Re: Good enough for crypto?

"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.

--
r.e.s.