Chapter 11 | PARADOXES OF PROBABILITY | ||||

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In this paper we have examined some probability theory, the concept of a random sequence coming from a random process, and ways of analyzing a sequence of numbers to determine how likely it is they came from a random process.

We then examined the inside of a linear congruential random number generator which is the most prevalent type of random number generator in use today. We dissected 5 commonly found linear congruential generators, and then analyzed them using the (chi-square, pronounced "KI-square") and KS (Kolmogorov-Smirnov) tests. We found it was possible to detect non-randomness in each of these generators after a few million iterations, except for the defective RANDU generator, which failed the 3-D test after less than 800 iterations.

A technique for shuffling the random numbers was given and tested with excellent results. Shuffling the output of any random number generator using the technique given is therefore highly recommended.

Analysis of the Data Encryption Standard (DES) as a random number generator was also performed. A software implementation of the Data Encryption Standard DES was found to be too slow for any practical use and the randomness of the results was found to be less than that obtained by shuffling the output of a good linear congruential generator.

Finally, a brief mathematical explanation of what an ideal random number generator really is and how it differs from a computerized random number generator was given. For further reading on this topic, consult a book on Information theory and read about the different types of information sources defined there.

Chapter 11 | PARADOXES OF PROBABILITY | |||

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