There are many methods of generating pseudorandom numbers. Some of them are middle square (not very good), Mersenne twister, linear congruential generator (one the oldest used in math libraries, but subject to sequential corellation artifacts), and cryptographically secure generators.

A secure pseudo-random generator

Pseudorandom numbers can affect the accuracy of a simulation by accidentally causes pattens that could be missed by the system. This could skew the accuracy.

Random numbers are used to determine the statistics and generate frequency rules. Pseudorandom numbers can skew the resultant frequencies and greatly alter the accuracy of simulation.

PCTools has a software program for password generation. All it takes is a simple algorithm and a number generator to create as many passwords needed to secure a site.