[RC5] RC5 roughly doubling at this point?

Elektron elektron_rc5 at yahoo.ca
Fri Mar 4 18:13:57 EST 2005


On 4 Mar, 2005, at 21:59, Daniel Quintiliani wrote:

> Actually, we will only need to wait until December to know for
> sure. According to Moore's Law, processing time is supposed to
> double every 18 months, and after 36 months (from December 2002)
> we can see if the processing power doubled.

You can never know for sure. There's so much random variation in the 
stats that claiming that 'it doubles' without much data doesn't work 
too well. There are methods to predict exponential growth, which work 
in the stock market, but the stock market doesn't have the daily/weekly 
variations that we do. You have to take the sum over each week to have 
a reasonable chance of getting rid of those variations.

There also appears to be some sort of variation with a period of a 
month or two, but that could just be random (or have something to do 
with how the buckets for the graph were set up)

And Moore's law only says that the number of transistors on a chip 
doubles every 18 months, though now the estimate is more like 20. I'm 
especially sure that 'processing time' does not double.

There's also no reason why you have to wait for it to double. You could 
wait for processing speed to increase by any factor, even 1%. The 
problem is that processing speed goes up by 1% twice a day or something 
silly. Doubling is completely arbitrary (the math turns out nicer if 
you give the time to increase to a factor of e), except for PR in its 
various forms. Also, keep in mind that the keyrate started at 0, as 
people slowly migrated to the new version of the client which supported 
RC5-72, which lasted until at least may/june 2003 (the early part looks 
a lot like a square-root graph).

As an analogy, Hong Kong announced the return of inflation over the 
summer, because something-or-other increased year-on-year. This was 
predicted in a comic a few days earlier, since there was inflation for 
the 6 months prior. Sure, there's random variation, but you only need 2 
months with some sort of consistent trend to say when something is 
going to double.

In our case, the most you can say is that there's consistent linear 
growth (this is substantially worse than exponential) of about 100 
Gkeys/s every 16 months, or 2411 keys/s/s. The solution is similar to 
acceleration (s = 1/2 a t^2 => t = sqrt(2s/a)), for about 1.98e9 
seconds, or 63 years.

When I did it assuming exponential growth about a year ago (or so), it 
came out to be 17 years, so linear growth isn't that bad. 
Unfortunately, growth rates may be levelling off (the keyrate stayed 
constant at about 120 GKeys/s for the final few years of RC5-64, though 
that graph seems to have disappeared), which means most of us may be 
dead before it's cracked.

There's not much point debating about RC5's growth, though. Quantum 
computing is around the corner. On the other hand, there's only so long 
Moore's law can last, and both of these are probably going to happen 
within 17 years.

- Purr



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