🚀 go-pugleaf

In article <1992Jul29.143808.241@nutmeg.hnrc.tufts.edu> jerry@nutmeg.hnrc.tufts.edu (Jerry Dallal) writes:
>In article <55413@mentor.cc.purdue.edu>, hrubin@pop.stat.purdue.edu (Herman Rubin) writes:

>> I would not accept anything with a short seed (say at least several 
>> hundred bytes) as acceptable.  Other than the believed cryptographically
>> strong Shamir and Blum-Miccaeli (sp?) procedures, which are extremely
>> costly, I know of none.  The problem is at least moderate-term independence,
>> and correlations, periods, etc., do not answer the question.


>Two questions of Professor Rubin:

>1) What generator *would* you recommend?

At this time, I would recommend starting with some more-or-less random
source, like the news articles repeatedly added in blocks, and then 
using some long-gap system like 

	x[n] = x[n-460] OP x[n-607]

where OP is exclusive or, or preferably full-word integer add.  On some
machines, one can be done with larger pieces than the other.  There are
others available of this type with longer gaps.

There are several reasons for this; on vector machines, the smaller gap 
to a previous item should be at least the length of the vector register,
and on vector stream machines, the newest item used should have been
stored before it is used.

If one can get a reasonable set of physical random numbers, XOR with them
is a good idea.  The supply is not likely to be enough for the whole job,
so recycling is likely to be necessary.

>2) The last time you generated pseudorandom numbers on a computer, what
>generator did you use?

The last time I did simulation, I do not believe that these procedures
were generally known.  Also, there were timing constraints.  What I used
was a congruential generator, to guarantee uniformity, and I recycled
a binary version of the RAND numbers.  The actual simulation used
2,560,000 exponential and normal random variables, and with the 
quite efficient procedures I used, this required probably less than
5.5 million uniforms.  The RAND numbers were 69,066 words, 0 in the
first 12 bits, and 48 random bits; they were used on a CDC 6500, which
accounts for the peculiar format.

Also, at that time, memory was a major problem, not like the situation
now.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)