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12 Aug '09

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by Maria Todd 12 Aug '09

12 Aug '09

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12 Aug '09

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12 Aug '09

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12 Aug '09

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Fwd: Ultimate limits to computation
by R.A. Hettinga 12 Aug '09

12 Aug '09

Begin forwarded message: > From: hal(a)finney.org ("Hal Finney") > Date: August 11, 2009 2:47:27 PM GMT-04:00 > To: leichter(a)lrw.com > Cc: cryptography(a)metzdowd.com > Subject: Ultimate limits to computation > > [Note subject line change] > Jerry Leichter writes: > >> Since people do keep bringing up Moore's Law in an attempt to justify >> larger keys our systems "stronger than cryptography," it's worth >> keeping in mind that we are approaching fairly deep physical limits. >> I wrote about this on this list quite a while back. If current >> physical theories are even approximately correct, there are limits to >> how many "bit flips" (which would encompass all possible binary >> operations) can occur in a fixed volume of space-time. You can turn >> this into a limit based solely on time through the finite speed of >> light: A computation that starts at some point and runs for n years >> can't involve a volume of space more than n light years in radius. >> (This is grossly optimistic - if you want the results to come back to >> the point where you entered the problem, the limit is n/2 light >> years, >> which has 1/8 the spacial volume). I made a very approximate guess >> at >> how many bit-flips you could get in a time-space volume of a 100 >> light- >> year sphere; the answer came out somewhere between 2^128 and 2^256, >> though much closer to the former. So physical limits prevent you >> from >> doing a brute force scan - in fact, you can't even enumerate all >> possible keys - in 100 years for key lengths somewhere not much more >> than 128 bits. > > Things may not be quite as favorable as this. Here is a posting I made > to cypherpunks in 2004: > > To: cypherpunks(a)al-qaeda.net > Date: Wed, 4 Aug 2004 11:04:15 -0700 (PDT) > From: hal(a)finney.org ("Hal Finney") > Subject: Re: On what the NSA does with its tech > > MV writes: >> Yes. They can't break a 128 bit key. That's obvious. ("if all the >> atoms in the >> universe were computers..." goes the argument). > > Not necessarily, if nanotechnology works. 128 bits is big but not > that big. > > Eric Drexler, in Nanosystems, section 12.9, predicts that a nanotech > based CPU fitting in a 400 nm cube could run at 1000 MIPS and consume > 60 nanowatts, performing 10^16 instructions per second per watt. > > Let's design a system to break a 128 bit cipher. Let's suppose it has > to do 2^10 instructions per test, so this is 2^138 instructions total, > or about 10^41. Let's let it run for four months, which is 10^7 > seconds, > so our necessary processing rate is 10^34 instructions per second. > > This means we need 10^34 IPS / 1000 MIPS or 10^25 of Drexler's > gigahertz > cubes, call it 10^25 cubic microns or 10^7 cubic meters, a cube about > 220 meters on a side. > > The system will consume 10^25 * 60 nanowatts or about 6 * 10^17 watts. > Now, that's a lot. It's four times what the earth receives from the > sun. > So we have to build a disk four times the area (not volume) of the > earth, > collect that power and funnel it to our computers. Probably we would > scatter the computers throughout the disk, which would be mostly > composed > of solar collectors. (Keeping the disk gravitationally stable is left > as an exercise for the student, as is the tradeoff involved in making > it smaller but moving it closer to the sun.) > > Fortunately, exhaustive key search is perfectly parallelizable so > there > is no need for complex communications or synchronizations between the > processors. > > As you can see, breaking 128 bit keys is certainly not a task which is > so impossible that it would fail even if every atom were a computer. > If we really needed to do it, it's not outside the realm of > possibility > that it could be accomplished within 50 years, using nanotech and > robotics > to move and reassemble asteroids into the necessary disk. > > Now, 256 bit keys really are impossible, unless the whole contraption > above can be made to operate as an enormous, unified quantum computer, > in which case it could theoretically break even 256 bit keys. > > 512 bit keys... now those really are impossible. > > Hal Finney > > --------------------------------------------------------------------- > The Cryptography Mailing List > Unsubscribe by sending "unsubscribe cryptography" to majordomo(a)metzdowd.com

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Ultimate limits to computation
by Eugen Leitl 12 Aug '09

12 Aug '09

----- Forwarded message from "\"Hal Finney\"" <hal(a)finney.org> -----

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12 Aug '09

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by ~Euphoric_Intercourse~ 12 Aug '09

12 Aug '09

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12 Aug '09

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