# [RC5] RC5 question

Décio Luiz Gazzoni Filho decio at revistapcs.com.br
Fri Oct 3 23:48:03 EDT 2003

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On Friday 03 October 2003 22:05, Elektron wrote:
> Taking the latest RC5-64 numbers,
> 10,428,970,063,364,096 Keys were completed yesterday (0.056536% of the
> keyspace) at a sustained rate of 120,705,672,030 Keys/sec.
>
> That's 3809103098378452560 Keys/year (let's call it k). If computing
> power doubles every 18 months (1.5 years), then a^1.5=2, or a=2^(1/1.5)
> or approx. 1.587401051968. So our keyrate with respect to time t
> (years) is ka^t, so our keys tested (big K) (by integration) is ka^t
> ln(a) + C, and since we have no keys tested when t=0, k ln(a) + C = 0,
> so K = ka^t ln(a) - k ln(a). K=2^128.
>
> 2^128 = k ln(a) (a^t-1)
> 2^128/(k ln(a)) = a^t-1
> 2^128/(k ln(a)) + 1 = a^t
> t = ln(2^128/(k ln(a)))/ln(a) = 101.08435774324143022752
>
> Of course, I'm assuming RC5-128 is as fast as RC5-64 (which it isn't),
> and that moore's law holds (which it might). Interestingly, the last
> time I did this, I got 600 years. Somebody hit me if I did my math
> wrong. But either way, 101 years is a lot more than my lifetime.

While the argument is valid, I think it's assuming Moore's law will hold in a
century is overly optimistic. Sure, there will be breakthroughs, maybe
quantum computing, maybe DNA computing, maybe some other buzzword. But the
fact is, we're going to see radical changes (like quantum computing), not the
evolutionary changes that we're seeing today, because they can't go on for
much longer. Think of it this way -- by the time we reach single-atom
transistors, they'll probably not abide by the principles that we use to
design electronics today. But if Moore's Law is to hold, we'll have to reach
this milestone before a hundred years.

Another point to take home is that 128-bit keys won't be exactly relevant a
century from now. Do you think the cracking of some sort of ``Enigma on
steroids'' would be relevant today, even if it'd make sense in the WWII
timeframe? And it's only been 60 years from then. So I think it's better to
stick around with short term contests.

Décio
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