Beyond Linear Congruential Generators

Abstract

Developing random number generators which involve some nonlinear operation in their generation schemes has been a central research issue in this area, since the nonlinearity has long been believed to be useful to make the resulting sequences look more random. In this chapter, we discuss three types of nonlinear generator. The first and second ones are defined by slightly modifying linear congruential generators, using polynomial arithmetic and multiplicative inversion, respectively. The third type consists of random number generators for cryptographic applications, which require the sequences produced to have a certain property of ‘ unpredictability.’ This property turns out to be strongly connected with the ‘nonlinearity’ involved in the generation scheme. In fact, linear congruential sequences are known to be unsuitable for such applications because of their polynomial-time ‘predictability.’

Article FootNote

Random number generation is too important to be left to chance. — Robert R. Coveyou (1969)