Mathematical Notes

, Volume 82, Issue 5–6, pp 836–842 | Cite as

Some remarks on arithmetical properties of recursive sequences on elliptic curves over a finite field

  • V. E. Tarakanov
Article

Abstract

In connection with problems of information theory, we study arithmetical progressions constructed at the points of elliptic curves over a finite field. For certain types of such curves, we establish the distribution of the quadratic residues at the x-coordinates of the sequence of points corresponding to progressions if the elliptic curves is defined over a simple field. A description of the set of all progressions on elliptic curves over a finite field is also given.

Key words

Weierstrass normal form elliptic curve arithmetical progression finite field generator of pseudorandom numbers Sylow subgroup 

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Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • V. E. Tarakanov
    • 1
  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesRussia

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