On Wed, 24 Apr 2002, David Howe wrote:
> "Jim Choate" <[EMAIL PROTECTED]> wrote:
> > But that changes the game in the middle of play, the sequence of digits
> > in pi is fixed, not random. You can't get a random number from a constant.
> > Otherwise it wouldn't be a constant.
> PRNG output is fixed/repeatable too - that is a properly you *want* from a
> PRNG.
No it isn't. You -want- a RNG but you can't have one. Nobody -wants- a
PRNG, they -settle- for it. What one wants is a bit sequence which is
-random-. There are many definitions of random, but they boil down to
-unpredictable- outside of chance with respect to predicting individual
bit results as well as sequences of bits (they are not the same
statistically speaking, re probability distributions).
Ideally what one would want is a situation where each bit has a 50/50
chance of being in either state and there are -no- inter-bit dependencies.
That implies no modulo (though it doesn't prevent clustering which can
fool you if you don't test your sub-strings well enough - re Gamblers
Ruin).
Which raises an interesting aspect for me, what happens if you put a PRNG
into a 'Garden of Eden' state?
> any subset of the digits of pi is as close to RNG output as you would
> need to satisfy any entropy tests - unless you *knew* you had derived it
> from pi you couldn't distinguish it from a true random string of the same
> size.
Satisfying an -entropy test- is -not- equivalent to -being- a RNG. It only
says that within a particular error margin you're -close enogh-.
> > You can't stop them from using their tables. Slow them down, not stop
> > them. You can't use that huge a seed, hardware limitations. They can match
> > you.
> *shrug* given that adding a bit to the seed doubles the quantity of data
> they would have to cache in their tables, it can quickly become unworkable;
Really? The offset into the sequence is a fixed width and the result is
alaways a single character. Where do you add a bit?
> the single-digit-of-pi formula is too slow to form a good stream cypher, but
> is otherwise ok;
Maybe for you, I sure as hell wouldn't use it either as a key or as a
seed into a known hashing/whiting algorithm.
Let me ask you a more pointy question. Are you selecting some offset and
then taking the sequence of digits from pi, or are you selecting the
digits out of order? In either of these cases it isn't the sequence of pi
that is providing the randomness (which is apparently the claim) but
rather the selection process; which is both undescribed at this point
-and- simply moves the argument from one area to another - this -proving-
nothing.
--
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