Re: Randomness from data

From: Mok-Kong Shen (mok-kong.shen_at_t-online.de)
Date: 12/07/04 

Date: Tue, 07 Dec 2004 23:13:08 +0100

Arnaud Carré wrote:

>>If one
>>successively considers the next following digits/bits,
>>at some point the fluctuations will become apparent and
>>this phenomenon is likely to rapidly enhance as one goes
>>to the more and more 'less significant' digits/bits and
>>one would (at least subjectively) regard certain less
>>significant digits/bits to be 'random'. Is this view of
>>thus having obtained 'randomness' justified?
>
>
> Well, depends :-) It depends of the natural phenomena you're sampling, but
> if you sample a physical phenomena at very small scale, it's a good entropy
> source. But it depends the goal of that "random" data: sampling a physical
> phenomena is an entropy source, not a "random" source. That is, you have to
> use strong HASH func to shuffle that entropy on a large area.
> I build a random generator using the electrical noise of my sound-card as
> entropy source. I use the bit 0 of each 16bits sample. when I collect 8 of
> these bits, I "add" that byte to a circular 256 bits buffer. Each step I add
> the byte, I "SHA-256" the buffer, then I can output 32 or 64bits of that
> buffer. Data generated looks very like random :-)
>
>
>>If yes,
>>is there a reasonable (correct) way to determine from
>>the value of the variance of such a variable the position
>>of the digits/bits of the measured values beyond which
>>everything could be justifiably taken as 'random'?
>
>
> I don't know if I enderstand well. You mean, if an attacker gets only the
> less significant bit of the entropy source, can he deduces the sampled
> values ?? In the majority of case, my answer is not. The best case (or
> worst, depend if you're the attacker :-)) is a geiger counter output. By
> nature ( quantic mechanic ), geiger counter output is considered as
> "random", so you can't deduce anything on the high significant bits of
> sampled value using less bits only, even if the phenomena you're sampling is
> "natural".
>
> But maybe I'm totally out of topic of your question ??

Let me give a (possibly somewhat poor) example. A person's
pulse has a 'roughly' constant period. However, even one
is at rest, that constant has some fluctuations, apparently
because the nature doesn't care to make the heart to be a
'perfect' mechanism. Let's say that period in sec is
1.xxxx.... where the x's are digits assumed to be absolutely
accurate for each individual measurement but varies from
one measurement to the next. One can as usual compute
statistically the mean value and the variance of such data.
My original question is whether and, if yes, starting from
which one of the digits x one could justifiably collect
randomness. (Whether that randomness is to be further
processed to remove bias etc. is another issue that we at
first don't consider.) For, if one knows that specific digit
position, one could relax our hypothetical assumption that
the measuring device is absolutely accurate so that, for
purpose of collecting randomness, one would need only to
employ measuring devices that have an accuracy higher than
what corresponds to the said digit position. Hope that
this is more readable than my original post.

M. K. Shen

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