Re: Good enough for crypto?

"Scott Wilber" <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]
> "r.e.s." <[EMAIL PROTECTED]> wrote in message
news:<[EMAIL PROTECTED]>...
> > "Scott Wilber" <[EMAIL PROTECTED]> wrote in message
> > news:[EMAIL PROTECTED]
> > > "r.e.s." <[EMAIL PROTECTED]> wrote in message
> >  news:<[EMAIL PROTECTED]>...
> > > > "Scott Wilber" <[EMAIL PROTECTED]> wrote ...
> > > > > Peter Fairbrother <[EMAIL PROTECTED]> wrote ...
> > > > > > Scott Wilber  wrote
> > > > > >
> > > > > >> > snip..
> > > > >  The autocorrelation function of a non-deterministic sequence will
> > > > >  always decrease with increasing order.  The decrease will either
be
> > > > >  monotonic or the function will oscillate, and the amplitude of
the
> > > > >  oscillations will decrease monotonically.  This is proved by
proving
> > > > >  the behavior of the generalized autocorrelation function of the
> >  random
> > > > >  process, including its measurement device - something I will not
try
> > > > >  to show in this setting.
> > > > >
> > > > >  To the best of my knowledge, this theorem on non-deterministic
> > > > >  sequences is original and has never been published before.  But,
its
> >  a
> > > > >  big world and if anyone has seen this before, I would like to
know.
> > > > >
> > > > > Could you be a little more substantive in your question?
> > > > >
> > > > > Scott
> > > > > >
> > > > > > What theorem are you referring to? I don't follow.
> > > > > >
> > > > > > -- Peter Fairbrother
> > > >
> > > > (To Scott:)
> > > >
> > > > Your "theorem" isn't true, as this counterexample shows:
> > > > Y_i = a*X_0 + b*X_(i+1)  (a,b <> 0) (i = 0, 1, 2, ...),
> > > > where X_0, X_1, X_2, ... are nondegenerate iid on {0,1}.
> > > > The autocorrelation function for the Y-sequence is
> > > > R(0) = 1,  R(k)(k > 0) = 1/(1 + b**2/a**2) = constant.
> > >
> > > The theorem relates specifically and only to non-deterministic
> > > sequences as is clearly stated.  No inference may be made from this
> > > concerning deterministic generators.
> >
> > Eh?  The Y-sequence *is* non-deterministic.
>
> Perhaps I missed the invention of algorithimic true random number
> generators.  What is the source of entropy in this generator?

Your snideness is uncalled for.
Do you understand what nondegenerate iid random variables are?