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Old 06-08-2004, 08:00 PM
Guy Harrison
 
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Default A question about speed and size.

Big Bill wrote:

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A recurring thought has been keeping me awake of late and that is
whether someone without your private key and without your passphrase
can decrypt a message encrypted with your public key. Often, the
argument revolves around applying greater and greater computer power
to the task as key lengths become longer and longer.

But it seems to me that there is an ultimate limit to the power of
computers beyond which no technological breakthrough can reach.


The imagination.

Bear with me whilst I explain.If we reduce the size of a byte of
memory to an atom of oxygen (which has eight electrons, one for each
bit in the byte), it still takes a non-zero amount of time to flip
the spin-state of each electron. This defines the ultimate speed of
both a memory chip and a processor. Note that it takes the same
amount of time to flip the spin-state of the one electron in an atom
of hydrogen, so we don't gain anything by changing atoms.


Use smaller particles.

If we pack the atoms of our megacomputer as dense as possible
without creating a neutron star, there is still a non-zero distance
between atoms. It takes a finite amount of time for a signal to
travel that distance. That defines the overall speed of the
computer.


Quantum mechanics.

If we take all the atoms in the universe (oxygen, hydrogen, and all
the others), that defines the ultimate size of a computer. We can
allocate the atoms between memory and processor. Just remember,
the number of atoms is finite; and we must reserve some for the
nuclear power plant that will run this infernal device. Thus, the
memory of our megacomputer is limited.


Use two universes.

I saw this concept in some very old technical periodical where the
capacity and speed of an ultimate computer were quantified. The
article was published just before the dawn of PCs, when minicomputers
and microcomputers were being installed with faster capabilities at
far less cost than mainframes. The point is that we can conceive of
finite problems to be solved on a computer that exceed the capacity
of any computer that could ever exist.


Mine still won't make a cup of tea.

As there is indeed a limit to computer power before conjecturing
about a future super-computer cracking a PGP-encrypted message,
we should consider whether that computer could fit into the universe.


Perhaps we're inside that computer.

Your thoughts on this would be very welcome. I have run out avenues
to explore and worse still my GP will not increase my dose of
Nembies.


Re above: read something somewhere a bit back about time travel. If... one
had enough resources, one could simulate all possibilities of past events.
Throw away all the invalid scenarios and you're left with a snapshot of
what happened in the past. Ergo time travel.

There's a nasty caveat ;-)

Should one subscribe to this view then it follows that of all possible
simulations only one is the real one (running the simulations). It also
follows each simulation must be accurate, is real to its inhabitants, &
thus is a universe in its own right. One is forced to conclude that the
chances of ourselves being the real "in charge" universe is bugger all.

Sleep tight! g

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