Post
Topic
Board Development & Technical Discussion
Merits 3 from 2 users
Re: Why would make the extra merkle commitment asicboost uneconomical?
by
tromp
on 12/04/2017, 14:26:25 UTC
⭐ Merited by vapourminer (2) ,ETFbitcoin (1)
If one collects collisions on a central server (the most efficient way to find a lot of collisions in a big pool), one needs about 3 billion hashes to create 25 million 4-way collisions.  If one can live with 5 seconds delay (i.e. blocks miss some high-fee transactions from the last 5 seconds), one can  reduce this to 5 billion hashes in 5 seconds,

Your analysis appears correct. To elaborate on the math above:

Given x * 2^32 hashes, the probability of a k-way collision on a particular 32 bit value equals
choose(x * 2^32, k) * (2^-32)^k * (1 - 2^-32)^{x * 2^32 - k} which is about x^k/k! * e^-x.

For x=3/4 we get a fraction of 25M/4B 4-way collisions.
And for x=5/4 we get a fraction of 125M/4B 4-way collisions
(we actually get more than an extra quarter of that in useful collisions from k=5 and higher).