All the free energy in the universe...

[tcmay@netcom.com (Timothy C. May)]

> You had better not have any "secure thoughts" then.  "Forever" is enough
> time to break _any_ cipher.
> 
> --
> Lefty (lefty@apple.com)

Not to split universes here, but it is interesting to consider that
some ciphers may not be breakable in _our_ universe, in any amount of
time.

Our universe presumably has some finite number of particles (currently
estimated to be 10^73 particles). This leads to the "even if every
particle were a Cray Y-MP it would take..." sorts of thought
experiments.

But I am considering _energy_ here. Ignoring reversible computation
for the moment, computations dissipate energy (some disagree with this
point). There is some uppper limit on how many basic computations
could ever be done with the amount of free energy in the universe. (A
rough calculation could be done by calculating the energy output of
stars, stuff falling into black holes, etc., and then assuming about
kT per logical operation. This should be accurate to within a few
orders of magnitude.)

I haven't done this calculation, and won't today, but the result would
likely be something along the lines of X joules of energy that could
be harnessed for computation, resulting in Y basic primitive
computational steps.

I can then find a modulus of 3000 digits or 5000 digits, or whatever,
that takes more than this number of steps to factor.

Caveats:

1. Maybe there are really shortcuts to factoring. Certainly
improvements in factoring methods will continue. (But of course these
improvements are not things that convert factoring into a less than
exponential-in-length problem...that is, factoring appears to remain
"hard.")

2. Maybe reversible computations (a la Landauer, Bennett, et. al.)
actually work. Maybe this means a "factoring machine" can be built
which takes a fixed, or very slowly growing, amount of energy. In this
case, "forever" means Lefty is probably right.

3. Maybe the quantum-mechanical idea of Shore is possible. (I doubt
it, for various reasons.)

Anyway, this post is of no practical importance.

However, I continue to find it useful to think of very large numbers
as creating "force fields" or "bobbles" (a la Vinge) around data. A
5000-decimal-digit modulus is as close to being unbreakable as
anything we'll see in this universe.


--Tim May


-- 
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