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On Pseudorandom Properties of Certain Sequences of Points on Elliptic Curve

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Abstract

In this paper we study the pseudorandom properties of sequences of points on elliptic curves. These sequences are constructed by taking linear combinations with small coefficients (e.g. \(-1,0,+1\)) of the orbit elements of a point with respect to a given endomorphism of the curve. We investigate the linear complexity and the distribution of these sequences. The result on the linear complexity answers a question of Igor Shparlinski.

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Acknowledgements

The author is partially supported by the Austrian Science Fund FWF Project F5511-N26 which is part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications” and by Hungarian National Foundation for Scientific Research, Grant No. K100291.

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Authors and Affiliations

  1. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstr. 69, 4040, Linz, Austria

    László Mérai

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  1. László Mérai
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Correspondence to László Mérai .

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Editors and Affiliations

  1. University of Rennes, Rennes, France

    Sylvain Duquesne

  2. University of Leuven, Leuven, Belgium

    Svetla Petkova-Nikova

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Mérai, L. (2016). On Pseudorandom Properties of Certain Sequences of Points on Elliptic Curve. In: Duquesne, S., Petkova-Nikova, S. (eds) Arithmetic of Finite Fields. WAIFI 2016. Lecture Notes in Computer Science(), vol 10064. Springer, Cham. https://doi.org/10.1007/978-3-319-55227-9_4

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  • DOI: https://doi.org/10.1007/978-3-319-55227-9_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55226-2

  • Online ISBN: 978-3-319-55227-9

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