Re: New algorithm for finding prime factor of large numbers

From: Anders Sandberg (asa@nada.kth.se)
Date: Sat Aug 31 2002 - 04:45:27 MDT


On Sat, Aug 31, 2002 at 03:00:24AM -0700, Robert J. Bradbury wrote:
>
> At any rate -- could someone offer any thoughts on how much
> privacy/security gets lost if quantum computing falls out of
> the sky on top of our collective heads? (Presumably the
> government has a lock on quantum computers for the first
> N years (where N is hopefully in single digits)). [I think
> its the folks at the Univ. of Michigan that seem to be
> pushing the edge of the envelope here and its moving much
> faster than I would have expected.]

If we assume some unexpected breakthrough allows useful (hundreds or
thousand bit quantum computers) then you could start doing discrete
logarithms, and it would be a boon to NSA et al. Still, the main problem
is the sheer amount of data; just opening up files of known suspects and
people under investigation would likely keep various agencies extremely
busy. Sifting through everything else would be even worse; while having
something RSA encrypted is right now a signal that it is at least
interesting most encrypted stuff is irrelevant anyway. Echelon-style
sifting produces enormous amounts of data, a bit like the Demon of the
Second Type in _The Cyberiad_: it all seems interesting and relevant, but
there is too much of it and it comes unsorted.

Note that such sudden breakthroughs are unlikely to remain isolated. If
the originators kept it secret and used it for cracking crypto, then
they couldn't be too overt about using the information gained (the usual
enigma problem). If it gets out that it is doable then a lot of people
are going to start working on it, likely soon figuring out the trick
("OK, we know the team includes Dr. Venkmann - he is an expert of phonon
scattering in superconductors. Could it be that they use *phonons*?
Let's try!"). A bit like the Soviet hydrogen bomb - knowing it can be
done makes it much more manageable. And of course, I seriously doubt
this kind of Hollywood breakthrough (from useless device to powerful
world-changer nearly instantly) is very likely in the first place.

Once the news is out people will start moving to other cryptos - elliptic
curves seem a good start. of course, cryptographers are going to start
hunting for ways of quantum break them too. Investing in quantum crypto
systems is probably a good idea.

My guess is that altogether such a breakthrough would cause a temporary
but sizeable advantage for the discovering group, lead to the capture and
conviction of a lot of bad guys (by whatever definition used), a bit of
software upheaval but not any huge changes in the world. One interesting
effect would be that after the tech got out, archives of communications
from before the breakthrough might contain now open but sensitive
information that could be dug up - I would expect plenty of people would
try to find old incriminating or sensitive stuff and erase it, to the
chagrin of future historians.

Let's not forget Grover's O(sqrt(N)) search algorithm on unsorted lists
- that might be potentially more important. But I guess it requires even
larger quantum computers to be world-changing. And if de Garis claim
about a quantum GA optimizer holds true then the effects would be truly
amazing - essentially instant optimisation of any finite system. Protein
folding and automated design would be practical; I would go out in the
streets with a "The Singularity Is Nigh" sign immediately :-)

-- 
-----------------------------------------------------------------------
Anders Sandberg                                      Towards Ascension!
asa@nada.kth.se                            http://www.nada.kth.se/~asa/
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