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The entire first chapter of Donald Knuth’s seminal work Seminumerical Algorithms is taken up with the subject of random number generation. I really don’t think an SO answer is going to come close to describing the issues involved. Read the book.

The Wikipedia page is a good reference.

The actual algorithm used is going to be dependent on the language and the implementation of the language.

To exactly answer you answer, the random function is provided by the operation system (usually).

But how the operating system creates this random numbers is a specialized area in computer science. See for example the wiki page posted in the answers above.

random() is a so called pseudorandom number generator (PRNG). random() is mostly implemented as a Linear congruential generator. This is a function of the form X(n+1) (aXn +c) modulo m. Xn is the sequence of generated pseudorandom numbers. The genarated sequence of numbers is easy guessable. This algorithm can’t be used as a cryptographically safe PRNG.

Wikipedia:Linear congruential generator

And take a look at the diehard tests for PRNG PRNG Diehard Tests

It turns out to be surprisingly easy to get half-way-decent pseudorandom numbers. For decades the gold standard was a remarkably simple algorithm: keep state x, multiply by constant A (32×32 => 64 bits) then add constant B, then return the low 32-bits, which also become the new x. If A and B are chosen carefully this actually works fairly well.

Pseudorandom numbers need to be repeatable, too, in order to reproduce behavior during debugging. So, seeding the generator (initializing x with, say, the time-of-day) is typically avoided during debugging.

In recent years, and with more compute cycles available to burn, more sophisticated algorithms are available, some of them invented since the publication of the otherwise quite authoritive Seminumerical Algorithms. Operating systems are also starting to provide hardware and network-derived entropy bits for specialized cryptographic purposes.

One thing you might want to examine is the family of random devices available on some Unix-like OSes like Linux and Mac OSX. For example, on Linux, the kernel gathers entropy from a variety of sources into a pool which it then uses to seed it’s pseudo-random number generator. The entropy can come from a variety of sources, the most notable being device driver jitter from keypresses, network events, hard disk activity and (most of all) mouse movements. Aside from this, there are other techniques to gather entropy, some of them even implemented totally in hardware. There are two character devices you can get random bytes from and on Linux, they behave in the following way:

  • /dev/urandom gives you a constant stream of bytes which is very random but not cryptographically safe because it reuses whatever entropy is available in the pool.
  • /dev/random gives you cryptographically safe random numbers but it won’t give you a constant stream as it uses the entropy available in the pool and then blocks while more entropy is collected.

Note that while Mac OSX uses a different method for it’s PRNG and therefore does not block, my personal benchmarks (done in college) have shown it to be every-so-slightly less random than the Linux kernel. Certainly good enough, though.

So, in my projects, when I need randomness, I typically go for reading from one of the random devices, at least for the seed for an algorithm in my program.