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Re:Physical Limits to Computation (2000) [pdf] by amelius on Monday June 01, 2015 @07:29AM (#9637815)
So after 2^(2^35) steps my computer has certainly finished its computation. The state it is now in can be described by 0 bits of information, a priori. The question is, how is this useful in any way? :)
Re:Physical Limits to Computation (2000) [pdf] by lisper on Monday June 01, 2015 @10:30AM (#9638792)
You're missing the point, which is that a physical computer in this universe could enumerate no more than 2^500 distinct states. How is this useful? Well, for example, it lets you put hard upper bounds on the size of crpyto keys. For symmetric crypto, assuming your algorithm is a CSPRNG, you will never need a key larger than 512 bits no matter how advanced computer technology gets.
Re:Physical Limits to Computation (2000) [pdf] by amelius on Monday June 01, 2015 @05:14PM (#9642204)
Is that true? Cracking a key is a highly parallellizable operation, where little communication is needed between processors. Would your statement still hold here?
Re:Physical Limits to Computation (2000) [pdf] by lisper on Monday June 01, 2015 @05:29PM (#9642296)
Yes. Just look at the details of the calculation. It makes very (very!) liberal assumptions, and produces a very loose upper bound, i.e. 2^500 is almost certainly a gross overestimate of what is actually achievable even given arbitrarily advanced technology. The point here is that even a very loose upper bound is still quite small.