Nonlinear Methods for Pseudorandom Number and Vector Generation

The principal aim of pseudorandom number generation is to devise and analyze deterministic algorithms for generating sequences of numbers which simulate a sequence of i.i.d random variables with given distribution function. We shall deal here exclusively with pseudorandom numbers for the uniform distribution on the interval [0,1], i.e. with uniform pseudorandom numbers. We refer to Knuth [16], Niederreiter [18], Ripley [25], and to the recent survey by Niederreiter [24] for a general background on uniform pseudorandom number generation.