# [RC5] RC5 question

aSe aSe at SysFail.com
Sat Oct 4 06:37:14 EDT 2003

```At 11:45 PM 10/3/2003 -0400, you wrote:
>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
>>
>>
>>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."
>
>before this project finishes.

Moore's law comes from a guy by the name of Gordon Moore. When intel was
creating the first microprocessor. He predicted that the number of
transistors in a microprocessor would double every 18 months.

Most people assume more that just means computers will double in speed. Not
exactly true, but there is a collation between the number of transistors
and the processing power. A good url including his original paper is
included below.

http://www.intel.com/research/silicon/mooreslaw.htm

- Gordon Keesler [aSe at SysFail.com]

```