Quote from: BurtW on September 20, 2013, 12:12:31 PM

Quote from: jackjack on September 20, 2013, 08:51:36 AM

The thread is about brute forcing private keys, not about breaking secp256k1

I will try one more time.

This is the algorithm for "bute forcing" a public/private key pair:

a) Key_public = G, Key_private = 1
b) Is Key_pubic the key we are looking for?
c) If yes Key_private is the one you are looking for so quit
d) else Key_public = Key_pubic + G, Key_private = Key_private + 1
e) goto b)

Note the following:

The operation Key_pubic + G requires many mathematical steps
If you are looking for a Bitcoin address you have to do even more mathematical steps on each trial to hash the public key three times

Now consider this much easier problem, just Key_private = Key_private + 1

Imagine a physical device which simply counts the numbers from 1 to n where n is the largest possible private key, a simple 256 bit counter. That is all it does is count. It is only the simplest part of the algorithm described above.
This counter can be made using any possible future technology, it just has to obey the laws of physics and thermodynamics.

This perfect device will count a fast a physically possible using the lowest physically possible amount of energy to do it.

How long would it take to just count from 1 to n?

How much energy would it take?

BTW n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141

Hmm, yeah I know I've been saying this in many posts...
I was answering Nagan who said that breaking secp256k1 would help brute-forcing private keys