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International Conference on Parallel Processing and Applied Mathematics

PPAM 2013: Parallel Processing and Applied Mathematics pp 96–105Cite as

Engineering Nonlinear Pseudorandom Number Generators

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8384))

Abstract

In the era of multi and many-core processors, computer simulations increasingly require parallel, small and fast pseudorandom number generation. Although linear generators lend themselves to a simpler evaluation that ensures favorable properties like guaranteed period, they may adversely affect the result of simulations or be quite large. Conversely, nonlinear generators may provide apparently random sequences, but are either very slow or difficult to analyze regarding their period.

This is the case of our previous functions, Tyche and Tyche-i. Despite being among the fastest in their class and having average periods of \(2^{127}\), they may contain smaller cycles of arbitrary size. To overcome this limitation, in this paper we explore different forms of counters impacting either the state or the speed of the generator. We also introduce two number-theoretic generators that use \(2 \times 127\) bits for periods of \(2^{116}\) and \(2^{125}\) and low to moderate computational costs. We experimentally demonstrate the efficiency of our new generators and observe that they exchange speed for period guarantees in a tradeoff that seems widespread in state-of-the-art random number generators.

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Notes

  1. 1.

    Most known efficient formulas for various curves and point representations are found in the Explicit-Formulas Database: http://hyperelliptic.org/EFD/index.html

  2. 2.

    The order of Montgomery curves is always a multiple of 4.

  3. 3.

    Counters that add an odd constant different from 1 are often known as Weyl generators.

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Acknowledgments

This work has been supported by the project CMU-PT/RNQ/0015/2009, TRONE — Trustworthy and Resilient Operations in a Network Environment.

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Authors and Affiliations

  1. CISUC, Department of Informatics Engineering, University of Coimbra, Coimbra, Portugal

    Samuel Neves & Filipe Araujo

Authors
  1. Samuel Neves
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  2. Filipe Araujo
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Correspondence to Samuel Neves .

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Editors and Affiliations

  1. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Department of Computer Science, Knoxville, Tennessee, USA

    Jack Dongarra

  3. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

  4. Technical University of Denmark Informatics and Mathematical Modelling, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Neves, S., Araujo, F. (2014). Engineering Nonlinear Pseudorandom Number Generators. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2013. Lecture Notes in Computer Science(), vol 8384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55224-3_10

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  • DOI: https://doi.org/10.1007/978-3-642-55224-3_10

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  • Print ISBN: 978-3-642-55223-6

  • Online ISBN: 978-3-642-55224-3

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