Pseudorandom Generators

Abstract

According to the Encyclopedic Dictionary of Mathematics,¹ a sequence of random numbers is a sequence of numbers that can be considered as realizations of independently and identically distributed random variables. Such sequences or tables of random numbers are useful in applications of the Monte Carlo method (e.g. Monte Carlo primality tests), in cryptography, and in the design of efficient probabilistic algorithms. However, as was mentioned in section 3, it is impossible to have perfectly random sampling through an unbiased execution of an experiment (like flips of a coin). In applications therefore, one is led to use pseudorandom sequences of numbers, i.e. finite sequences of numbers produced by efficient deterministic algorithms, but which appear to be sufficiently random. These finite algorithms, also called pseudorandom generators, take a short input, called the seed,and produce a longer sequence of numbers. The pseudorandom sequences must have no apparent regularities and must also pass certain statistical tests (e.g. X ², Kolmogorov — Smirnov), as well as empirical tests on frequency, uniformity, gaps, permutations and subsequencies (see [K2]).

Il faut donner quelque chose au hasard.

(French Proverb)