[Cryptography] Throwing dice for "random" numbers

[Howard Chu]

John Denker via cryptography wrote:
> On 08/15/2018 07:20 AM, Dave Horsfall wrote:
> 
>> it occurred to me that it's not as simple as it seems, with the
>> generated output (e.g. modulo 10) not being as uniform as one would
>> hope.
> 
> Suppose you want decimal digits.  Twelve 6-sided dice can
> be treated as a 12-digit base-6 number.  In decimal that
> is a number from 0 to 2.18e9.  Roll the dice.  Whenever
> there is an outcome greater than or equal to 2e9, throw
> it away and re-roll.  Take the result modulo 1e9.  That
> gives you a uniform distribution over 9-digit decimal
> numbers, limited only by imperfections in the dice, with
> no non-uniformity introduced by the modulo operation.
> 
> The same procedure generalizes to bases other than 10,
> including 2, 8, 16, and 36 or 62 (i.e. alphanumeric).
> Discarding out-of-range outcomes has been standard
> practice since the 1940s (which is kind of a long
> time in the computer business).
> 
> Also, for what it's worth (which is not much):  8-sided
> dice are cheap and widely available (more so than
> 16-sided dice).  You can use those to generate bytes
> or words having any integer number of bits, with no
> need to re-roll.  This is not worth much because the
> inefficiency introduced by re-rolling is very small.
> It's at most a cosmetic issue, not a serious issue.

There are 10 and 20-sided dice, if you must have decimal numbers.

-- 
   -- Howard Chu
   CTO, Symas Corp.           http://www.symas.com
   Director, Highland Sun     http://highlandsun.com/hyc/
   Chief Architect, OpenLDAP  http://www.openldap.org/project/