Re: why compression doesn't perfectly even out entropy

[rick hoselton <hoz@univel.telescan.com>]

At 05:34 PM 4/16/96 -0400, Perry E. Metzger wrote:

>> ...it is possible ... for Hamlet to appear out of a random number generator,

>> But even if it came from a completely random source, it would 
>> still make a bad one-time pad.

>No it wouldn't. 

Are you sure you want to claim that the text of Hamlet would make 
a good key for a one-time pad?

>There is a tiny but nonzero probability that xoring
>your one time pad with your text will result in a cyphertext equal to,
>say, the Bible. Big deal. 

Most unusual, and you're right, its inconsequential.  But if you use the 
text of Hamlet or the text of the Bible for your KEY to a one-time-pad,
you're very likely to get broken.  I think any pad that is likely to get 
broken is a bad pad.

>If the key is really random, the
>cryptanalyst has no way to tell what the underlying text was.

But that silly cryptanalyst might not know that you got Hamlet from 
your random number generator.  He might think you copied it out of a 
book!  Then, Hamlet stops being a random number.  The context changes.

>> In the context of "fair coin flips" the text of Hamlet is NOT compressible.

>There is only one context in which things are compressable or not --
>is there a smaller representation for them.

Suppose that somewhere on the web is an archive of "The Encyclopedia"(tm).
I could add a preprocessor to zip that would compare the input file to 
"The Encyclopedia".  If it finds a match, it outputs a zero-byte.
If it doesn't find a match, it outputs a one-byte followed by an 
ordinary zip file.

The decompressor compares the compressed file to a single zero, and if it is 
equal, accesses "The Encyclopedia" and sends it to the output file.  Otherwise 
it just unzips the rest of the file normally.

I now have a one-byte representation for "The Encyclopedia".
(by the way, this will work with 6 and 7 and 8 and 9 and 12-bit bytes!)

That's not really fair.  I took advantage of a particular situation.  
But that's what ALL compressors do.  They take advantage of particular 
patterns. And patterns are determined by context.

This is where it gets interesting.  The "randomness" of "The Encyclopedia" 
depends on whether some archive is online!  If someone deletes "The
Encyclopedia"
archive, or disconnects my communications, my special compressor stops working, 
and the smallest (reversable) representation jumps many orders of magnitude.  
When the context changes, the smallest representation changes.

As you point out, when the Hamlet comes out of a good random number generator, 
it is just as random as any other number.  But I contend that when Hamlet 
can XOR with your ciphertext to reveal your plaintext, then Hamlet is NOT 
a random number.  When did it stop being random?  When then context changed.











>
>> Because no string is more likely than any other.  Any algorithm that could 
>> compress that string, will, on the average INCREASE the length of 
>> "fair coin flip" strings it tries to compress.
>
>True enough, but the claim was that a random string has no
>representation which is smaller than itself.
>
>.pm
>