We know that for generating TRN almost we use hardware system and natural phenome. In PRN we use computer programs for generate random number.
if we design, frequency of number, of this algorithms, we see uniformly
histogram. but in TRN generator almost we have not uniformly histogram.
so, generating TRN my be very difficult than PRN, and regenerating the same stream of number, be came hard or impossible.
in conclude, if we could use software method to generate TRN may be very excellent and useful.
I think that given enough samples, any true random number generator must show an even distribution, or there's a problem of bias involved. One example might be rain drops falling on a flat sheet of paper. If the drops aren't soon very uniform, on the sheet, then you would suspect some mechanism biasing that distribution. Using such natural phenomena may possibly create the best TRN sequences.
But you made the correct observation, in my opinion. Recreating that TRN stream after the fact is essentially impossible, if you have used a natural phenomenon such as the rain drops. Which makes such a TRN generator difficult to use in cypher, or in models, unless you can find a (secure, in the case of cyber) way to distribute the very long TRN sequence, to everyone who must decode messages, or for rerunning that Monte Carlo model to see if each result matches the previous test.
Or, another possibility is to use well-known irrational numbers, such as pi or e. The infinite sequence of digits is supposedly random, I've read, and in this case, you can reproduce it independently. At least, to some level of accuracy.
Hello, you can use Monte Carlo simulation for true random number generator.
Dear Albert Manfredi
What do you mean by the random behaviour of decimal expansion of pi or e? Do you have any proof for the same?
I think it is a conjecture which may be hard to prove.
Dear Karen A. Darbinyan
Can you please explain how Monte Carlo simulation will help?
Tapas, see this:
https://cs.stackexchange.com/questions/106774/can-we-generate-random-numbers-using-irrational-numbers-like-π-and-e
If the sequence shows no repeating pattern, and if there is an even distribution of values, then the sequence can be said to be random. (I don't buy the philosophical notion of "predictable," because that's too easily misinterpreted. Pi might be "predictable," in the sense that we know what it is, but you will find it hard to predict the sequence unless you have it printed in front of you.)
On the question of Monte Carlo simulations, I'm also unsure what Karen is saying. I would have said that a true random number generator can be used when you run a Monte Carlo simulation. However, if you have not saved that true random pattern, you won't be able to repeat the Monte Carlo iterations with exactly the same sequence of random numbers, which can be a problem. Sometimes, you want to make changes in your model, and you want to see how the changes affect the results, for each iteration.
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