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..