Ultimate limits to computation
Hal Finney
hal at finney.org
Tue Aug 11 11:47:27 PDT 2009
[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:
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