2) How much longer would it take to break triple DES versus standard DES using one of the key-breaking machines described?
Using brute force, it would take the cube of the time it takes to break single DES.
Hmm... I can't figure out what it would mean to cube time. For two-key (112 bit) triple DES, it should be 2^56 times longer to exhaustively search the keyspace, with three keys, 2^112 times longer. This assumes the keysearch engine is pipelined, so each trial encryption takes the same amount of time, despite the additional rounds. Such a machine would cost more, of course, since it would have a longer pipeline, but wouldn't otherwise be significantly different in design. Back-of-the-envelope calculation: a design like the "7-hour exhaustive keysearch" engine for 2-key triple DES would take 50 trillion years or so to exhaust the keyspace. That's for a cost on the order of $1 million (it should be buildable for less than three times the cost of the 56-bit key version). Seems secure, but as Perry says,
Whether a more sophisticated techinque is possible is unknown.
Joe
Joe Thomas says:
2) How much longer would it take to break triple DES versus standard DES using one of the key-breaking machines described?
Using brute force, it would take the cube of the time it takes to break single DES.
Hmm... I can't figure out what it would mean to cube time. For two-key (112 bit) triple DES, it should be 2^56 times longer to exhaustively search the keyspace, with three keys, 2^112 times longer.
Lets assume we are using three keys, which I what I meant. Lets say 1 is the time do one encryption. (On a parallel machine, just think of things as being on a uniprocessor going N times faster.) It would take 2^56*N time to break single DES. My claim is that it should take (2^56)^3 = 2^56*2^56*2^56 = 2^168. Your claim, which is that it would take 2^56*2^112=2^168, which is the same. The only difference is that I didn't assume piplineing so there is a constant factor different floating around somewhere. Perry
participants (2)
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Joe Thomas -
Perry E. Metzger