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I have been assigned to generate 15000+ homogeneous and uniform random numbers for a work.

I have been searching if Mersenne Twister generate homogeneous distribution of numbers but I don't find nothing. I have found a lot of test and proprieties but I do not know if any of those proprieties/tests refers to the homogeneity.

Can you explain me if the algorithm generates homogeneous numbers, why and what are the proprieties involved in?

By homogeneity I think that I mean this.

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    $\begingroup$ "homogeneous" is not a standard term, what do you mean? $\endgroup$ – kodlu Oct 18 '15 at 6:32
  • $\begingroup$ @kodlu I mean this $\endgroup$ – Jesús Martín Berlanga Oct 18 '15 at 11:42
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    $\begingroup$ @otus I'm doing a cryptoanalysis work and I have to generate random inputs to test a cipher, The work requieres that the samples are uniform and homogeneus. $\endgroup$ – Jesús Martín Berlanga Oct 18 '15 at 19:42
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I think the Mersenne twister satisfies the requirement for homogeneity, since it produces numbers that are equally distributed (with 32-bit accuracy) in up to 623  dimensions.

But in a cryptography context, it could hardly be described as "uniform", because you only need to observe 624 outputs in order to predict all the following values with 100% accuracy.

I would recommend using a cryptographically secure PRNG such as AES-CTR instead. This should provide you with at least 100 MB of random data per second.

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  • $\begingroup$ I will have no attackers, I just will use the numbers to test a cipher. The generated numbers are the input. $\endgroup$ – Jesús Martín Berlanga Oct 19 '15 at 13:15
  • $\begingroup$ Will it be ok in that context? $\endgroup$ – Jesús Martín Berlanga Oct 19 '15 at 13:23
  • $\begingroup$ @jmb95 I don't know. If you just want to see if the numbers going into your cipher are the same as the ones coming out, then yes, it's probably fine. But then I'd have to ask why homogeneity is so important. What's so difficult about using a CSPRNG? $\endgroup$ – r3mainer Oct 19 '15 at 19:22

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