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Mat. Zametki, 2007, Volume 82, Issue 6, Pages 926–933 (Mi mz4192)  

This article is cited in 2 scientific papers (total in 2 papers)

Some Remarks on Arithmetical Properties of Recursive Sequences on Elliptic Curves over a Finite Field

V. E. Tarakanov

Steklov Mathematical Institute, Russian Academy of Sciences

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.

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

DOI: https://doi.org/10.4213/mzm4192

Full text: PDF file (412 kB)
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English version:
Mathematical Notes, 2007, 82:6, 836–842

Bibliographic databases:

Document Type: Article
UDC: 511
Received: 20.01.2007

Citation: V. E. Tarakanov, “Some Remarks on Arithmetical Properties of Recursive Sequences on Elliptic Curves over a Finite Field”, Mat. Zametki, 82:6 (2007), 926–933; Math. Notes, 82:6 (2007), 836–842

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Chervyakov N.I., Babenko M.G., Deryabin M.A., Kucherov N.N., Kuchukova N.N., “The EC Sequences on Points of an Elliptic Curve Realization Using Neural Networks”, Proceedings of the Second International Afro-European Conference for Industrial Advancement AECIA 2015, Advances in Intelligent Systems and Computing, 427, eds. Abraham A., WegrzynWolska K., Hassanien A., Snasel V., Alimi A., Springer-Verlag Berlin, 2016, 147–154  crossref  isi  scopus
    2. Cherviakov N.I., Babenko M.G., Shabalina M.N., “Development of a Secure System For Distributed Data Storage and Processing in the Clouds Based on the Concept of Active Security in Rns”, Proceedings of 2017 Xx IEEE International Conference on Soft Computing and Measurements (Scm), IEEE, 2017, 558–560  crossref  isi  scopus
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