random technical thoughts from the Nominet technical team

Testing randomness

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Posted by jad on Dec 1st, 2006

I wrote about installing a Araneus Alea I the other day. Since then I have been reading about how you test random number generators.

There is a discussion of this subject at Hotbits. This a web based random number generator that uses radioactive decay to generate the numbers. They have a program called ENT for testing binary data sequences.

Generating 1000000 random bytes with the Alea I can be done like this.

time ./randomfile -b 1000000 > /tmp/myrandom

real    1m21.073s
user    0m0.066s
sys     0m0.134s

Testing with the ENT program gives these results

./ent /tmp/myrandom
Entropy = 7.999817 bits per byte.

Optimum compression would reduce the size
of this 1000000 byte file by 0 percent.

Chi square distribution for 1000000 samples is 252.96, and randomly
would exceed this value 50.00 percent of the times.

Arithmetic mean value of data bytes is 127.5287 (127.5 = random).
Monte Carlo value for Pi is 3.144636579 (error 0.10 percent).
Serial correlation coefficient is 0.000713 (totally uncorrelated = 0.0).

According to the ENT manual this is very random data. Next I will be looking at what the NIST random number test tools have to say.

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