Random number not random?
Author Message
Random number not random?

Using LF95v5.5 with -quad switch, the following code

program random
implicit none
real(8) :: X(3,2),const(3)
call random_number(X(:,1))
call random_number(X(:,2))
const = X(:,2)/X(:,1)
write(*,*) const(1)
write(*,*) const(2)
write(*,*) const(3)
stop
end program random

produced the following results

181.92417239099116525563296898994316
181.92417239099116525563296898994316
181.92417239099116525563296898994316
Program Completed
Press Enter to Continue.

i.e. the two random vectors are identical if multiplied by a constant
scalar.  Is this normal?  It cost me quite a lot of time to find out this
change when I port one of my programs from double to quad precision.

Thanks.

S. Yuan

Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?
ifirc, certain random number generators are known
to produce highly correlated PAIRs of numbers.
That is, if consequtive pairs are plotted as (x,y)
points they fall on a couple of straight lines.
Maybe this applies here?
Roger Caffin

Quote:

> Using LF95v5.5 with -quad switch, the following code

> program random
>    implicit none
>    real(8) :: X(3,2),const(3)
>    call random_number(X(:,1))
>    call random_number(X(:,2))
>    const = X(:,2)/X(:,1)
>    write(*,*) const(1)
>    write(*,*) const(2)
>    write(*,*) const(3)
>    stop
> end program random

> produced the following results

> 181.92417239099116525563296898994316
> 181.92417239099116525563296898994316
> 181.92417239099116525563296898994316
> Program Completed
> Press Enter to Continue.

> i.e. the two random vectors are identical if multiplied by a constant
> scalar.  Is this normal?  It cost me quite a lot of time to find out this
> change when I port one of my programs from double to quad precision.

> Thanks.

> S. Yuan

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Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?

Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?
During a browse of the following ATHLON vs. PENTIUM-III  benchmarking
(btw, highly recommended)

http://www.review-zone.com/hardware/processors/athlon_vs_pentium_III/...
.shtml

In the VERY long review, I came across following statement about Pentium-III

<<
A much more beneficial addition is the thermistor based
pseudo random number generator. Better quality random number generation (since
it has nothing to do with the logical state of the computer system)
can be a huge boon to encryption.

I recall making this suggestion (as I believe others have also)
in a random number discussion several years back

Heres a question for nit-pickers here,
why is a random number fetched from the thermister fed random number
"register" still referred to as "psuedo"
why not call it a  "genuine" random number ?

Dave

Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?
Hello,

Quote:

<snip>

> <<
> A much more beneficial addition is the thermistor based
> pseudo random number generator. Better quality random number generation (since
> it has nothing to do with the logical state of the computer system)
> can be a huge boon to encryption.

> I recall making this suggestion (as I believe others have also)
> in a random number discussion several years back

<snip rest and sig>

There is a huge disadvantage to using resister based random numbers,
to wit, repeating the sequence you got last time for debugging
purposes.

If only one path thru your program leads to the bug, then you
need the exact sequence to reproduce the bug in order to understand
it and fix it.

--

Cheers!

Purple Sage Computing Solutions, Inc.

Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?

Quote:

>There is a huge disadvantage to using resister based random numbers,
>to wit, repeating the sequence you got last time for debugging
>purposes.
>If only one path thru your program leads to the bug, then you
>need the exact sequence to reproduce the bug in order to understand
>it and fix it.

Another possible disadvantage: is this random number generator slow
enough to be the limiting factor in fortran Monte Carlo simulations?
It looks like it couldn't be used for the RANDOM_NUMBER intrinsic
because of the reproducibilty requirement, but it seems sensible
for x86 compilers to use this RNG for the effect of RANDOM_SEED()
with no arguments if CPUID shows it to be available.

Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?

Quote:

> Heres a question for nit-pickers here,
> why is a random number fetched from the thermister fed random number
> "register" still referred to as "psuedo"
> why not call it a  "genuine" random number ?

I'd say because it isn't really random - at least not in time, which is
what I think you're getting at.

Look at the temperature fluctuations in a computer case. They reach a
reasonable equilibrium in  - Oh... let's call it 24 hrs. After that,
assuming no gale-force winds come in the room, the temp of the chip is
rock solid. I say this having done thermal chip research in the past.

If you want random you need to look to a process that has no relation
whatsoever to the physical system. Or, you can do a little work with
stats and make a pseudo random generator a more nearly randomg generator
by processing the output. I remember there's a way to turn uniform PDF to
a gaussian PDF while removing a significant amount of the predictibility
of the data.

Anyway... long story short - it's not random in time. While it may be
random from my house to yours that's not good enough.

Thanks,

The Man from S.P.U.D.
We will write no code before it's designed.

Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?

Quote:
> A much more beneficial addition is the thermistor based
> pseudo random number generator.

Does this have a uniform distribution?

--
Victor Eijkhout

Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?

Quote:

> > ITS ABOUT TIME !!!

> > Heres a question for nit-pickers here,
> > why is a random number fetched from the thermister fed random number
> > "register" still referred to as "psuedo"
> > why not call it a  "genuine" random number ?

> I'd say because it isn't really random - at least not in time, which is
> what I think you're getting at.

> Look at the temperature fluctuations in a computer case. They reach a
> reasonable equilibrium in  - Oh... let's call it 24 hrs. After that,
> assuming no gale-force winds come in the room, the temp of the chip is
> rock solid. I say this having done thermal chip research in the past.

> If you want random you need to look to a process that has no relation
> whatsoever to the physical system. Or, you can do a little work with
> stats and make a pseudo random generator a more nearly randomg generator
> by processing the output. I remember there's a way to turn uniform PDF to
> a gaussian PDF while removing a significant amount of the predictibility
> of the data.

> Anyway... long story short - it's not random in time. While it may be
> random from my house to yours that's not good enough.

>                         Thanks,

>                         The Man from S.P.U.D.
>                         We will write no code before it's designed.

The measurements are also subject to non-random influences, 60hz being big in
the us. The difficulty of filtering makes it hard to get really high quality
random numbers even from a quantum source.

Tony

Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?

Quote:

>I'd say because it isn't really random - at least not in time, which is
>what I think you're getting at.

>Look at the temperature fluctuations in a computer case. They reach a
>reasonable equilibrium in  - Oh... let's call it 24 hrs. After that,
>assuming no gale-force winds come in the room, the temp of the chip is
>rock solid. I say this having done thermal chip research in the past.

>If you want random you need to look to a process that has no relation
>whatsoever to the physical system. Or, you can do a little work with
>stats and make a pseudo random generator a more nearly randomg generator
>by processing the output. I remember there's a way to turn uniform PDF to
>a gaussian PDF while removing a significant amount of the predictibility
>of the data.

>Anyway... long story short - it's not random in time. While it may be
>random from my house to yours that's not good enough.

I havent researched what Intel claims for their random numbers
but I would be mightily surprised if they delivered anything other
than a pure random number register that delivered a uniform distribution
from  0 -> FFFFFFFF (hex) as fast as one addressed the register...
otherwise they might not have bothered....

Dave

Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?
Quote:

> I havent researched what Intel claims for their random numbers
> but I would be mightily surprised if they delivered anything other
> than a pure random number register that delivered a uniform distribution

^^^^^^^^^^^^^^^^^^

Quote:
> from  0 -> FFFFFFFF (hex) as fast as one addressed the register...
> otherwise they might not have bothered....

What is that?  Just nitpicking, but it is impossible to prove anything
is purely random (see G. Chaitin's work).  A uniform distribution isn't
proof since one can be generated but in a predictable way.  The closest
thing I've seen to a "pure random number" generator is the setup used by
HotBits which counts decays of a radioactive sample.  Even that is
subject to possible bias (not in the physics of radioactive decay but
in the manner in which it is recorded, etc.)

I would be suspicious of a temperature based technique.  It might be "better"
than a pseudo-random generator but it is still subject to bias (as was
previously mentioned).

Ron Kneusel

Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?
Below <SNIP> is from   intel.com site  random number FAQ...

<<<
What is the Intel Random Number Generator?
The Intel RNG is a silicon-based hardware device that will improve
cryptography, digital signing, and other security protocols for a variety of
Internet applications by providing truly random seed numbers.

What are the key features of the hardware-based Intel RNG?
Key features of Intel RNG include: truly random number generation for stronger
encryption, digital signing and security protocols, high-performance, and
ubiquitous solution when included as part of the Intel 8XX series chipsets.

Why are random numbers important?
Random numbers are basic building blocks for cryptography, which in turn is the
foundation of security technology. Seeds created from truly random numbers
generate stronger encryption keys for digital signing and other Internet
software applications.

What is the key differentiating factor between hardware-based RNG and
software-based pseudo RNG?
The best random number generator (RNG) produces statistically random and
non-deterministic numbers. Only hardware RNG meets both of these requirements.
Software-based pseudo RNGs do not generate numbers that are completely random
and non-deterministic. This lack of randomness provides a security hole for
hackers to exploit. Software pseudo RNGs attempt to get around this by
generating "seeds" from a number of sources in the system. However, the fact
that these seed sources are not random means the system is still vulnerable to
attack. Hardware RNG will significantly improve the process of generating
random numbers in the system by serving as a truly random seed source.

How does Intel RNG create truly random numbers?
The hardware-based Intel RNG uses thermal noise from a resistor which is used
to generate a random, non-deterministic stream of bits that is unpredictable
and non-repeating.

How is RNG implemented in the system?
The hardware RNG will be part of the 8XX series chipsets from Intel, starting
with the Intel? 810 Chipset. The Intel RNG is implemented in a new component of
the chipset called the Intel? 82802 Firmware Hub Device (FWH).

What is the FWH?
The firmware hub (FWH) is a component in the Intel 810 Chipset that uses flash
technology to store and manage system and video BIOS, eliminating a redundant
nonvolatile memory component, and enabling new security capabilities.

Availability of Intel RNG
Intel RNG will begin shipping in June 1999, with the Intel 810 Chipset. It will
also be included when the chipset for the performance market segment is
introduced later this year.

What types of applications and services will use Intel RNG?
The Intel RNG is designed to strengthen security capabilities such as
encryption, digital signing, and other security protocols. These security
capabilities will be used by software developers to enhance the security
capabilities of a wide variety of applications, such as:

Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?
Below <snip> was inadvertantly not included in previous...

Has the Intel RNG been validated as a better seed source?
Yes, Intel has validated Intel RNG throughout the design and manufacturing
process:

Pre-design validation w/ a number of security & manufacturing statistical
testing experts;
Export review w/ the U.S. Department of Commerce and Europe;
Post design validation with Cryptography Research Inc.(CRI);
Passes Federal Information Processing Standards (FIPS) 140-1 test, diagnostic
tests level 3 for statistical randomness.

Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?

Quote:

> : Below <SNIP> is from   intel.com site  random number FAQ...

> : How does Intel RNG create truly random numbers?
> : The hardware-based Intel RNG uses thermal noise from a resistor which is
used
> : to generate a random, non-deterministic stream of bits that is
unpredictable
> : and non-repeating.

> This is probably true, but I doubt if the distribution is uniform.

There are ways to make it extremely close. See below.

Quote:
>  It's
> been many years since I learned about thermal noise in resistors, but I
> seem to recall that the voltage on a resistor has a Gaussian distribution
> over time.

This turns out not to matter.

Quote:
> It would be interesting to know how they actually use the thermal noise
> to generate a random number.

I don't know how Intel does it, but here's a few ways.

Get two independent samples, subtract them. The sign of the difference is a
uniform and independent bit. If you want 32 random bits then 64 samples are
needed but you can generate them all in parallel, or pregenerate them
serially.

This is actually a special case of an algorithm which gets more bits per
sample:

Generate n independent deviates and then sort them. The permutation that was
required to sort them is a random permutation of n; and this means you get

O(log(n!)) = O(n log n)

bits in n samples. This works out to O(log n) bits per sample, but you have
to do O(n log n) serial work or O(log n) parallel time to get these bits.

Note that these deviates don't have to be Gaussian, or even all that close.
Any i.i.d. samples with continuous density will do. In fact the density
doesn't have to be continuous, just such that the chances of two samples
having the same value is extremely small. You might actually want to
transform the distribution _away_ from Gaussian or whatever it is by
stretching it and wrapping it around (aliasing by ignoring the few most
significant bits) in order to control this probability.

Many nonparametric statistics tests provide ways to convert i.i.d. samples
into uniform samples, because that's how you compute the significance of
such a test.

I don't know what Intel actually chose, but they had a lot of available
choices to get uniformity.

The trick might be to ensure independence; but I'd expect all that requires
is a settling time to allow the correlations between consecutive
observations to decay and good separation between parallel random components
to control for spatial correlations. Both of these can be controlled by
ensuring that the temperature of the device is _high_ enough. (Now there's a
new one in computing....)

Later,
Andrew Mullhaupt

Wed, 18 Jun 1902 08:00:00 GMT
Random number not random?

Quote:
> Just nitpicking, but it is impossible to prove anything
> is purely random (see G. Chaitin's work).

Yup, and you can see my latest discussion of this
at http://www.umcs.maine.edu/~chaitin/lowell.html
Rgds,
GJC

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Wed, 18 Jun 1902 08:00:00 GMT

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