On what the NSA does with its tech

[Hal Finney]

MV writes:
> Yes.  They can't break a 128 bit key.  That's obvious.  ("if all the
> atoms in the
> universe were computers..." goes the argument).

Not necessarily, if nanotechnology works.  128 bits is big but not
that big.

Eric Drexler, in Nanosystems, section 12.9, predicts that a nanotech
based CPU fitting in a 400 nm cube could run at 1000 MIPS and consume
60 nanowatts, performing 10^16 instructions per second per watt.

Let's design a system to break a 128 bit cipher.  Let's suppose it has
to do 2^10 instructions per test, so this is 2^138 instructions total,
or about 10^41.  Let's let it run for four months, which is 10^7 seconds,
so our necessary processing rate is 10^34 instructions per second.

This means we need 10^34 IPS / 1000 MIPS or 10^25 of Drexler's gigahertz
cubes, call it 10^25 cubic microns or 10^7 cubic meters, a cube about
220 meters on a side.

The system will consume 10^25 * 60 nanowatts or about 6 * 10^17 watts.
Now, that's a lot.  It's four times what the earth receives from the sun.
So we have to build a disk four times the area (not volume) of the earth,
collect that power and funnel it to our computers.  Probably we would
scatter the computers throughout the disk, which would be mostly composed
of solar collectors.  (Keeping the disk gravitationally stable is left
as an exercise for the student, as is the tradeoff involved in making
it smaller but moving it closer to the sun.)

Fortunately, exhaustive key search is perfectly parallelizable so there
is no need for complex communications or synchronizations between the
processors.

As you can see, breaking 128 bit keys is certainly not a task which is
so impossible that it would fail even if every atom were a computer.
If we really needed to do it, it's not outside the realm of possibility
that it could be accomplished within 50 years, using nanotech and robotics
to move and reassemble asteroids into the necessary disk.

Now, 256 bit keys really are impossible, unless the whole contraption
above can be made to operate as an enormous, unified quantum computer,
in which case it could theoretically break even 256 bit keys.

512 bit keys... now those really are impossible.

Hal Finney

---------------------------------------------------------------------
The Cryptography Mailing List
Unsubscribe by sending "unsubscribe cryptography" to majordomo at metzdowd.com

----- End forwarded message -----
-- 
Eugen* Leitl <a href="http://leitl.org">leitl</a> http://leitl.org
______________________________________________________________
ICBM: 48.07100, 11.36820 http://www.ativel.com http://postbiota.org
8B29F6BE: 099D 78BA 2FD3 B014 B08A  7779 75B0 2443 8B29 F6BE