# [RC5] RC5 question

Sat Oct 4 00:45:56 EDT 2003

```On Fri, 03 Oct 2003 21:32:56 -0400, Daniel Quintiliani

> On Sat, 4 Oct 2003 09:05:04 +0800, Elektron <elektron_rc5 at yahoo.ca>
> 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.
>>
>
> Using yesterday's RC5-72 rate for a more accurate measure of time:
>
> 114327804047 Keys/s * 60 * 60 * 24 * 365.25
> (goes upstairs and grabs TI-83+ from backpack)
> k = 3.607911127 * 10^8
>
> Plugging it into your formula:
>
> t = ln(2^128/((3.607911127*10^8) ln(2^(1/1.5)))) / ln(2^(1/1.5))
>
> t = 101.201789 years
>

k should be 10^18, I copied it wrong into the e-mail.

More interesting information (the stats were updated since the original e-
mail):

K = 2^64 using the RC5-64 (all) stats produces t = 5.084313307 years (5
years, during the first month into the year). RC5-64 finished just under 5
years at 89% of the keyspace, so this is a good formula.
K = 2^72 using the RC5-72 stats produces t = 17.20178906 years (17 years,
during the third month into the year)

Up to 17 years on this project. Now I can see why you don't want to go any
further in RSA's secret key contests. Do you think anyone else will try at
their next contest?

BTW, you might want to see this. A web search on "Moore's Law" (I hadn't
heard of it before this discussion) found one of those Wiki things called
"Webopedia.com" which included a link to this 1997 CNET article:

http://news.com.com/2100-1001-203750.html?legacy=cnet

"CNET article (September, 1997) that summarizes a speech by Moore in which
he predicts that transistor miniaturization will reach physical limits
around the year 2017."