using "reserved" IPv6 space
Karl Auer
kauer at biplane.com.au
Fri Jul 20 01:07:17 UTC 2012
On Thu, 2012-07-19 at 19:30 -0500, Jimmy Hess wrote:
> > The ratio of the number of bits doesn't tell you anything about
> > whether the number was random or not.
>
> Sure it does. A ratio of 1s to 0s of a sufficient deviation, is a
> sufficient but not a necessarily condition, for establishing that a
> sequence of binary numbers shown almost certainly was not chosen
> randomly.
A *sequence*, yes. A single number in isolation, no. Whether the bits
within a single value are distributed randomly or not is irrelevant. You
seem to be confusing the randomness of a sequence of bits (i.e., within
a particular prefix) with the randomness of a sequence of prefixes. You
have the entire bit sequence of a particular prefix available to
inspect, so you can make a call on the randomness of the bits, but you
do NOT have the entire prefix sequence, so CANNOT make a call on the
randomness of the prefix.
You can say, for a sufficient number of bits, whether the bits are
distributed randomly. Agreed. But given a specific bit, without knowing
the other bits, you cannot tell whether that specific bit was chosen
randomly. If my prefix generating algorithm is to choose 39 bits
completely randomly but always set bit 7, you cannot tell that bit 7 has
been set non-randomly by inspecting only one prefix, because in a
certain number of genuinely random prefixes, bit 7 will be set anyway.
Maybe the one you happen to be looking at is such a one. The same is
true of any two bits, and any three bits - and so on, all the way out to
40 bits.
> However, there _are_ many non-random strings that exist which a
> 'lazy' or broken ULA ID generator might pick, that can be very easily
> detected as non-random with sufficient confidence, to tell the user
> "Hey, sorry, you can't use that. Please generate a new ULA ID".
You can pick them against human criteria; you can't pick them against
mathematical criteria unless you have the sequence as well as the value.
All zeros is exactly as likely as insert-any-prefix-here.
But: IANAS (I Am Not A Statistician :-) so I think I'll stop now. I am
either flogging a dead horse or digging an embarrassing hole for
myself :-)
Regards, K.
--
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Karl Auer (kauer at biplane.com.au)
http://www.biplane.com.au/kauer
GPG fingerprint: AE1D 4868 6420 AD9A A698 5251 1699 7B78 4EEE 6017
Old fingerprint: DA41 51B1 1481 16E1 F7E2 B2E9 3007 14ED 5736 F687
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