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In article <gilchr.720707527@ee.ualberta.ca> gilchr@ee.ualberta.ca (Andrew Gilchrist) writes:
>
>What are theoretic ways to deter a plaintext attack?
>[stuff deleted]
>if the attacker knows both plaintext and ciphertext, the solution is
>trivial, and the key is discovered.  How can one modify such a
>method to make discovery of the key more difficult?
>
Plaintext attack can be defeated if the cipher behaves like the Random Cipher
Model.  One particular alorithm which satisfies such a model is the
Monkey in Box Algorithm.  Imagine a monkey inside an encryption box
which accepts plaintext and generates ciphertext with the following rule.
Plaintext are accepted and a random ciphertext is generated which has 
nothing to do with the original plaintext except in the event of 
a repeated plaintext.  In other words, each time the monkey gets data, 
she compares it with a log of previous data and if there is a match,
send out the same sample ciphertext otherwise generate a new random number.
This cipher is strong because there are no statistical or algorithmic
weakness.

Now the answer to your question of how to prevent plaintext
attack follows.  The cipher must behave statistically like the random
cipher model.  It is conjectured that satisfying the following two
properties would guarantee strong statistics for a non-expanding block 
cipher of length m bits.

Property 1: mth order correlation immunity.
Property 2: mth order differential correlation immunity.

Property one is a fancy way of saying that output bits should not be 
dependant on input bits.  The second property which is less 
intuitive says that the relationship between an output pair 
and an input pair should not be independant.  Satisfying property
two provably prevents differential cryptanalysis.

So the short answer to your question of how to make a cipher strong
against plaintext attack is for your cipher to have both property 1 and 2.
Note the non-expanding condition guarantees a 0/1 balanced output for
balanced input.

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| Luis Toshio Yu                  | "Now, if only I have something clever to |
% lcmyu@crypto2@uwaterloo.ca      % say about that..." :-)                   %
% Electrical Engineering          % Opinions expressed here are mine, so     %
| University of Waterloo, Ontario | credit me for your happiness.            |
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