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There is an asic bitcoin miner which can generate 500GH/s which retails for 22k$. What if you had a billion dollars to crack encryptions?

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You would be able to break weak passwords, but you wouldn't be able break PGP with decent key sizes.

Reason? Physics: http://security.stackexchange.com/questions/25375/why-not-us...

Let's assume one hash is exactly equivalent to one attempt at brute force and the keys are 256 bits. 5GH/s * ($5B / $22K) is about 10^17 GH/s. There are 2^256 possibilities, which is about 10^77. So to try them all you need about 10^60 seconds. Granted that is the worst case for the cracker, but the average case is also going to take quite a while.

> Granted that is the worst case for the cracker, but the average case is also going to take quite a while.

The average case for finding something equaly distributed in a space is half the time, or about 5 * 10^59 seconds, what is about the same thing, because with numbers that big "about" usualy means anything from *10 to /10.

Of course, RSA keys aren't equaly distributed at the key space. That gives an speedup of sume number between 1 and 2 that I can remember (still about the same thing), and there are search algorithms that reduce the number of tries by some non-trivial amount. I'm not up-to-date on them.

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