Relation between number theory and cryptography

[Clark Reynard <clark@metal.psu.edu>]

Hi.  Me again.  

I asked this one a while back and got no response.  sci.crypt
was equally unresponsive.  It concerns the possibly obscure
relation between cryptography, number theory and information
theory.  

Is there considered to be a one-to-one isomorphism between
the units in a plaintext-cyphertext pair?  By this, I mean,
are they considered to contain the same information?

If not, does encryption lessen or increase the amount of
information in the units of the plaintext-cyphertext pair,
and why?  

Is this affected by whether or not the key is known?  If the
key has been irretrievably lost, does this lessen the amount
of information, or does the 'potential' informational content
remain the same?

Is cryptography considered to be as simple as, say, Huffman
coding, for purposes of informational content?  That is, is
the relationship between the units of a plaintext-cyphertext
pair considered to be more or less 'transparent,' or entirely
isomorphic?

Does the Second Law of Thermodynamics enter into this?  Is there
a minimum amount of energy required to extract information from
cyphertext, or a minimum amount of waste of energy?

If these questions are too difficult to answer in a short article,
does anyone have citations to a source which could explain this to
me?  I'm not certain how much research has been done into this
rather esoteric topic, and my main interest is theoretical, though
I'd be interested in knowing any practical applications of 
information theory and number theory to cryptography.  
----
Robert W. Clark             Just Say No! to the
rclark@nyx.cs.du.edu        Big Brother Chip