david wong

Hey! I'm David, a security engineer at the Blockchain team of Facebook, previously a security consultant for the Cryptography Services of NCC Group. I'm also the author of the Real World Cryptography book. This is my blog about cryptography and security and other related topics that I find interesting.

How does the Mersenne's Twister work? posted February 2016

Someone asked that question on reddit, and so I replied with a high level answer that should provide a clear enough view of the algorithm:

From a high level, here's what a PRNG is supposed to look like:

prng

you start with a seed (if you re-use the same seed you will obtain the same random numbers), you initialize it into a state. Then, every time you want to obtain a random number, you transform that state with a one-way function \(g\). This is because you don't want people to find out the state out of the random output.

You want another random number? You first transform the state with a one way function \(f\): this is because you don't want people who found out the state to be able to retrieve past states (forward secrecy). And then you use your function \(g\) again to output a random number.

Mersenne Twister (MT) is like that, except:

  • your first state is not used to output any random numbers
  • a state allows you to output not only one, but 624 random numbers (although this could be thought as one big random number)
  • the \(g\) function is reversible, it's not a one-way function, so MT it is not a cryptographically secure PRNG.

With more details, here's what MT looks like:

mersenne twister

the \(f\) function is called "twist", the \(g\) function is called "temper". You can find out how each functions work by looking at the working code on the wikipedia page of MT.

Well done! You've reached the end of my post. Now you can leave me a comment or read something else.

Comments

mm

Very elegant explanation. :) Very helpful.

Thou I think it's 623 dimensions. [http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.pdf]

Thanks.

test

test

rd

Thanks for the explanation.

Sam

Great article! Thanks

Daz

Hi David.
Great explanation. I find these mathematical concepts and applications fascinating. Someone told me recently that one of our Lotto systems in Australia generates its numbers using a RNG. I would assume these systems would be water tight and that it would be impossible to crack them in a normal lifetime. Hence I guess they wouldn't use them, unless they use them with people thinking that is the case in the hope that no one would even contemplate trying lol. I'd be interested in your thoughts on this topic.
Thanks and best regards
Daz
([email protected])


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