Beyond Linear Congruential Generators

  • Shu Tezuka
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 315)


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.’


Turing Machine Kolmogorov Complexity Continue Fraction Expansion Combine Sequence Successive Minimum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Shu Tezuka
    • 1
  1. 1.IBM Japan, Ltd.Kanagawa-kenJapan

Personalised recommendations