Do stateless random number generators exist?

Question

Is there a difference between generating multiple numbers using a single random number generator (RNG) versus generating one number per generator and discarding it? Do both implementations generate numbers which are equally random? Is there a difference between the normal RNGs and the secure RNGs for this?

I have a web application that is supposed to generate a list of random numbers on behalf of clients. That is, the numbers should appear to be random from each client's point of view. Does this mean I need retain a separate random RNG per client session? Or can I share a single RNG across all sessions? Or can I create and discard a RNG on a per-request basis?

UPDATE: This question is related to Is a subset of a random sequence also random?

Answer 1

A random number generator has a state -- that's actually a necessary feature. The next "random" number is a function of the previous number and the seed/state. The purists call them pseudo-random number generators. The numbers will pass statistical tests for randomness, but aren't -- actually -- random.

The sequence of random values is finite and does repeat.

Think of a random number generator as shuffling a collection of numbers and then dealing them out in a random order. The seed is used to "shuffle" the numbers. Once the seed is set, the sequence of numbers is fixed and very hard to predict. Some seeds will repeat sooner than others.

Most generators have period that is long enough that no one will notice it repeating. A 48-bit random number generator will produce several hundred billion random numbers before it repeats -- with (AFAIK) any 32-bit seed value.

A generator will only generate random-like values when you give it a single seed and let it spew values. If you change seeds, then numbers generated with the new seed value may not appear random when compared with values generated by the previous seed -- all bets are off when you change seeds. So don't.

A sound approach is to have one generator and "deal" the numbers around to your various clients. Don't mess with creating and discarding generators. Don't mess with changing seeds.

Above all, never try to write your own random number generator. The built-in generators in most language libraries are really good. Especially modern ones that use more than 32 bits.

Some Linux distros have a /dev/random and /dev/urandom device. You can read these once to seed your application's random number generator. These have more-or-less random values, but they work by "gathering noise" from random system events. Use them sparingly so there are lots of random events between uses.

Answer 2

The use of a secure PRNG depends on your application. What are the random numbers used for? If they're something of real value (e.g. anything cryptographically related), you wouldn't want to use anything less.

Secure PRNGs are much slower, and may require libraries to do operation of arbitrary precision, and primality testing, etc etc...

Answer 3

If you create a RNG and generate a single random number from it then discard the RNG, the number generated is only as random as the seed used to start the RNG.

It would be much better to create a single RNG and draw many numbers from it.

Answer 4

Normally seeding a new state takes quite while for a serious PRNG, and making new ones each time won't really help much. The only case I can think of where you might want more than one PRNG is for different systems, say in a casino game you have one generator for shuffling cards and a separate one to generate comments done by the computer control characters, this way REALLY dedicated users can't guess outcomes based on character behaviors.

A nice solution for seeding is to use this (Random.org) , they supply random numbers generated from the atmospheric noise for free. It could be a better source for seeding than using time.

Edit: In your case, I would definitely use one PRNG per client, if for no other reason than for good programming standards. Anyways if you share one PRNG among clients, you will still be providing pseudo-random values to each, of a quality equal to your PRNG's quality. So that's a viable option but seems like a bad policy for programming