On 12/24/2021 3:02 PM, Christian Huitema wrote:
The collision risk itself depends on the population size. If call
signs are used as "pet names", they are only expected to be unique in
the small scope of "pets". But if thy are expected to be unique
worldwide and forever, then they have pretty much the same design
constraints as IPv6 addresses. They can probably be a little shorter
because there is no expectation of routability, but I would be
surprised if this required fewer than 80 bits -- I would probably go
for 96 bits.
If you're looking for statistical uniqueness, this is the birthday
collision problem.
If you set the desired chance of collision in the random space at less
than 1 in 100,000,000 , 8 octets covers about 600K identities, 10
octets about 155 million and 11 octets about 2.5 billion. Varying the
acceptable collision risk up or down assuming everyone is using good
quality RNGs with negligible bias changes the number of bits you need to
generate to cover an expected space.
https://en.wikipedia.org/wiki/Birthday_problem
n = sqrt (2*d * ln(1/1-p)) where n is the number of expected picks, d
is the size the space (e.g. unique identities), and p is the probability
of a collision. E.g. p = 10^-8, d = 2^64 gives ~600K for the 8 octets.
(I calculated the above numbers a while back for certificate issuance
given random serial numbers).
That's a long winded way to say that 10 octets (96 bits) is probably not
enough for a space of trillions as PHB proposes.
Mike
