You wrote:
The probability of a duplicate assignment somewhere is
N^2/2^38...
which is not quite correct. The probability of at least one duplicate
out of N assignments out of a space of size X is
P = 1 - product(1..N)(1-(i-1)/X)
Which is a bit hard to compute, and certainly does not result in N^2/X.
Using a log approximation, you get
Log (1-P) = sigma(1..N) log (1 - (i-1)/X)
= sigma(1..N)(-(i-1)/X) + 0(N^3/X^2)
Thus
(1-P) ~= e^-(N.N-1/2.X) ~= e^-(N^2/2.X)
P ~= 1 - e^-(N^2/2.X) if N^3 << X^2
I would suggest you correct your phrase to be a bit less assertive,
something like "The probability of a duplicate assignment somewhere
becomes significant is N^2 becomes close to 2^38" -- or just mention the
birthday paradox.
> -----Original Message-----
> From: Paul Francis [mailto:[EMAIL PROTECTED]]
> Sent: Monday, February 26, 2001 10:41 AM
> To: [EMAIL PROTECTED]
> Subject: Near-Unique Site-Local Identifier draft
>
>
>
> I've posted a draft on assigning random site-local
> identifiers at
> http://www.aciri.org/francis/draft-francis-ipngwg-unique-site-
> local-00.txt.
>
> This was submitted in time to make the Minn. ID deadline.
>
> Thanks,
>
> PF
>
> Abstract
>
> For many or most sites, site-local addresses are used for packets
> between nodes within the site. The fact that site-local addresses
> are not globally unique makes their usage and administration more
> difficult than they would be if there were globally unique (or
> nearly globally unique). For instance, before two sites can be
> merged, one of them has to be renumbered. The meaning of
> site-local
> addresses becomes ambiguous when they are taken out of the
> immediate
> context of the IPv6 layer, for instance when they are conveyed in
> email or stored in text files.
>
> All other things being equal, it would be preferable if the prefix
> of addresses with site-local scope were as globally unique as
> possible. This draft expands the format of the site-local address
> to allow them to be near-unique. It does not, however, change the
> definition or usage of the site-local address. This draft
> describes
> the format and assignment method of near-unique site-local
> prefixes.
> It also outlines some usage scenarios.
>
>
>
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