I'm currently developing an electronic component to create true random numbers. I like to know if there is a method to calculate how 'random' the generated numbers are. Mathematically this may be impossible. How about more practical approach such as suitability of using these numbers for encryption. Thanks
Dear Peter, Thanks for the quick response.
I googled before posting and in fact Wikipedia was my first. So let me try to put more details and explain why I'm little confused.
The electronic circuit in discussion have a chaotic behavior and I intend to use it for "True" random number generation.( It is hardware based and no algorithms running. ) . The wiki says "Statistical randomness does not necessarily imply "true" randomness." Then it go on describing pseudo random generators. Since I want to build a TRNG I'm not sure the tests described can be accurately used.
The second thing I like to clarify is the test of checking correlation between successive numbers. Say I got a sequence of '2,2,2,2,2' Does that imply it can not be generated by a RNG? On the other hand if I got something like '4,9,1,5,5' does that mean it is actually random ? If I remember correctly you can fit a curve of nth degree (Or a function with n variables) to any sequence with 'n' elements.
I'm basically in to electronics and programming, and I'm not an expert on statistics (or mathematics) . Therefor any further help would be greatly appreciated :)
Dear Gayan
It is not possible at all to say is a finite series of numbers is random or not.
It is a consequence of the Gödel's incompleteness theorems.
Therefore, as Peter said, you do not have to care about the the absolute randomness of your numbers, but if their random enough for your purposes.
You are right that the number series 2 2 2 2 2 2 2 2 can be part of a random series, but up to know it is not. Similarly, if you have a series of n number that seems random, even at the best test, you can only says that these numbers are random, starting from n+1 the series can be repeated, and you do not know until you generate other numbers.
The only way to ensure true randomness is at the source (before number generation), it cannot be done at the end (whose true randomness as Gianpiero indicates is untestable in principle, unless you accept a nonzero threshold value of uncertainty)
Generally speaking you cannot generate a true random sequence without ongoing random seed input - the instant you do away with random seed input, your number generation has become pseudo-random.
The best random seed inputs typically arise from the far to the right decimal values of something based on time (say, using as the seed the numbers between the 10th and the fifteenth decimal place of a seconds timer) where the mechanism triggering the timer is loosely based on an unpredictable process, such as Brownian motion.
Between two seed inputs you can tolerate a short pseudo-random sequence which for all practical purposes is a random pseudo-random sequence.
You can easily by the way statistically skew, or bias, the random value outcomes (their statistical distribution or signature) without detracting from their quality of randomness
Dear All,
Thank you very much. I think I got the idea of what to do. I already have a data set obtained by the device. As Peter suggested I would try some standard tests and see what happens.
And Chris thank you very much for the insight you provided. As you say true randomness can be determined at the source, but any idea how it can be done without generating numbers? (Because I'm trying to use a chaotic voltage signal at the heart of the device and only way to measure it is through an ADC, which basically provide me with a number) Or if I'm guessing correctly, what you suggests is to use the theory to prove the ideal system is random and then apply it to the practical application.
And Thanks again everyone. :-)
Dear Gayan,
Standard tests for randomness are available in the statistical literature.
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