I quickly discovered the Large Bitcoin Collider.
https://lbc.cryptoguru.org/aboutWow this is a serious project.
Basically thousands of distributed servers generating and checking 26 Trillions (!!!) of private keys on a daily basis.
Over the first three years, they managed to find 7 private keys. Thats a lot! I imagined the odds were much lower., but probably there is some kind of bug in some wallet utilising a suboptimal random number generator to create keys.
A few basic comments on the LBC.
For starters, I'd like to point out that I personally am convinced that the LBC is a huge waste of time, effort, energy and money.
It has no academic value whatsoever, is unlikely to yield any results that contradict common understanding of cryptography and will not determine any empirically establishable "constants of nature".
When you're using Bitcoin, what you are basically doing is play a game.
The game is "I'm thinking of a random number, if you can guess it, here's a dollar".To make it easy, I can start with "I'm thinking of a number between one and ten".
Your chances of getting that dollar are 10 per cent.
In a harder game, I'll think of a number between one and one thousand.
To make it a challenge, I'll ask you to donate 1 US cent for every guess to a good cause.
A dollar will yield 100 guesses, so your chances of even making you dollar back are only 10 per cent.
Now, in Bitcoin, I'm thinking of a number between one and 2^160 (in fact, it's a little less, but let's not delve into technical details too much).
For a single guess, I want you to donate a tiny amount of computing power, i.e. electrical energy to, well, thermodynamics (because that energy is obviously wasted).
But in Bitcoin, there are actually more than just two players.
I may ask for a number between one and 2^160, but
others just ask for a number between one and ten.
If you guess "nine", your chances of getting their number right are ten per cent, but at the same time, you also have a (much slighter) chance of guessing my number right (I could have used "nine" as well, it's in the space of 2^160, after all).
And that is what the LBC does.
It doesn't guess random numbers in the range of 2^160, but rather numbers in the range of one to ten, then 11 to 100, then 101 to 1000, etc.
All the time, it's obviously
also guessing numbers in the wider range of 2^160.
For the LBC to
claim that it's guessing numbers in that range is pretty far fetched, though.
Now, the collisions the LBC found so far were all in those much narrower search ranges, they have nothing to do whatsoever with collisions in the wider space of 2^160, other than that they inadvertently lie in that range as well.