Quote from: 1bitc0inplz on July 09, 2011, 05:04:39 AM

There is a ~~very~~ non-0 chance that two nodes can generate the same address, and nobody would be none the wiser.

There is not a VERY non-0 chance.

Quote from: 1bitc0inplz on July 09, 2011, 05:03:16 AM

you'd ~~almost~~ 99.999% be guaranteed to never find a single collision.

Nor an ALMOST.

There has NOT been one SINGLE documented crack of a conventionally generated 160 bit SHA-1 hash. It could happen (if god played dice). Perhaps someone will come up with a fantastically clever new non-brute force algorithm. Perhaps computers will compute faster than currently understood physical limits (such as infinite quantum states).

1 - (number of blocks, 135483) * (new addresses per block, 1 to 10) / (key space, 2^160) = 1 - 10^(5 or 6) / 10^49

99.9999999999 9999999999 9999999999 9999999999 9 % chance that it's not gonna happen

(give or take a 9, minus the chance of god playing dice, new published algorithm crack, or yet unknown technological innovation)

Quote from: Yatta99 on July 09, 2011, 03:31:20 PM

The ~~only~~ real protection (if you want to call it such) is to have many addresses in your wallet with all your Bitcoins spread among them. If/when an address is compromised you will potentially lose a little rather than everything.

No. You'll then have only divided a seemingly infinitely improbable chance by a tiny finite number (number of your wallet keys with value). You can remove a '9' from my estimate above. If someone can crack one hash, then they can probably crack a huge number of them. Though not putting "all your eggs in one basket" is good advice for other reasons.

EDIT: strike-outs are mine.