A Fast Jump Ahead Algorithm for Linear Recurrences in a Polynomial Space

  • Hiroshi Haramoto
  • Makoto Matsumoto
  • Pierre L’Ecuyer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5203)


Linear recurring sequences with very large periods are widely used as the basic building block of pseudorandom number generators. In many simulation applications, multiple streams of random numbers are needed, and these multiple streams are normally provided by jumping ahead in the sequence to obtain starting points that are far apart. For maximal-period generators having a large state space, this jumping ahead can be costly in both time and memory usage. We propose a new jump ahead method for this kind of situation. It requires much less memory than the fastest algorithms proposed earlier, while being approximately as fast (or faster) for generators with a large state space such as the Mersenne twister.


Stream Cipher Polynomial Multiplication Pseudorandom Number Generator Linear Feedback Shift Register Linear Recurrence 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hiroshi Haramoto
    • 1
  • Makoto Matsumoto
    • 1
  • Pierre L’Ecuyer
    • 2
  1. 1.Dept. of Math.Hiroshima UniversityHiroshimaJapan
  2. 2.Département d’Informatique et de Recherche OpérationnelleUniversité de MontréalMontréalCanada

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