A Good and SIMPLE Measure of Randomness

Question

What is the best algorithm to take a long sequence of integers (say 100,000 of them) and return a measurement of how random the sequence is?

The function should retu

Answer 1

Although this question is old, it does not seem "solved", so here is my 2 cents, showing that it is still an important problem that can be discussed in simple terms.

Consider password security.

The question was about "long" number sequences, "say 100.000", but does not state what is the criterium for "long". For passwords, 8 characters might be considered long. If those 8 chars were "random", it might be considered a good password, but if it can be easily guessed, a useless password.

Common password rules are to mix upper case, numbers and special characters. But the commonly used "Password1" is still a bad password. (okay, 9-char example, sorry) So how many of the methods of the other answers you apply, you should also check if the password occurs in several dictionaries, including sets of leaked passwords.

But even then, just imagine the rise of a new Hollywood star. This may lead to a new famous name that will be given to newborns, and may become popular as a password, that is not yet in the dictionaries.

If I am correctly informed, it is pretty much impossible to automatically verify that a password selected by a human is random and not derived with an easy to guess algorithm. And also that a good password system should work with computer-generated random passwords.

The conclusion is that there is no method to verify if an 8-char password is random, let alone a good and simple method. And if you cannot verify 8 characters, why would it be easier to verify 100.000 numbers?

The password example is just one example of how important this question of randomness is; think also about encryption. Randomness is the holy grail of security.