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Matematicheskie Zametki, 2007, Volume 82, Issue 6, Pages 926–933
DOI: https://doi.org/10.4213/mzm4192 (Mi mzm4192) 		 
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
Full-text PDF (412 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm4192
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.
Received: 20.01.2007
English version:
Mathematical Notes, 2007, Volume 82, Issue 6, Pages 836–842
DOI: https://doi.org/10.1134/S0001434607110284
Bibliographic databases:
Document Type: Article
UDC: 511
Language: Russian
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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    • This publication is cited in the following 2 articles:
    1. 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
    2. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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