On Wed, 24 Apr 2002 [EMAIL PROTECTED] wrote:
> That is, to get the infinite cycle, you'd have to have some method of
> generating a uniform random integer 0 to infinity for the
> initial state, and you'd need an infinite amount of memory
> to store the current internal state. Neither of which
> is acheivable ion practice.
Actually neither of these are requirement for RNG's. You're fist comment
about 'some method' tends to shoot your argument in the foot right off.
As to the second, no you don't need infinite ram to create a RNG. Please
demonstrate the proof. What you need is -continuity-, not -infinity-.
They're not the same thing. If all it took was infinite memory then a
standard Turing machine could, by your thesis, generate a RNG and we know
from basic principles that isn't possible. Why? Their tape is of infinite
length and zero access time.
> Conversely, a PRNG whose cycle is "only" 2^256 bits long
> will never repeat itself during the lifetime of the device, or
> the lifetime of the universe for that matter.
Depends on the key, in general the modulus of the PRNG is key dependent.
This is another weakness PRNG's.
In addition, the vast majority of PRNG's have a modulus considerably below
2^256. Most of them I've worked with have had modulus lengths less than a
couple of million.
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