Re: Random number generation using radioactivity

From: Phil Carmody (thefatphil_demunged_at_yahoo.co.uk)
Date: 08/09/04 

Date: 09 Aug 2004 11:35:20 +0300

"Michael Jørgensen" <ingen@ukendt.dk> writes:
> <juuitchan@hotmail.com> wrote in message
> news:9159d95e.0408082112.428be67b@posting.google.com...
> > I wonder if this would be a good method for random number generation
> > using radioactive decay:
> >
> > You have a radioactive source and a Geiger counter. This setup is
> > connected to a computer. The computer's internal timer is good enough
> > to split the average time between two consecutive decays into several
> > hundred parts.
> >
> > You take the intervals between successive decays modulo P (P is a
> > smallish prime number, like 41 or 59). When you get about 30 or so of
> > these numbers, you concatenate them, read it as a single base-P
> > number, convert it to decimal, throw away the first 10 or so digits,
> > and keep the rest as random digits.
>
> Well, it won't be *exactly* uniform.
>
> Each measured interval follows an known distribution (geometric?) with an
> average value of around 200 (you wrote "several hundred parts"). Taken
> modulo 41, we have a random integer in the range [0, 40]. The distribution
> is still not uniform, there will be a substantial bias towards low numbers.
>
> What happens after that I'm not quite sure about. However, if we look at
> information content, then each measurement gives you approximately 5 bits of
> information. After collecting 30 values and converting to decimal and
> throwing away 10 digits we get (5*30 - 10*3) = 120 bits of information. That
> should give you approximately 40 random digits, but keeping the
> non-uniformity in mind, I would not trust them all to be independent.
>
> Here's an alternate approach, that tries to achieve uniformity:
>
> [disclaimer: This is something I just thought of, while replying to this
> post. Use at your own risk!]
>
> Take the difference between pairwise measurements. This gives an integer in
> the range [-40, 40], with a peak at the value 0. Now add together 8 of such
> values (using a total of 16 measurements). This gives an integer in the
> range [-15*40, 15*40] which almost follows a normal distribution. You must
> now normalize, so that the standard deviation becomes 1.

It doesn't take into account the refractory period of the detector.

Phil 

-- 
1st bug in MS win2k source code found after 20 minutes: scanline.cpp
2nd and 3rd bug found after 10 more minutes: gethost.c
Both non-exploitable. (The 2nd/3rd ones might be, depending on the CRTL)