Re: How long would it take?
Its generally unwise to make the assumption that the only possible attack on your conventional scheme is a brute force attack. Certainly the attacks used on many previous generations of cryptosystems were never brute force -- and certainly every generation of naive cryptographer has said "well, using brute force it would take N years to break my cypher". A simple vingenere cypher with a 12 letter key would seem to be very strong indeed (stronger than DES), and yet we know you can break one in a few moments because there are better attacks than brute force. We have suprisingly little in the way of general theory on what would or would not make a conventional cryptosystem strong. Certainly differential cryptanalysis will not be the last thing people come up with. Until we know everything the NSA knows, I will be hesitant to say "unless something better comes up" and more comfortable saying "until something better comes up." Indeed. The key length is a worst-case analysis for the cryptanalyst; they can do no worse than that. We can be confident that NSA has cracked DES because an exhaustive search engine is within their means, but we don't know how much better they can do. A while back, Shamir gave a talk on differential cryptanalysis here at Murray Hill. He mentioned Coppersmith's letter, which said that IBM knew about differential cryptanalysis back when they built DES, and they designed it to resist the attack. That's obviously the case -- so Shamir said that he asked Coppersmith to state that in the intervening 18 years, IBM had not come up with a stronger attack on DES. Coppersmith was silent, from which you can draw any conclusions you wish.
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