Random # STATS

Anthony Stephen Szopa

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Sep 8, 1997, 3:00:00 AM9/8/97

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I generated one 10 million digit stream using my random number generator
and then counted how many times each digit appeared. The results are in
column one of the first table. Then I generated completely different 1
million digit streams and did the same thing. The results are in the
remaining ten columns.

10MB 1MB 1MB 1MB 1MB 1MB

0 = 1000161 100042 99530 100231 100062 99897

1 = 998372 99684 99718 99963 99956 100234

2 = 999389 100128 99685 99663 99474 99987

3 = 999848 100075 99751 100060 99946 99895

4 = 999160 100461 99962 100075 100238 99181

5 = 1001662 99967 100642 99942 99973 100296

6 = 998909 99440 100391 100180 100062 100011

7 = 999930 99905 100402 100058 100531 100188

8 = 1000427 99834 99933 100150 99654 99943

9 = 1002142 100464 99986 99678 100104 100368

1MB 1MB 1MB 1MB 1MB

0 = 100068 99706 100287 99782 100198

1 = 99768 100005 99678 100534 99634

2 = 100667 99767 99546 100135 99766

3 = 99916 99853 100245 99668 100044

4 = 100414 100552 99837 100319 100393

5 = 99583 99772 99394 99729 100283

6 = 99494 100195 100382 100239 99456

7 = 100177 99823 100482 99755 99929

8 = 100020 99994 100071 100439 100210

9 = 99893 100333 100078 99400 100087

I plan to do this same analysis with digit pairs: 00 - 99, with digit
threesomes: 000 - 999, and with the number 0 - 255 as generated with
this software.

AS

PS: I will be adding a bonus software program to generate both digits
and numbers (0 - 255) with the Original Absolute Priviacy - Level3
software package.

Michael Sierchio

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Sep 8, 1997, 3:00:00 AM9/8/97

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I generated one 10 million (decimal) digit stream using my random number generator

and then counted how many times each digit appeared.

0 1 2 3 4 5 6 7 8 9
1000000 1000000 1000000 1000000 1000000 1000000 1000000 1000000 1000000 1000000

for (i=0; i<10000000; i++)
printf("%d\n", i%10);

Brett Weiss

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Sep 8, 1997, 3:00:00 AM9/8/97

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Why is this posted to misc.legal.computing?

Brett

Anthony Stephen Szopa wrote in article <341477...@ciphile.com>...

Colin Dooley

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Sep 9, 1997, 3:00:00 AM9/9/97

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Anthony Stephen Szopa wrote:
>
> I generated one 10 million digit stream using my random number generator
> and then counted how many times each digit appeared. The results are in
> column one of the first table. Then I generated completely different 1
> million digit streams and did the same thing. The results are in the
> remaining ten columns.
>

Did you try doing the same test on this stream:

012345678901234567890123456789012 ....etc.

This would give a nice even spread of numbers as well.

Hint: counting frequency of numbers is useless as a test of
a random number generator.

--
<\___/> | Everything is controlled by a small evil group to which,
/ O O \ | unfortunately, no one we know belongs.
\_____/ FTB. |

Gary Ardell

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Sep 9, 1997, 3:00:00 AM9/9/97

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On Mon, 08 Sep 1997 15:10:54 -0700, Anthony Stephen Szopa
<ant...@ciphile.com> wrote:

>I generated one 10 million digit stream using my random number generator
>and then counted how many times each digit appeared. The results are in
>column one of the first table. Then I generated completely different 1
>million digit streams and did the same thing. The results are in the
>remaining ten columns.

cut . . .

>
>I plan to do this same analysis with digit pairs: 00 - 99, with digit
>threesomes: 000 - 999, and with the number 0 - 255 as generated with
>this software.
>
>AS
>
>
>PS: I will be adding a bonus software program to generate both digits
>and numbers (0 - 255) with the Original Absolute Priviacy - Level3
>software package.

Anthony,

There is little reason to invent or code custom tests. may I suggest
you download Diehard from:

http://stat.fsu.edu/~geo/diehard.html

It is free and will give you a well rounded picture of what is good
and bad with your stream of puedo random numbers.. I have found
Diehard an invaluable tool. This site also has good pointers to other
sites.

For a good online discussion of the state of the art in random number
generation see:

http://www.webnz.com/robert/recent/lottery.html

and follow the threads.

Good luck,

Gary

Richard L. Grubb

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Sep 9, 1997, 3:00:00 AM9/9/97

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Colin Dooley wrote:
>
> Hint: counting frequency of numbers is useless as a test of
> a random number generator.

Useless is a bit strong. It is certainly not sufficient for crypto
usage.
--
Richard Grubb
BCAG, 737NG Stress, Wichita
rlg...@sgmail.ks.boeing.com
#include "std_disclaimers.h"

Barry Margolin

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Sep 9, 1997, 3:00:00 AM9/9/97

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In article <341477...@ciphile.com>,

Anthony Stephen Szopa <ant...@ciphile.com> wrote:
>I generated one 10 million digit stream using my random number generator
>and then counted how many times each digit appeared. The results are in
>column one of the first table. Then I generated completely different 1
>million digit streams and did the same thing. The results are in the
>remaining ten columns.

The stream 01234567890123456789... would pass this test, but I don't think
anyone would consider it random.

>I plan to do this same analysis with digit pairs: 00 - 99, with digit
>threesomes: 000 - 999, and with the number 0 - 255 as generated with
>this software.

The stream 00010203...97989900010203...979899... would pass the 1-digit and
2-digit tests, but again it isn't very random. There's a similar stream
that will pass the 1-, 2-, and 3-digit tests, and so on.

As you can see, it's not enough that a sequence contain all the possible
elements in equal numbers, but that the *order* of those elements be
unpredictable.

--
Barry Margolin, bar...@bbnplanet.com
GTE Internetworking, Powered by BBN, Cambridge, MA
Support the anti-spam movement; see <http://www.cauce.org/>
Please don't send technical questions directly to me, post them to newsgroups.

Matthew D. Healy

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Sep 9, 1997, 3:00:00 AM9/9/97

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In article <3419F0...@vlc.servicom.es>, Colin Dooley
<co...@vlc.servicom.es> wrote:

...

>
> Did you try doing the same test on this stream:
>
> 012345678901234567890123456789012 ....etc.
>
> This would give a nice even spread of numbers as well.

Then try frequency counts on the streams:

314159265358979323846264338327950288419716939937510582097494459...

141421356237309504880168872420969807856967187537694807317667973...

161803398874989484820458683436563811772030917980576286213544862...
--------
Matthe...@yale.edu http://ycmi.med.yale.edu/~healy/
As of 5 Sep 1997, only 847 days until Y2K....
Any person with a phone line can become a town crier with a voice
that resonates farther than it could from any soapbox.
--The US Supreme Court, overturning the Communications Decency Act

Wayne D. Hoxsie Jr.

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Sep 11, 1997, 3:00:00 AM9/11/97

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On Mon, 08 Sep 1997 15:10:54 -0700, Anthony Stephen Szopa
<ant...@ciphile.com> wrote:

>I generated one 10 million digit stream using my random number generator
>and then counted how many times each digit appeared. The results are in
>column one of the first table. Then I generated completely different 1
>million digit streams and did the same thing. The results are in the
>remaining ten columns.

How about making several blocks of these numbers (say blocks of 64K or
so) available for download somewhere so that we can run some tests on
them that actually mean something!

--
Wayne D. Hoxsie Jr.
wa...@hoxnet.com
http://www.hoxnet.com