[LTP] [PATCH] getrandom02: relax check for returned data
Cyril Hrubis
chrubis@suse.cz
Wed Feb 8 15:08:55 CET 2017
Hi!
> > gnuplot> comb(n,k) = gamma(n+1)/(gamma(k+1) * gamma(n - k + 1))
> > gnuplot> plot [6:30] 256 * comb(x, int(6 + x * 0.2)) / (256 ** int(6 + x * 0.2))
>
> This does not look correct to me. Try it with old formula, it goes above 1:
> gnuplot> comb(n,k) = gamma(n+1)/(gamma(k+1) * gamma(n - k + 1))
> gnuplot> plot [6:30] 256 * comb(x, int(x * 0.1)) / (256 ** int(x * 0.1))
You are right, this would be for if we fail the test test when
table[i] >= max, which would fail with 100% probability for most of the smaller
buffers, hence we get results that does not make much sense. We have to
add 1 to the int(x * 0.1) in the formula.
Try plotting this:
plot [10:60] 256 * comb(x, int(x * 0.1) + 1) / (256 ** (int(x * 0.1) + 1))
which pretty much shows the same you are saying for N=19 the old formula
has about 70% chance of failing. Well your script with poisson
aproximation gets close to 50% but the order of magnitude seems to be
the same for both formulae.
> ---
>
> With old formula, for N<20 (and max=1), this is pretty much birthday
> problem [1] with smaller pool - we don't have 365 days, we have 256 bytes.
>
> With birthday problem you get 50% chance of having 2 people with same
> birthday if number of people is 23. Since we have smaller pool, I'd expect
> we reach 50% chance sooner.
>
> With N>=20, max increases and it gets a lot more complicated. Best advice
> I've found online was to use Poisson approximation [2].
>
> Based on that (see attached python snippet) I'm getting that:
> "x*0.1" is quite bad, specially for N=19
> "6+x*0.2" is a lot better, with chance ~10^-16
I'm getting the same with the fixed formula in gnuplot:
plot [10:60] 256 * comb(x, int(6 + x * 0.2) + 1) / (256 ** (int(6 + x * 0.2) + 1))
This shows a peak for 15 which is about ~10^-16.
> I'll send v2, with "6+x*0.2".
Agreed.
--
Cyril Hrubis
chrubis@suse.cz
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