[RC5] RC5-64 HAS BEEN SOLVED

Marcin Sochacki wanted at panda.bg.univ.gda.pl
Sat Sep 28 18:56:53 EDT 2002


I will reply to my own post, just to attach an e-mail from Adam Luter
which he sent directly to me. His in-depth analysis is really worth reading.
My estimation of doubling the rate every year was in fact too optimistic.
Currently the growth is linear with the factor of about 0.2 (which Adam
chose in his calculation).

If you look at http://n0cgi.distributed.net/statistics/rc5-64/rate.png
you'll notice, that only the last two years have shown such a slow growth.
Previously the rate was much better, but then many people got bored, and
stopped installing clients on new machines. Some of them have also switched
to SETI and other projects.

I think D.Net shouldn't focus on RC5-72 yet. The machines are still
too slow to challenge this, and also people want something new, something
interesting, with reasonable chances for success. With a new exciting project
we could get close to exponential growth rate again.

OK, here is the above mentioned post. Best wishes,
Marcin

==============
Date: Fri, 27 Sep 2002 09:57:49 -0500
To: Marcin Sochacki <wanted at panda.bg.univ.gda.pl>
Subject: Re: [RC5] RC5-64 HAS BEEN SOLVED
User-Agent: Mutt/1.4i
From: Adam Luter <luterac at bellsouth.net>

I agree that his calc is wrong, but your's is too :)

(I'd reply to the list, but I can't, nor can I unsubscribe!)

Comp power for the average new system may double every year, but the
power of our d.net "super computer" does not.

d.net's growth, in fact, is best described as linear.  So you need to
know how much it grows in a year.  (I am not at a computer where
looking at a graph would be possible so I am pulling the next few
numbers out the air).

So say we look at a graph and see that right now we are doing 1TFlops
(or whatever unit they use), and last year we did 0.8, and the year
before 0.6.  So we grow 0.2 TFlops a year.

Now you use this equation:

xf = x0 + v0*t + 1/2*a*t*t

Where a = 0.2 TFlops/Year/Year
v = 1TFlops/Year
x0 = 0
xf = 256

(xf = 256 because our current rate is 1, and you say we can do
 rc5-64 at this rate in one year.  So 72 is 256 longer, so xf is
 1*256)

This equals:

256 = 1*t + 0.1*t*t

or:

t^2 + 10t + 25 = 2535

(t+5)^2 = 2535

t+5 = 50 (approximately)
t = 45 (years)

But this is with a made up growth rate.  If you can get the real
number, you can follow the same steps to get the right number.

(For instance if we are going 8TFlops and the growth is 1TFLops:

256*8 = 8*t + 0.5*t^2
4032 = (t+8)^2
12 = t
)

-Gryn (Adam Luter -- the perpetually cursed to be on the list)
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