Re: why compression doesn't perfectly even out entropy

["Perry E. Metzger" <perry@piermont.com>]

rick hoselton writes:
> At 05:34 PM 4/16/96 -0400, Perry E. Metzger wrote:
> 
> >> ...it is possible ... for Hamlet to appear out of a random number generato
r,
> 
> >> 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?

If the text of Hamlet were produced by a truly random number
generator, then it would make a fine one time pad. A cryptanalyst
seeing patterns in it would have no way of knowing that the patterns
were caused by the input being "Hamlet" -- he would have no way to
demonstrate that just because the first five hundred words of the key
appear to have been "Hamlet" that the rest would be -- and indeed,
there would be far more cases where the rest wouldn't be. If, on the
other hand, what you are doing is using books as keys for ciphers,
then "Hamlet" is a very poor one.

> >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.

IF you are using a one time pad system that truly has a random source
of keying material, AND the 1 in 2^1460536 event of the key being
Hamlet occurred, THEN no, you aren't likely to get broken. Note that
the probability of having this happen is astronomically low, but then
again, the probability of ANY given one time pad being generated is
astronomically low. If you are just picking books off the shelf and
playing one time pad with them, yes, you are correct, you will likely
be broken.

> >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.

I don't think you are considering this clearly.

It is far, far more probable for the cryptanalyst, thinking the
key was "Hamlet", to get out a plausible but totally bogus text, than
it is for the key to actually be "Hamlet". Of course, it is also far,
far more probable for you to be stupid than for a random number
generator to put out "Hamlet", but if you go around getting rid of
RNGs that produce "Hamlet" or anything close, you have in theory given
information to the attacker that gives them a slightly better chance
of attacking you since your pads are no longer purely random.

The reason all this isn't stupid to discuss and actually has some
importance is just this fact. If you build a system that discards
things that "don't look like they have enough entropy" (which certain
people around here have proposed), you are giving the cryptanalyst a
very strong piece of information about the key, so your key is no
longer totally unpredictable. An irony, but something important to
keep in mind. Every once in a while (once in every four billion bits,
or so) your random number generator will put out 32 1's in a row if it
is functioning properly. Any given small segment of the output of a
good RNG might not look "random", but "random" isn't a property of a
given number -- it is the property of the infinite sequence itself.

Perry