[IPv6]Re: Analysis of Ungleich ULA Registry

[David Farmer <[e-mail]>]

On Mon, May 27, 2024 at 5:09 PM Kyle Rose <[e-mail]> wrote:

> On Mon, May 27, 2024 at 12:18 PM David Farmer <[e-mail]> wrote:
>
>> While the Ungleich ULA Registry demonstrates significant support for full
>> registration, something like draft-hain-ipv6-ulac provides. My
>> primary concern is a mechanism that allows for ULA prefixes shorter than
>> /48 as a result of the practical restrictions of 10 ULA prefixes created by
>> known-local ULA. I could accept a consensus to accomplish that through
>> randomized local ULA assignments of ULA prefixes shorter than /48 instead
>> of centralized ULA assignments. However, unfortunately, it is unclear to me
>> that there is a consensus for either way forward.
>>
>
> As I've previously stated, I am fine with loosening the language on prefix
> generation along with an extra loud warning about the greater chance of a
> future conflict requiring renumbering as the prefix size gets shorter.
>
> This seems fine to me because it literally only hurts the orgs that choose
> to accept the incremental risk. And frankly I'd be shocked if there weren't
> orgs already doing this because it just made sense for them to do so,
> versus wrangling many separate /48s.
>

Actually, the math shows that aggregating ULA prefixes produces a lower
probability of collision than the equivalent number of discrete /48
prefixes.

For example, merging a /48 into a ULA network with a /44 aggregate is less
likely to cause a collision than merging an additional /48 into a network
with 16 discrete /48 ULAs, or a total of 17 /48s.

This is because the latter is the probability of 17 discrete random 40-bit
variables colliding; even though they are less densely packed, creating a
lower probability for each collision, many more of them create more chances
for them to collide. The former is the probability of 2 discrete random
36-bit variables colliding; even though they are packed more
densely, creating a higher probability for each collision, far fewer of
them create fewer chances for them to collide.

Let me run you through the math. RFC4193 gives us the following formula;

   P = 1 - exp(-N**2 / 2**(L+1))
   Where P is the probability of collision, N is the number of
interconnected Global IDs, and L is the length of the Global ID.

The odds of a /48 colliding with a /44 are the same as two /44s colliding.
The last 4 bits of the /48 are irrelevant. The first 36 bits of the Global
ID are all that matter;
   P = 1 - exp(-2**2/2**(36+1) = 2.91038E-11

And the odds for 17 /48s, with a Global ID of 40 bits;
   P = 1 - exp(-2(17**2/2**(40+1) = 1.31422E-10

For comparison, the odds for 8 /48s, with a Global ID of 40 bits;
   P = 1 - exp(-2(8**2/2**(40+1) = 2.91038E-11

And the odds for 2 /48s, with a Global ID of 40 bits;
   P = 1 exp(-2(2**2/2**(40+1) = 1.81899E-12

For all these cases, the probability of collision is fairly remote; it is
just a little more likely for the 17 /48s at approximately 72 times 2 /48s.
Compared to a /48 and a /44, which is approximately the same as 8 /48s, at
unsurprisingly 16 times 2 /48s.

Thanks.

-- 
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