Bitcoin Forum

So, I've been playing around with Vanity keygen, (I found lots of keys that start with "1Lucas..."  :), which made me wonder, if you enter in someone's public key as the target to search for, might you not eventually stumble upon their private key?

I know the odds are against it such a thing ever happening, but lots of things happen that aren't "supposed" to... The financial crisis wasn't supposed to happen from a mathematical perspective, I understand... and even satoshidice's max payout pool has been won far more times than should have been, based on probabilities (again, per my understanding.)

But just for perspective, if the entire hashing power of the network was instead devoted to searching out one private key from a public key, how long would such as search take? Like at a hashrate of 1 TH, how long would it take to search the entire keyspace? Because, even if a TH seems like a lot now, between Moores law and huge numbers of potential new users/miners, the hashing power online now is nothing compared to what it one day could be..

Type in a whole private key (or as many letters as it will let you) and scale by network hash rate then scale by # of letters you weren't able to enter.  It's like 10^30 years to find one.

The idea is that it's more profitable to mine bitcoins than to try to brute force a private key.

Its more possible that you win 5 times the lottery and instantly a lightning kills you.
(Mathematically speaking).

There are as many private keys as there are atoms in the visible universe.

Nope.

total number of private keys = 0.0012 x atoms in visible universe

i.e. 0.12%

how did you arrive at that number? I was thinking there's more keys than subatomic particles in the universe

http://www.wolframalpha.com/input/?i=2%5E256

A quick calculation of mine confirms that, assuming 10^80 atoms.  Although I have to admit, I also thought there would be more private keys ... guess that must be because 256 > 80, but the bases are different.