big numbers

The number of atoms in the entire observable universe is estimated to be within the range of 10^78 to 10^82 Read more: http://www.universetoday.com/36302/atoms-in-the-universe/#ixzz2aAM7OxsI

10^78 ~= 2^259 10^82 ~= 2^272

So, an attacker has as much chance of randomly selecting the correct 272 bit key as randomly selecting a single "correct" atom in the observable universe. In practical terms, attempting to brute-forcing a 256 bit key is pretty dumb. A motivated adversary is going to use other channels.

What about a 128 bit key? That is more manageable. Assume the adversary can test 1 trillion keys per second (currently available only to rich governments), or 3.15576e+19 or 2^64.77 keys in 1 year. So sorry to bear bad news: Your secret is only safe for a quintillion (10^18) years.

The point being: (in my probably-naive opinion) current state-of-the-art cryptography, properly implemented, is pretty unassailable by naive brute force attacks against the key.

How does this relate to passwords? Many experts agree that the strongest passwords are randomly generated just like encryption keys. If there is any pattern/structure to the password, and that structure becomes known to the adversary, he has a much better chance of guessing the password with a reasonable effort.

http://security.stackexchange.com/questions/22873/how-much-added-security-do-i-really-get-with-a-longer-key-size

http://crypto.stackexchange.com/questions/3615/what-is-the-effect-of-the-different-aes-key-lengths https://www.schneier.com/blog/archives/2009/07/another_new_aes.html http://security.stackexchange.com/questions/6141/amount-of-simple-operations-that-is-safely-out-of-reach-for-all-humanity/6149#6149