Relation between number theory and cryptography
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
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Clark Reynard