Random number generators are important in many kinds of technical applications, including physics, engineering or mathematical computer studies (e.g., Monte Carlo simulations), cryptography and gambling (on game servers).
With appropriate initialisations, passes all current empirical test suites, and is formally proven to converge.
However, generally they are considerably slower (typically by a factor 2–10) than fast, non-cryptographic random number generators.
These include: A few cryptographically secure pseudorandom number generators do not rely on cipher algorithms but try to link mathematically the difficulty of distinguishing their output from a `true' random stream to a computationally difficult problem.
They include: These approaches combine a pseudo-random number generator (often in the form of a block or stream cipher) with an external source of randomness (e.g., mouse movements, delay between keyboard presses etc.