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International Conference on Sequences and Their Applications

SETA 2014: Sequences and Their Applications - SETA 2014 pp 212–219Cite as

On the Lattice Structure of Inversive PRNG via the Additive Order

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8865))

Abstract

One of the main contributions which Harald Niederreiter made to mathematics is related to pseudorandom sequences theory. In this article, we improve on a bound on one of the pseudorandom number generators (PRNGs) proposed by Harald Niederreiter and Arne Winterhof and study its lattice structure. We obtain that this generator passes general lattice tests for arbitrary lags for high dimensions.

Dedicated to Harald Niederreiter on the occasion of his 70th birthday.

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Notes

  1. 1.

    If \(j=0\), we will denote \(d_0=0\), although the lags are \(d_1,\ldots , d_{L-1}\).

  2. 2.

    Because we always consider \(w_{i,1}=0\). It is also equivalent to discard \(x_1\), i. e. working in \(\mathbb {R}^{r-1}\).

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Acknowledgement

This work is supported in part by the Spanish Ministry of Science, project MTM2011-24678.

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Authors and Affiliations

  1. University of Cantabria, Avd. Los Castros s/n, Santander, Spain

    Domingo Gómez-Pérez & Ana Gómez

Authors
  1. Domingo Gómez-Pérez
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  2. Ana Gómez
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Corresponding author

Correspondence to Domingo Gómez-Pérez .

Editor information

Editors and Affiliations

  1. Otto-von-Guericke University, Magdeburg, Germany

    Kai-Uwe Schmidt

  2. Austrian Academy of Sciences, Linz, Austria

    Arne Winterhof

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Gómez-Pérez, D., Gómez, A. (2014). On the Lattice Structure of Inversive PRNG via the Additive Order. In: Schmidt, KU., Winterhof, A. (eds) Sequences and Their Applications - SETA 2014. SETA 2014. Lecture Notes in Computer Science(), vol 8865. Springer, Cham. https://doi.org/10.1007/978-3-319-12325-7_18

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  • DOI: https://doi.org/10.1007/978-3-319-12325-7_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12324-0

  • Online ISBN: 978-3-319-12325-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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