Pseudo-random numbers and their seed

We are going to start with the conceptual part and saying that the Spanish translation of seed is seed .

A seed is used by a PSEUDO-random number generation algorithm to calculate the next number.

And that is that random number generation functions are, after all, deterministic functions . I quote Wikipedia:

a deterministic algorithm is an algorithm that, loosely speaking, is completely predictive if its inputs are known.

The English Wikipedia article: Pseudorandom number generator starts by saying:

A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's seed (which may include truly random values). Although sequences that are closer to truly random can be generated using hardware random number generators, pseudorandom number generators are important in practice for their speed in number generation and their reproducibility.

My translation and emphasis of the quoted is:

A pseudo-random number generator (PNGS), also known as a deterministic random bit generator (DGB), is an algorithm for generating a sequence of numbers whose properties approximate the properties of random number sequences . The sequence generated by GNPA is not truly random , because it is completely determined by an initial value, called the GNPA seed.(which can include truly random values). Although the closest to truly random sequences can be generated using hardware random number generators, pseudo-random number generators are important in practice for their speed of number generation and their reproducibility.

What does all this mean in practice?

• That the function is deterministic, we can explain it like this:
  • If you know the initial seed and the algorithm used to generate a sequence of pseudo-random numbers, you can completely reproduce the sequence. I mean, there's nothing random about it, it just looks random. A truly random function would not be deterministic.
  • If you call a pseudo-random number generator a million times and the million times you pass the same seed value to it, the million times it will return the same number
• To generate sequences of numbers, many GNPA functions use the value obtained in one execution as a seed to calculate the value of the next execution.
• Although the seed and result of the pseudo-random generation function is usually represented by a floating point number, in general, the seed and result is nothing more than a sequence of bits that the algorithm uses to generate a new sequence of bits.
• Many environments, to provide unique sequences on each run, derive an initial seed from some combination of values ​​that is sufficiently unique. This may include the current date and time, system information, etc.
• Some linux (and other *nix) distributions implement/dev/random , /dev/urandomand the like which accumulate entropy from system noise to generate truly random seeds which are then fed to a GNPA to return truly random numbers.
• random.org offers services to get truly random numbers.

Why do we settle for pseudo-random numbers?

For a common computer there is no real way to generate a completely random number. Computers are great at doing calculations that deliver accurate and repeatable results, but the poor processor has nowhere to go when it comes to asking for a simple random number. And it is that random numbers have some statistical characteristics, mainly that their distribution is uniform.

That is why, through the genius of some people, we have arrived at the current state of things. Pseudo-random numbers are good enough to be indistinguishable from truly random numbers.

*nix's approach of capturing entropy , for example, from noise heard by Wi-Fi adapters and other electrical sources is great and the best approach I know of to get unpredictable numbers .