Quote from: jackjack on September 04, 2013, 06:18:59 PM

Quote from: tspacepilot on September 04, 2013, 03:28:05 PM

Quote from: jackjack on September 03, 2013, 10:24:45 PM

Hashes are impossible by hand...
Wouldn't a LiveCD on an offline HDD-less PC enough?

I haven't looked at the details of the hashing algorithm used to generate the public address from the private key. However, I don't think impossible is correct. I mean, everything a computer does can (in principle) be simulated using a very long tape and a pencil (see universal Turing machine).

Im just saying, difficult/tedious != impossible.

You want to play with semantics?

Ok, let's play.

Let's take a human, the super-hero kind, who can:
a/ Calculate a 32-bit operation in 10 seconds
b/ Work from midnight to midnight everyday
c/ Calculate a 32-bit operation without any errors

A hash takes about 5000 32-bit operations. So make it 10000 for ripemd160(sha256()).
That makes (10*10000) = 100k seconds = 38.4 hours = 1.6 day non-stop.
Possible.

Now here comes the fun.

This time we take a real human, the super smart kind.

A/ He calculates a 32-bit operation in 30 seconds (please try a 32-bit addition and tell me how much time it took)
This raises the total time to calculate one hash to 115.2 hours

B/ The guy must sleep, so he can "only" work from 8am to midnight.
This makes the total time to calculate one hash equal to 4.8 days.
Still possible.

C/ The lower brain failure rate in the best conditions is 5%. As he's super smart his is only 1%.
The probability of him finding the correct hash on one try is P = 1/2^(100000*1%) = 1/2^1000 ~ 1/10^300

D/ He starts the hashing calculation at birth and will stop at 100 years old.
This is (100*365) = 36500 days of calculation.
One try is 4.8 days, so he has 7604 tries available.
The odd of our super smart guy FINDING AT LEAST ONCE the correct hash in his entire lifetime is then:
R = 1-Q where Q = (1-P)^7604 = ( 1 - 1/2^1000 )^7604

Basic maths gives that Q > 1 - 7604/2^1000 = 1 - 10^(-297.149) > 1 - 10^(-297)
So R < 10^(-297) < 1/2^986
Yes, R < 1/2^986

TLDR

It's easier to crack 6 different bitcoin addresses with only 6 guesses than to a human to calculate a correct bitcoin address hash in his lifetime
Yes, I call that impossible

well the math is above me lol, but couldn't your 'super-smart' be a little smarter and instead of doing the math himself, be allocated to to the of task simply breaking it up into easier micro chunks of math to be distributed amongst an army of mental sweatshop laborers and then supersmart guy checks over for errors and does the final math on it? assuming a low amount of errors, it would reduce the time significantly would it not? In some countries right just paying the workers with food (some economical high protein stuff like peanut butter!) would be incentive enough.

note i'm am conscious of 3rd world war/global poverty issues and don't mean to be insensitive here, so please don't interpret as that.