Re: Random number generation using radioactivity

From: Ernst Lippe (ernstl-at-planet-dot-nl_at_ignore.this)
Date: 08/15/04 

Date: Sun, 15 Aug 2004 14:28:12 +0200

On Sun, 08 Aug 2004 22:12:35 -0700, juuitcha wrote:

> 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.
>
> No mind-bending hash functions required.

Uh, I think that you have just defined your own hash function.

The standard crypto solution in this case would be to feed
the full outputs of the Geiger counter into an algorithm
such as Yarrow or Fortuna. Yes, there are lots of mind-bending
hash functions in there, but there are there for a very good
reason.

Your approach is probably biased and/or not very efficient. The expected
distribution for the intervals is approximately an exponential distribution,
it will be different from the exponential distribution for short
time-intervals, because of the dead time of the Geiger counter. Because of the
shape of this distribution, (it is a very skewed distribution) the results of
computing the value modulo P are very likely to be biased towards the lower
values. Concatenating the outputs as a single base-P number and discarding
the top digits will not remove this bias. (BTW why should P be a prime, I see
no sound reasons for that choice.) Of course, you can make the bias smaller by
taking values for P that are tiny compared to the possible range of interval
values, but then you are discarding a lot of entropy, because you are
discarding all entropy from the higher order digits.

So, just stick to a standard solutions, there is no need
to reinvent the wheel.

Ernst Lippe

Relevant Pages

  • Re: Random number generation using radioactivity
    ... > to split the average time between two consecutive decays into several ... it won't be *exactly* uniform. ... The distribution ... Take the difference between pairwise measurements. ...
    (sci.math)
  • Re: Prove that Randomness Exists?
    ... I provide a design for a truly random number generator. ... but the distribution would become less even. ... In an uneven distribution, the ... decays per second is 100, then that would be a pretty small sample. ...
    (talk.origins)
Quantcast