+     hrubin
From: (Herman Rubin)
Newsgroups: sci.crypt,sci.electronics

Subject: Re: Applicable idea for Truly Random Number hardware
Summary: Old ideas
Message-ID: <>
Date: 26 Sep 91 02:02:15 GMT
References: <> 
Followup-To: sci.crypt
Lines: 30
Xref: sci.crypt:4188 sci.electronics:17141

In article , (Mark  Johnson) writes:
> Suppose we have a sequence of bits, A = (a0, a1, a2, a3, ...).
> It is produced by some physical process, for example a zener
> diode or a Geiger-Muller tube.
> Also suppose that the hardware is not perfectly "balanced"
> (or "trimmed" or "optimized" or whatever word you prefer), so
> that the sequence A doesn't contain equal numbers of ONES
> and ZEROES.  


> Now, consider the new sequence C = A XOR B.  Each element ck of C
> is just the XOR of the corresponding elements of A and B,
> ck = ak XOR bk.
>  ==> What is the probability that an element of C is a ONE? <==

In a general situation, this is much better than A or B is, and this
can even be done conditionally.  If we define h(A) to be the 
probability that A is 0 minus the probability of 1, then if A and
B are independent, h(C) = h(A) * h(B).  This appeared not later than
the 1940s, and was proposed as a means of improving physical random
numbers back then.  A similar procedure, using decimal numbers, was
used to improve the randomness of the published RAND numbers.

Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054 (Internet, bitnet)   {purdue,pur-ee}!!hrubin(UUCP)