septillion operations per second

[Ian Goldberg]

In article <4.2.0.58.20010620115736.00b3ddb0 at pop.xs4all.nl>,
Barry Wels  <crypto6 at nah6.com> wrote:
>Hi,
>
>In James Bamford's new book 'Body of Secrets' he claims the NSA is
>working on some FAST computers. 
>http://www.randomhouse.com/features/bamford/book.html
>---
>The secret community is also home to the largest collection of
>hyper-powerful computers, advanced mathematicians and skilled language
>experts on the planet.
>Within the city, time is measured in femtosecondsone million billionth
>of a second, and scientists work in secret to develop computers capable
>of performing more than one septillion
>(1,000,000,000,000,000,000,000,000) operations every second.
>---
>
>If they ever build such a computer (or 1.000.000 of them) what would
>that mean for today's key lengths ?
>I am curious how long a computer capable of a septillion operations per
>second would take to crack one 128 bit or 256 bit key.
>Or a RSA 1024 or 2048 bit key for that matter ...

Work it out. A computer that could do a septillion ops per second.
Let's be generous, and suppose it could actually try a key in a single
operation.  To try 2^128 keys would take

2^128 / 1000000000000000000000000 seconds, or about

10790283 years.  To try 2^256 keys of course would take

2^256 / 1000000000000000000000000 seconds, or about

3671743063080802746815416825491118336290905145 years.

I'm not worried.  The question about RSA is harder, since we don't
actually have a good idea of the real complexity of that problem.
For all we know, the NSA already has better algorithms than we do.
Our current algorithms are limited more by memory than by computrons.

   - Ian



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