[Cryptography] All dice are loaded?

Stephan Neuhaus stephan.neuhaus at tik.ee.ethz.ch
Fri Aug 8 03:33:55 EDT 2014


On 2014-08-07, 23:21, Dave Horsfall wrote:
> It seems that someone actually did the experiment back in 1966, with about 
> 10,000 rolls, and found a "statistically significant" bias in favour of 
> "6" being uppermost.

(I can't find the article or the follow-up.) Oh dear.  Let's assume for
the moment that the test was carried out competently.  Two things need
to be borne in mind:

(1) If you make N large enough, systematic deviations from uniformity
will eventually become "statistically significant" at any level.

(2) The die used in the experiment may indeed be biased so that sixes
appear more than 1/6 of the time, but is the size of the effect
something to worry about?  (If this bias caused a reduction of effective
key strength from 256 to 255 bits then that's interesting, but nothing
to worry about.  This is especially so since that reduction will very
likely not be confined to a certain bit position, but instead be spread
over all the 256 bits in an interesting and nonlinear way.)

(Incidentally, ans slightly OT, people often think "p < 0.05, yay, I've
made a discovery", but that's often not the case.  See
http://www.dcscience.net/?p=6473 and http://www.dcscience.net/?p=6518
for how this works.)

Add to that the fact that even such seemingly simple tests can be
screwed up in so many ways and it becomes an interesting data point
among many others.  Something that, as you say, belongs in the "tin
foil" category.

Fun,

Stephan


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