# Re: [tor-talk] NSA supercomputer

```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 Ã elapsed time

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

decryptions = speed Ã 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

2ÂÂâ = speed Ã elapsed time

or, if you prefer,

340282366920938463463374607431768211456 = speed Ã elapsed time

If you want the time, just divide 2ÂÂâ by the speed.  If you want
the requisite speed to finish in a specified time, just divide 2ÂÂâ
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 2ââ by 90 billion; the answer is given in seconds.

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

--
Seth Schoen  <schoen@xxxxxxx>
Senior Staff Technologist                       https://www.eff.org/
Electronic Frontier Foundation                  https://www.eff.org/join
815 Eddy Street, San Francisco, CA  94109       +1 415 436 9333 x107
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