You can't just access a wallet if you know it's address. You need to know the private keys, which are private.

lol that wallet would be worth "mining"

This doesn't even apply to point groups...just hashes.  I know you still can't get the keys.  Just a question about hash functions in general.

So I've tried to stare at hash code and stare and stare and figure out what actually make its irreversible.  Obviously, I lost track of the bits (I was trying to keep it together up here ->    but I didn't follow along..lost it somewhere around xor...).

But... is the irreversibility actually fundamental?  if you could ultra slow motion camera the bits literally flipping due to electrical impulses in the CPU, could you not play the movie backward discovering the inverse of the hash?

Parity and time reversal NeOne!?

Let's see... 150,000,000 keys per sec on a 7970, or 1.5 * 10^8 k/s.  There are maybe 1.0 * 10^8 Bitcoin addresses with unspent outputs.

If I remember right, the complexity of addresses is 2^128.  So, you have 1/(1.0 * 10^8 2^128) = 3.4 * 10^30 keys as the inverse of your probability for finding any private key to some unspent output (or basically, your reduced search space after accounting for all keys with unspent outputs).

That's (3.4 * 10^30 k [1.5 * 10^8 k/s]) = 2.3 * 10^22 seconds to find a single private key to spend a random address' Bitcoins with a single 7970.  

That's only 52,000 * the age of the entire universe, so you should find one pretty quick!

That's 100m public addresses with unspent outputs divided by the number of all possible addresses including collisions, or more simply the probability of any address of having an unspent output.

edit: Oh, duh, it's the inverse of that, sorry. X)

You'd have to do the math but even if 100 billion years pass in a few seconds how many seconds would it take to count to 2^256. Probably a incomprehensible amount of seconds.

Might want to rethink that...

115792089237316195423570985008687907853269984665640564039457584007913129639936 addresses

and

3155760000000000000ish seconds in 100000000000 years. I'll let you figure up the rest of the math.

I don't think you understand the concept of "...they strongly imply that brute-force attacks against 256-bit keys will be infeasable until computers are built from something other than matter and occupy something other than space."

I imagine in this thread I know the least about the technical aspects of cryptocurrencies and this may be a bit off topic, but when bitcoins reached $1,200 I was curious to know how secure they were, so I gave my kid a task. He had 2 hours to see how many bitcoin addresses he could generate while checking each one for a positive balance. He found 3 accounts that contained many many bitcoins, I was so tempted to take them, that I had to delete his internet history.