### Re: septillion operations per second

```
On Wed, 20 Jun 2001, Barry Wels wrote:

> 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. ---

this is of course, science fiction. (remember Planck constant, speed of
light, etc.)

> 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
> ...

2^128/10^24=340282366920938.4634633746077 (seconds), so even assuming such
a computer would do 10^24 key searches per second (as opposes to 10^24
'instructions'), it would still take ten million years for one computer.

Helger

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### Re: septillion operations per second

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> 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 ...

take a peek at the chapter on key lengths in Schneier's Applied
Cryptography.  it is an entertaining read.  in short, he makes the
case that computers as we understand them simply cannot conduct brute
force attacks against 128-bit or larger semetric keys.  (i won't
repeat his explanation here.)

RSA keys are a bit dodgier.  new techniques for prime number factoring
could conceivably weaken keys that are considered strong today.

having said all that, there are often weaknesses other than key
length: predicting the key generation, keystroke monitoring, bribing

--mkb

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### Re: septillion operations per second

```
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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### Re: septillion operations per second

```
At 12:16 PM 6/20/01 +0200, 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

surveillance
of Soviet radars just after getting back from visiting the dish [1].

Re: fast computers.  All crypto thinkers will assume that the Adversary has
got each fundamental particle in the universe cranking away at insane
speeds on your key until the Restaurant at the End of the Universe closes.

You're obviously a newbie, but that's cool, you're here to learn, like the
rest of us.

[1] 800 stairs at noon near the solstice in the tropics.  Fun fun fun [2].
Microwave ductwork
you could stand in.  As a bonus, the US decided to stop bombing a Puerto Rican
tourist isle while we were visiting.

[2] With a 30+++ pound infant that insists on being carried, no less.

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### Re: septillion operations per second

```
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 ...

10^24 is roughly 2^80. So, to _count_ to 2^128 would take 2^48 seconds.
That's around 9 million years. Or, for a million of them, 9 years.

Cheers,

Ben.

--
http://www.apache-ssl.org/ben.html

In Boston 'til 1st July.

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### Re: septillion operations per second

```
In article <[EMAIL PROTECTED]>,
Barry Wels  <[EMAIL PROTECTED]> 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 / 1 seconds, or about

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

2^256 / 1 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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### Re: septillion operations per second

```
In article <[EMAIL PROTECTED]>,
>take a peek at the chapter on key lengths in Schneier's Applied
>Cryptography.  it is an entertaining read.  in short, he makes the
>case that computers as we understand them simply cannot conduct brute
>force attacks against 128-bit or larger semetric keys.  (i won't
>repeat his explanation here.)

Actually, his explanation (which involves the energy required to erase
bits) isn't correct; look up "reversible computing", which is a way
to do computations at lower energy than the limit he proposes.

- Ian

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### Re: septillion operations per 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 any single component is to change state this many times per
second, it has to be no bigger than (3*10^8 m/s) * (10^-24 s) =
3*10^-16 m, or around the size of a proton.

If you have an enormous collection of larger, slower parts, less
stringent limits apply.

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### Re: septillion operations per second

```
At 01:50 PM 6/20/01 -0700, Mike Brodhead wrote:
>having said all that, there are often weaknesses other than key
>length: predicting the key generation, keystroke monitoring, bribing

Both Aldrich Ames (CIA) and Bob Hanssen (FBI counterintel) cost under
1.5 million plus you get their wives' complicity for some time.

dh

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