Ultimate limits to computation

[Hal Finney]

[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: