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How good does a hardware generator need to be?

Of course it depends what you want it for.

George Marsaglia recommends combining each byte from the hardware generator with a byte from a pseudo-random number generator to reduce bias and correlation. I agree with this. But I would still like my original real random numbers to be a good as possible. I don't know why pseudo-random number generators work as well as they do. I suspect that even the most reliable ones will give misleading answers for some applications. When one is dealing with a very large simulation I don't know whether some undesirable characteristic of the pseudo-random number generator will be able to leak through if the hardware generator is not very good. So I would really like my hardware random number generator to be as good as possible and the pseudo-random number generator to be used to clean up the very small amount of correlation or bias that remains in the output from the hardware random number generator.

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This was my immediate application. The game emulates drawing numbered balls from an urn . We want each permutation of balls to have the same probability to, say, within 10%. This is a very stringent requirement since a minor bias is the generator can produce major differences in the probabilities of the different permutations of the balls. Using the Canadian generator as the base generator we get the required accuracy if we exclusive-or two bytes. I also exclusive-or the resulting number with a number from a pseudo-random number generator. Including the pseudo-random number generator may be not really necessary, but it gives us some protection against a generator unit failing during a game. It makes it impossible for anyone to take advantage of the little bit of variation left in the probabilities of the different permutations.

I don't think it is satisfactory to use a lower quality hardware random number generator in this situation, even though one is taking an exclusive-or with a pseudo-random number. Even with the Canadian one I decided that it was necessary to take the exclusive-or of two of its bytes to reduce bias. Although the numbers would probably meet the requirements 1 to 3 with a less accurate generator, the problem is to prove this under requirement 4.

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Statistical simulation

Taking an exclusive-or with a pseudo-random number must give a generator which is very close to being an exact method of generating real random bytes which are uniformly independently distributed. I am assuming, or course, that one is using a generator of the quality of a correctly working Canadian random number generator. It is probably overkill to exclusive-or two of the bytes from the hardware generator; the pseudo-random number generator will remove the effects of the little bit of bias.

The main problem is speed. The Canadian manufacturer recommended a maximum sampling rate of 20,000 bytes per second and this seems to be about right. This is too slow for practical computer simulations. However, one could install the card in an older, pensioned off, PC, and just leave the generator running, writing the numbers to disk. This way one could generate 1 to 2 gigabytes a day which could be read from disk as required.

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Encryption

You want a key of, say, 512 bits. You won't want to use pseudo-random numbers since then the key is really just your starting random seed (assuming the person trying to break your code has access to your program). It might be reasonable to use a real random number generator to generate the key. For 56 bit keys, maybe there are simpler ways. On the other hand, it is very important that these keys really are chosen randomly so that someone searching through keys can't just limit the search to most likely values , and a hardware random number generator may provide an easy way to do this.

For other information related to encryption see David Wagner's page and RFC 1750 .

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    Contact Form 30 Mar 2012 .. Can these random number generators help you win the record-high Mega Millions jackpot? Probably not, but it might be worth a try. What's newReplies (6) 

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