¿Cómo funciona el Mersenne Twister?

How does the Mersenne Twister work?

You start with a seed (if you re-use the same seed you will obtain the same random numbers), you initialise it into a state. Then, every time you want to obtain a random number, you transform that state with a one-way function /(g/).

You can mimic randomness by specifying a set of rules. For example, “take a number x, add 900 +x, then subtract 52.” In order for the process to start, you have to specify a starting number, x (the seed). Let’s take the starting number 77: Add 900 + 77 = 977.

One way is to give the entire internal state. The other way is to give a smaller “seed”, and from the seed generating an internal state in some devious way.

Initializes generator with the specified positive integer seed, such as 1. Initializes Mersenne Twister generator with seed 0 . This is the default setting at the start of each MATLAB session. Initializes generator based on the current time, resulting in a different sequence of random numbers after each call to rng.

The MT19937 algorithm keeps track of its state in 624 32-bit values. If an attacker were able to gather 624 sequential values, then the entire sequence—forward and backward—could be reverse-engineered. This feature is not specific to the Mersenne Twister, most PRNG have a state mechanism that is used to generate the next value in the sequence.

MT [ 117] is one of the most widely respected RNGs, it is a twisted GFSR. The underlying algorithm of MT is as follows: Set r w -bit numbers ( xi, i = 1,2,…, r) randomly as initial values. where Iw−1 is the ( w − 1) × ( w − 1) identity matrix and ai, i = 1,…, w take values of either 0 or 1.