cryptographic ergodic sequence generators?

[Victor.Duchovni at morganstanley.com]

On Sat, 6 Sep 2003, Perry E. Metzger wrote:

>
> For making things like IP fragmentation ids and other similar protocol
> elements unpredictable, it would be useful to have what I'll call a
> cryptographic ergodic sequence generator -- that is, a generator that
> will produce a sequence of n bit numbers such that there are no
> repeats until you pass the 2^nth number in the sequence (that is, the
> sequence is a permutation of all 2^n bit numbers) and such that it is
> very difficult to predict what the next number in the sequence might
> be beyond the fact that it will not be one of the numbers seen earlier
> in the sequence. It is also rather important that the generator be
> computationally inexpensive.
>

Why does it need to be strictly non repeating? Is 2^n always large enough
that sequences of length > 2^n are uninteresting?

If sequences longer than 2^n are practical and *every* subsequence of 2^n
elements is free of duplicates the entire thing is periodic, this may or
may not be a problem...

-- 
	Viktor.

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