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Date:      Sun, 23 Sep 2012 02:37:48 +0200
From:      Mariusz Gromada <mariusz.gromada@gmail.com>
To:        Pawel Jakub Dawidek <pjd@FreeBSD.org>
Cc:        Ben Laurie <benl@freebsd.org>, freebsd-security@freebsd.org, RW <rwmaillists@googlemail.com>, Jonathan Anderson <jonathan.anderson@cl.cam.ac.uk>, John Baldwin <jhb@freebsd.org>
Subject:   Re: Collecting entropy from device_attach() times.
Message-ID:  <505E59DC.7090505@gmail.com>
In-Reply-To: <20120922195325.GH1454@garage.freebsd.pl>
References:  <20120918211422.GA1400@garage.freebsd.pl> <20120919231051.4bc5335b@gumby.homeunix.com> <20120920102104.GA1397@garage.freebsd.pl> <201209200758.51924.jhb@freebsd.org> <20120922080323.GA1454@garage.freebsd.pl> <20120922195325.GH1454@garage.freebsd.pl>

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W dniu 2012-09-22 21:53, Pawel Jakub Dawidek pisze:
> Mariusz, can you confirm my findings? 

Pawel,

Your conclusions can be easily confirmed by shape analysis of the EDF. 
Usually maximum quantile difference (called D-statistic) gives you a 
kind of overview, function shape gives you a strong feeling, p-value 
gives you a formal proof.
D-statistic values (your data):

  6bit:   0.33%
  7bit:   0.29%
  8bit:   0.27%
  9bit:   0.21%
10bit:   6.34%
11bit:  19.07%
12bit:  54.80%

What I would say: increasing the number of bits from 6 to 9 does not 
affect distribution "uniformity", reaching the tenth bit results in 
sudden increase in the difference measure -  the more bits, the more 
difference is observed. Distribution shape analysis for the 10th bit 
shows non-linear function. Lack of "randomness" in the quntile 
difference curve - chart  shows completely lack of noise (pure 
functional relation).  These are very strong indicators that starting 
from 10th bit distribution was changed and is no longer uniform.

To formally confirm above conclusion for i.e. 5% significance level, 
which means that confidence level is 95%, I need some extra data 
regarding sample sizes. Please pass to me number of collected 
observations in each 6-12 bit experiment.

Regards,
Mariusz





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