6.3 Pseudo-random number generator

A common pseudo-random number generator makes use of two large prime numbers. It updates a seed value, and returns a value within the range of 0 (inclusive) and 1 (exclusive). Let $p_1$ and $p_2$ be the large prime number, and $s$ be the seed. The seed is updated as follow: $s \leftarrow (s\times p_1) \mod p_2$ . The output value is $\frac{s}{p_2}$ .

For such a pseudo-number generator, both the range and domain are $\{0,\ldots p_2-1\}$ . It is an injection and also surjective function. This means such a pseudo-number generator is a bijection.