True random numbers

This topic comes up often enough in c.l.f that I thought this would be of
interest.

Regards,

Mike Metcalf
 ========================================
============

a.. "True Randomness Upon Request"
Innovations Report (03/18/04)
The University of Geneva's Group of Applied Physics and its Computer Science
department have partnered with id Quantique, a company spun off from the
university, to launch the first Web site where true random numbers can be
generated and downloaded on demand. Users could request a specific sequence
of random numbers from the site by specifying the sequence's parameters, and
the numbers would be created by a quantum random number generator linked to
the server. The first practical quantum random number generator was
developed six years ago by the Group of Applied Physics, and the technology
was commercialized by id Quantique. The device produces binary random
numbers by harnessing the reflection or transmission of a photon on a
semi-transparent mirror. "Quantum physics is the only physical theory
predicting that the outcome of certain phenomena is random," explains Group
of Applied Physics director Nicolas Gisin. "It is thus a natural choice to
use it to generate true random numbers." The University of Geneva's Computer
Science department has devised a server/client application that would allow
researchers worldwide to download random numbers in the C, C+, Java, or
Fortran codes employed for their simulations. The Web site,
www.randomnumbers.info, is expected to evolve into the standard online
resource on randomness and random numbers. Random numbers are essential in
applications ranging from secure encryption of electronic communications to
lotteries to scientific calculations, but generating them has always been a
formidable challenge.

For more:
http://www.innovations-report.com/h...45.html

There is an enormous amount of confusion about the meaning of the term
"random".  Ask your friends for a definition, and consult a few books, and
you will discover a great variety of proposed meanings for the word.  I do
not have a pet definition to promote, but I would like to point out some
of the variety.

1.  Random does not imply inteterministic.  Indeed, dynamical chaos has
been aptly described (by the late Joe Ford) as "deterministic randomness".

2.  Usually, in statistics and in Monte Carlo simulations, "random" means
that certain kinds of correlations are absent.  Since there are an
infinite number of correlations that can be defined, there are infinitely
many degrees of statistical randomness.
The Geneva process is indeterministic, but that does not guarantee any
particular degree of statistical randomness.

3.  In cryptography, "random" means "unpredictable".  If you just ask me
for a number, my reply will be just as random (unpredictable) as a number
generated by the Geneva group.

4.  A few decades ago, the Rand Corporation published a book of "random
digits".  In those days, people seemed to think that "randomization" gave
an experimental design a kind of metaphysical virtue.  That belief is
no longer so common.

5.  "Ranodmness" as "unpredicability" is often desirable.  But now that
the Rand Corp. book and the Geneva sequence have been published, they are
no longer unpredictable.

In conclusion, I doubt that the published Geneva "random" numbers have any
significant value.  I will certainly continue to use established random
number subroutines in my Monte Carlo simulations.

Leslie Ballentine

Michael Metcalf <metcalfm@acm.org> wrote:
: This topic comes up often enough in c.l.f that I thought this would be of
: interest.

: Regards,

: Mike Metcalf
:  ========================================
============

: a.. "True Randomness Upon Request"
: Innovations Report (03/18/04)
: The University of Geneva's Group of Applied Physics and its Computer Scien
ce
: department have partnered with id Quantique, a company spun off from the
: university, to launch the first Web site where true random numbers can be
: generated and downloaded on demand. Users could request a specific sequenc
e
: of random numbers from the site by specifying the sequence's parameters, a
nd
: the numbers would be created by a quantum random number generator linked t
o
: the server. The first practical quantum random number generator was
: developed six years ago by the Group of Applied Physics, and the technolog
y
: was commercialized by id Quantique. The device produces binary random
: numbers by harnessing the reflection or transmission of a photon on a
: semi-transparent mirror. "Quantum physics is the only physical theory
: predicting that the outcome of certain phenomena is random," explains Grou
p
: of Applied Physics director Nicolas Gisin. "It is thus a natural choice to
: use it to generate true random numbers." The University of Geneva's Comput
er
: Science department has devised a server/client application that would allo
w
: researchers worldwide to download random numbers in the C, C+, Java, or
: Fortran codes employed for their simulations. The Web site,
: www.randomnumbers.info, is expected to evolve into the standard online
: resource on randomness and random numbers. Random numbers are essential in
: applications ranging from secure encryption of electronic communications t
o
: lotteries to scientific calculations, but generating them has always been 
a
: formidable challenge.

: For more:
: http://www.innovations-report.com/h...45.ht
ml

"Michael Metcalf" <metcalfm@acm.org> wrote in message
news:c3nf9l$8hj$1@ngspool-d02.news.aol.com...
> This topic comes up often enough in c.l.f that I thought this would be of
> interest.
>

My last inquiry about this subject drew ZERO response (see below from Google
archive)...

Search Result 1
From: David Frank (dave_frank@hotmail.com)
Subject: Is there a genuine random number routine?
This is the only article in this thread
View: Original Format
Newsgroups: comp.lang.fortran
Date: 2001-05-14 05:50:01 PST


re:  my 1999 subject  "genuine random numbers" which was debated at length
here in clf..

I'm curious,
does anyone YET have any info about reading  pentium 3's  (and I assume
pentium 4's) random number register?
If so, pls list the routine's assy instructions and any related info about
it, (timing restraints/etc.)

"David Frank" <dave_frank@hotmail.com> wrote in message
news:XYV7c.305283$jH.4291081@twister.tampabay.rr.com...

> My last inquiry about this subject drew ZERO response (see below from
Google
> archive)...

Intel put the RNG on the chipset, not on the chip itself
because verification of a chip with random characteristics
can be rather awkward.  You might want to have a look at:
http://www.intel.com/design/chipsets/manuals/298029.pdf
and see if you can get it to work.

--
write(*,*) transfer((/17.392111325966148d0,6.5794487871554595D-85, &
6.0134700243160014d-154/),(/'x'/)); end

John C. Bollinger <jobollin@indiana.edu> wrote:
> Leslie Ballentine wrote:
> 
>
> Indeed.  A glimpse at Webster's New Universal was enlightening, mostly
> because it didn't include a statistical definition of the term.
> Consultation of my nearest statistics text then surprised me when I
> discovered that although it defined "random variable", "random number",
> "random process", and a few other related terms, it never defined
> "random" itself.  Interesting.
> 
>
> I find that one clever because it seems so oxymoronic (to me), yet as
> you say, it's very apt.

"random" is a mathematical description and mathematical concept, like
say, "continuously differentiable function".

Physical things have properties, which in some limits, are best describable
by mathematical laws, which humans have constructed to fulfill the axioms
of probability theory.

In that theory there are devices called 'random variables'.

Reality is as reality is.

> The fact that the value of each future output put bit is indeterministic
> does not guarantee absence of correlation, true.  Nevertheless the
> underlying physical theory does not introduce such correlations, the
> equipment is designed to avoid introducing correlations as much as
> possible, and actual the self-correlation of the output has been
> examined and found to be quite small.  I am not well enough versed in
> the theory or knowledgable enough about the experiment to determine
> whether the observed tiny self correlations were in fact within the
> range of the experiment's reasonable statistical error.  Nevertheless, I
> certainly would assert that the reported degree of [non-]correlation
> should be at least as sufficient for statistical simulations as that of
> any pseudorandom number generation algorithm could be.

I would believe that any practical physical device would inevitably introduc
e
*more* correlation than a cryptographically strong, or even well-validated
statistical, PRNG.

It would be good to use a physical random number generator as a seed.

Dr Chaos <mbkennelSPAMBEGONE@NOSPAMyahoo.com> writes:

> "random" is a mathematical description and mathematical concept, like
> say, "continuously differentiable function".
>
> Physical things have properties, which in some limits, are best describabl
e
> by mathematical laws, which humans have constructed to fulfill the axioms
> of probability theory.
>
> In that theory there are devices called 'random variables'.
>
> Reality is as reality is.

Indeed.  As someone who has worked a lot in the field of system
identification, I find it critical to keep in mind the distinction
between reality and mathematical models.  Others have said it better
than either you or I are likely to.  A few relevant quotes
that I used in the introduction to one of my reports.  The writing
style seems a little strange to modern ears, but if you adapt to
the style, I think you'll see that these are pretty cogent comments.
(You'll also need to overlook the sexist phraseology typical of
the time).  All retyped from scratch as I don't have original
electrons, so I'm sure  there are plenty of typos.

From Bayes (1736), who did some "minor" work on statistics, as
translated by Barnard(1958)

"In is not the business of the mathematician to dispute
whether quaantities do in fact ever vary in the manner that is
supposed, but only whether the notion of their doing so be
intelligible; which being allowed, he has a right to take it
for granted, and then see what deductions he can make from
that supposition....He is not inquiring how things are in
matter of fact, but supposing things to be in a certain
way, what are the consequences to be deduced from them; and all
that is demanded of him is, that his suppositions be intelligible,
and his inferences just from the suppositions he makes."

Though as engineers rather than pure mathematicians, we might find
ourselves more in line with Bayes' later statement in the same
document

"So far as Mathematics do not tend to make men more sober and
rational thinkers, wiser and better men, they are only to be
considered as an amusement, which ought not take us off from
serious business."

Quoting myself next, because I don't think I can seque into the
next classic quotation any better now than I did in the report

"A few words are necessary in defense of the probalistic approach,
lest the reader decide that it is not worthwhile to pursue.  The
main issue here is the description of deterministic phenomena
as random.  This disagrees with common modern perceptions of
the meaning and use of randomness for physical situations, in
which random and deterministic phenomena are considered as quite
distinct and well delineated.  Our viewpoint owes more to the
earlier philosophy of probability theory - that it is a useful
tool for studying complicated phenomena which need not be
inherently random (if anything is inherently random).  Cramer
(1946, p. 141) gives a classic exposition of this philosophy:

[The following is descriptive of]...large and important
groups of random experiments.  Small variations in the
initial state of the observed units, which cannot be detected
by our instruments, may produce considerable changes in the
final result.  The complicated character of the laws of the
observed phenomenon may render exact calculation practically,
if not theoretically, impossible.  Uncontrollable action by
small disturbing factors may lead to irregular deviation
from a presumed "true value".

It is, of course, clear that there is no sharp distinction
between these various modes of randomness.  Whether we ascribe,
e.g. the fluctuations observed in the results of a series of
shots at a target mainly due to small variations in the
initial state of the projectile, to the complicated nature
of the ballistic laws, or to the action of small disturbing
factors, is largey a matter of taste.  The essential thing
is that, in all cases where on eor more of these circumstances
are present, an exact prediction of the results of individual
experiments becomes impossible, and the irregular fluctuations
characteristic of randomm experiments will appear.

We shall now see that, in cases of this character, there
appears amidst all irregularity of fluctuations a certain
typical form of regularity that will serve as the basis
of the mathematical theory of statistics."

--
Richard Maine                       |  Good judgment comes from experience;
email: my first.last at org.domain  |  experience comes from bad judgment.
org: nasa, domain: gov              |        -- Mark Twain

Leslie Ballentine wrote:

> There is an enormous amount of confusion about the meaning of the term
> "random".  Ask your friends for a definition, and consult a few books, and
> you will discover a great variety of proposed meanings for the word.

Indeed.  A glimpse at Webster's New Universal was enlightening, mostly
because it didn't include a statistical definition of the term.
Consultation of my nearest statistics text then surprised me when I
discovered that although it defined "random variable", "random number",
"random process", and a few other related terms, it never defined
"random" itself.  Interesting.

>                                                                      I do
> not have a pet definition to promote, but I would like to point out some
> of the variety.
>
> 1.  Random does not imply inteterministic.  Indeed, dynamical chaos has
> been aptly described (by the late Joe Ford) as "deterministic randomness".

I find that one clever because it seems so oxymoronic (to me), yet as
you say, it's very apt.

> 2.  Usually, in statistics and in Monte Carlo simulations, "random" means
> that certain kinds of correlations are absent.  Since there are an
> infinite number of correlations that can be defined, there are infinitely
> many degrees of statistical randomness.
>    The Geneva process is indeterministic, but that does not guarantee any
> particular degree of statistical randomness.

The fact that the value of each future output put bit is indeterministic
does not guarantee absence of correlation, true.  Nevertheless the
underlying physical theory does not introduce such correlations, the
equipment is designed to avoid introducing correlations as much as
possible, and actual the self-correlation of the output has been
examined and found to be quite small.  I am not well enough versed in
the theory or knowledgable enough about the experiment to determine
whether the observed tiny self correlations were in fact within the
range of the experiment's reasonable statistical error.  Nevertheless, I
certainly would assert that the reported degree of [non-]correlation
should be at least as sufficient for statistical simulations as that of
any pseudorandom number generation algorithm could be.

> 3.  In cryptography, "random" means "unpredictable".  If you just ask me
> for a number, my reply will be just as random (unpredictable) as a number
> generated by the Geneva group.

I'm not sure I agree.  I would instead say that cryptographers use
"random" numbers because they have the property of unpredictability.
Also because you aren't available to most of them to satisfy their needs
for unpredictable numbers. :-)

> 4.  A few decades ago, the Rand Corporation published a book of "random
> digits".  In those days, people seemed to think that "randomization" gave
> an experimental design a kind of metaphysical virtue.  That belief is
> no longer so common.

That definition of random goes more back to the question of correlation.
The idea, as I understand it, is that if a sequence of digits is
chosen from such a table (randomly, of course) all possible outcomes are
equally likely.

> 5.  "Ranodmness" as "unpredicability" is often desirable.  But now that
> the Rand Corp. book and the Geneva sequence have been published, they are
> no longer unpredictable.

Whoah, we seem to have jumped the tracks here.

In the first place, unpredictability relative to the Rand book is
obtained through the method of selecting digits from it.  It is
therefore exactly as unpredictable as asking you for a sequence of digit
indices can make it.  (Thus highly unpredictable :-).)

More importantly, however, what the Geneva group principally produced
was a device, not a sequence -- a device that plugs into your computer's
USB2 port and provides a 100 KHz stream of random bits.  Because the
device is based on a physical process that is fundamentally
unpredictable, their publication of the technique does not make the
output any more predictable.  Neither does their commercial distribution
of the device.

> In conclusion, I doubt that the published Geneva "random" numbers have any
> significant value.

I disagree.  As far as I can tell from the Geneva group's reports,
Random numbers produced by their device have excellent properties of
unpredictability, and they ought to be at least as useful for
simulations, modulo the bit rate, as a PRNG can offer -- provided you
don't ever need to repeat exactly the same simulation run.

>                      I will certainly continue to use established random
> number subroutines in my Monte Carlo simulations.

I imagine most people will.  Good PRNGs give satisfactory results in the
vast majority of cases.  A device like the one we're talking about is
more useful where unpredictability must be absolutely guaranteed.


John Bollinger
jobollin@indiana.edu