Could a billionaire brute force a private key?

[BlackHatCoiner]

Let's take this one: 35hK24tcLEWcgNA4JxpvbkNkoAcDGqQPsP

It's the address with the most bitcoins (255kBTC)

Let's assume now that a billionaire like Jeff Bezos spends 1B$ for equipment. How many hashes per second could this equipment produce? Above a million trillion hashes per second? He could do this for a month.

Could he brute force it? Or still unlikely to happen?

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[ranochigo]

Nothing remotely close. No one can possibly harness enough resources and defeat the effects of aging and the destruction of planet earth to be able to bruteforce a specific private key. The resources needed to create and check addresses is insanely huge and the keyspace to search would take millions of years even if you can harness all the computing power of the computers on earth.

Even if you have billions, you could have better ways to burn it than to use it on Bitcoin.

[mocacinno]

Let's take this one: 35hK24tcLEWcgNA4JxpvbkNkoAcDGqQPsP

It's the address with the most bitcoins (255kBTC)

Let's assume now that a billionaire like Jeff Bezos spends 1B$ for equipment. How many hashes per second could this equipment produce? Above a million trillion hashes per second? He could do this for a month.

Could he brute force it? Or still unlikely to happen?

Theoretically, yes, but he'd have a much better chance of winning his state lottery several times in a row... It's all about odds here, sure there is a chance you'll be hit by an astroid at the exact time you're sitting on the toilet while being spied on by a transexual paparazi photographer who thinks the earth is flat.... The odds, however, are not that big. Defenately not big enough to start bribing all transexual paparazo's not to take your pictures while you go to the toilet.

As for your exact question, a GPU vanitygen tool could find ~20.000.000 private key => public key => public key combinations/second
(https://en.bitcoin.it/wiki/Vanitygen_keysearch_rate)

There are 2^256 private keys,
It would take a GPU 183587153154040137340770841274560000000000000000000000000000000 years to scan the complete keyspace

But you say 1 billion worth of equipment... Let's assume Bezos gets bulk discounts, and he's able to buy GPU's + risers + motherboard + PSU's + shelves + S&H + taxes for the astronomically small amount of $250/GPU (everything included).

His 1 billion buys 4 million GPU's...
I found this study from 2018: https://news.bitcoin.com/study-finds-less-than-40-of-btc-addresses-are-economically-relevant/ It says there are 27.000.000 addresses in use. Let's assume by now there are 50 million addresses.

It would still take Bezos
91793576577020068670385420637278000000000000000 years to have a 10% chance of finding a private key belonging to a funded address.

The sun will only live ~10 billion years (https://spaceplace.nasa.gov/sun-age/en/)
Even if Bezos magically finds hardware that's 1 million times as performant as a GPU, it would still take the lifetime of 9.179.357.657.702.006.867.038.542.063.727 suns to have a 10% chance of finding the private key for a funded address.

I won't even start about the amount of power he'd burn while trying...

Offcourse, this theoretical example starts from completely random keys, if there's a flaw in the RNG a lot of variables change

[hugeblack]

In short, the private key is a number between 1 and 2^256 and trying to guess it might lead you to count to infinity. for more watch this^[1] and if you want it by diagrams ----> https://i.imgur.com/ag3KQ0L.png
it is possible to brute force some non-random Bitcoin addresses because some people generate their private keys in an unsafe way (poorly chosen passphrases,) this possibility is impossible if it is not sent from that address (generates more addresses without sending.)

[1] https://www.youtube.com/watch?time_continue=41&v=S9JGmA5_unY&feature=emb_logo