David SMITH wrote: > ...at the moment. Welcome to the Second Law of Thermodynamics! Enjoy your stay.
By the Second Law, every time a bit of information is erased you have to pay the entropy tax of (kT * ln 2) J. Let's assume that for each key you try, you have to erase 1000 bits of information--this is wildly optimistic, given how complex key schedules usually are, but it'll make for nice numbers. On average you'll have to brute-force 2**127 keys before you find the proper 128-bit AES key. 1000 = 10**3 2**127 approx. eq. 10**38 10**41 * (3 * 10**-21) = 3 * 10**20 J A one-megaton nuclear weapon liberates approximately 10**15 J of energy. 3 * 10**20 J divided by 10**15 J = 300,000 megatons By comparison, the 1863 Krakatoa explosion liberated about 21,000 megatons. If you're interested, we can also do a quantum-mechanical analysis of the minimum time required to do this computation. It gets equally silly. http://en.wikipedia.org/wiki/Rolf_Landauer http://en.wikipedia.org/wiki/Margolus-Levitin_theorem ... It's true that quantum computers and reversible computing will both reduce this number considerably. However, if you're going to talk about science fiction--which is what large-scale quantum and reversible computing is nowadays--then why not go whole-hog and posit the existence of a psychic who's 100% effective in predicting keys? _______________________________________________ Gnupg-users mailing list [email protected] http://lists.gnupg.org/mailman/listinfo/gnupg-users
