Generate Random numbers without using any external functions

Question

This was questions asked in one of the interviews that I recently attended.

As far as I know a random number between two numbers can be generated as follows

Answer 1

Typical pseudo-random number generators calculate new numbers based on previous ones, so in theory they are completely deterministic. The only randomness is guaranteed by providing a good seed (initialization of the random number generation algorithm). As long as the random numbers aren't very security critical (this would require "real" random numbers), such a recursive random number generator often satisfies the needs.

The recursive generation can be expressed without any "external" functions, once a seed was provided. There are a couple of algorithms solving this problem. A good example is the Linear Congruential Generator.

A pseudo-code implementation might look like the following:

long a = 25214903917;   // These Values for a and c are the actual values found
long c = 11;            // in the implementation of java.util.Random(), see link
long previous = 0;

void rseed(long seed) {
    previous = seed;
}

long rand() {
    long r = a * previous + c;
    // Note: typically, one chooses only a couple of bits of this value, see link
    previous = r;
    return r;
}

You still need to seed this generator with some initial value. This can be done by doing one of the following:

• Using something like the current time (good in most non-security-critical cases like games)
• Using hardware noise (good for security-critical randomness)
• Using a constant number (good for debugging, since you get always the same sequence)
• If you can't use any function and don't want to use a constant seed, and if you are using a language which allows this, you could also use some uninitialized memory. In C and C++ for example, define a new variable, don't assign something to it and use its value to seed the generator. But note that this is far from being a "good seed" and only a hack to fulfill your requirements. Never use this in real code.

Note that there is no algorithm which can generate different values for different runs with the same inputs without access to some external sources like the system environment. Every well-seeded random number generator makes use of some external sources.