[tor-talk] NSA supercomputer

[Seth David Schoen]

Andrew F writes:

> So lets look at this from another view.   How fast does a computer have to
> be to fully bruit force a 64,128,256 key?  ZettaFlops?  YottaFlops?
> http://en.wikipedia.org/wiki/Flops           Lets assume a classical
> computer.
> 
> George, crankup that abacus of yours and let us know.  I for one would be
> very interested.
> Or anyone else with big fat calculator?  My is the wimpy drugstore kind...

As Gregory pointed out, "flops" is not the right measurement here
because cryptographic operations are not floating-point operations.
Checking a candidate key doesn't involve any floating-point math,
but rather something like a block cipher decryption, which is a
different sort of computation.

The calculations to figure out brute-force speeds are really about
simple multiplication and division.

Just as the distance traveled by a moving object is given by

distance = speed × elapsed time

the number of decryptions attempted by a brute force search is given
by

decryptions = speed × elapsed time

For example, if you have a 128-bit symmetric key, and you want to
talk about a situation in which every possible key value has been
checked, the relationship is

2¹²⁸ = speed × elapsed time

or, if you prefer,

340282366920938463463374607431768211456 = speed × elapsed time

If you want the time, just divide 2¹²⁸ by the speed.  If you want
the requisite speed to finish in a specified time, just divide 2¹²⁸
by that time.  You just need to use consistent units, like measuring
speed in trial decryptions per second and measuring elapsed time in
seconds.

In 1998 EFF built a brute-force cracking machine

https://en.wikipedia.org/wiki/EFF_DES_cracker

which "was capable of testing over 90 billion keys per second",
against the DES system which used 56-bit keys.  To find the time
it would take that machine to be sure of testing every possible
key, just divide 2⁵⁶ by 90 billion; the answer is given in seconds.

(To convert seconds to days, divide by 86400.)

-- 
Seth Schoen  <schoen at eff.org>
Senior Staff Technologist                       https://www.eff.org/
Electronic Frontier Foundation                  https://www.eff.org/join
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