information
The third round has an analogous period of 26 3
= 17 576; 676 identical
substitutions follow one another.
The fourth round is a fixed substitution.
The fifth round is the reversion of the third round, the sixth round is the
reversion of the second round, and the seventh that of the first.
Moreover, character pairs are flipped before the first round and after the
seventh round, which corresponds to a particularly simple transposition.
(More specifically, we have nine rounds here.)
You recognize the method? Right, it's the Enigma. You already know that
the Enigma is more secure than any substitution. The third round by itself
is statistically easy to break: we look only at 676 identical substitutions and
derive the other rotor positions from them. But exactly because this third round
is combined with the other rounds, the method obtains the large period length
of 17 576, which is so critical for its security.
So, cleverly combining simple methods increases the security dramatically.
That's similar to solving equations:
Linear equations in the form ax
+
b
=
c are trivially solvable.
To solve quadratic equations, we know the formula from school.
To solve cubic equations, things are getting a bit more complex: we need
several formulas with some kind of case differentiation.
The solution formulas for fourth-order equations are pretty complex, but
still solvable.
In contrast, it has been proven that there is no generalized solution
formula (except perhaps using fundamental operations and roots) for fifth-
order equations and higher. This is a quality leap. Of course, there are
still solution formulas for special fifth-order equations, and it should also
be possible to write the general solution in closed form if you also use
special, novel functions.
These statements are easily transferable to the cryptanalysis of product algo-
rithms: product formation does not always increase the security; on the other
hand, there appear to be 'sound barriers'. For example, the most effective crypt-
analyses against the DES algorithm get stuck after eight rounds when things
get much harder.
Search WWH ::




Custom Search