septillion operations per second

[Arnold G. Reinhold]

At 12:16 PM +0200 6/20/2001, Barry Wels 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 ...
>

One septillion =  10**24 or about 2**80. If you assume 1000 
operations to test a key, a septillion ops per second machine tests 
about 2**70 keys per second. For a 128 bit key, that means you need 
about 2**57 seconds on average to find a key, or about 4.6 billion 
years, the age of the Earth.  A million of them (not likely) would do 
the job in only 4600 years.

Arnold Reinhold



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