Skip to main content
SpringerLink
Log in

Interrelation of families of points of high order on the Edwards curve over a prime field

  • Information Protection
  • Published:
Problems of Information Transmission Aims and scope Submit manuscript

Abstract

We propose a modification of the addition law on the Edwards curve over a prime field. We prove three theorems on properties of coordinates of high-order points and on a degenerate pair of twisted curves. We propose an algorithm for reconstructing all unknown points kP of the Edwards curve when only 1/8 of the points are known.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Edwards, H.M., A Normal Form for Elliptic Curves, Bull. Amer. Math. Soc. (N.S.), 2007, vol. 44, no. 3, pp. 393–422.

    Article  MATH  MathSciNet  Google Scholar 

  2. Bernstein, D.J. and Lange, T., Faster Addition and Doubling on Elliptic Curves, Advances in Cryptology-ASIACRYPT’2007 (Proc. 13th Int. Conf. on the Theory and Application of Cryptology and Information Security, Kuching, Malaysia, Dec. 2–6, 2007), Kurosawa, K., Ed., Lect. Notes Comp. Sci., vol. 4833, Berlin: Springer, 2007, pp. 29–50.

    Article  MathSciNet  Google Scholar 

  3. Bessalov, A.V., The Number of Isomorphisms and Torsion Pairs of Edwards Curves over a Prime Field, Radiotekhnika, 2011, vol. 167, pp. 203–208.

    Google Scholar 

  4. Bessalov, A.V., Dividing a Point by Two for the Edwards Curve over a Prime Field, Prikl. Radioelektron., 2013, vol. 12, no. 2, pp. 278–279.

    MathSciNet  Google Scholar 

  5. Bessalov, A.V., Kriptosistemy na ellipticheskikh krivykh (Cryptosystems on Elliptic Curves), Kyiv: Politekhnika, 2004.

    Google Scholar 

  6. Bessalov, A.V., Constructing an Edwards Curve Based on an Isomorphic Canonical-Form Elliptic Curve, Prikl. Radioelektron., 2014, vol. 13, no. 3, pp. 286–289.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Physics and Technology, National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kyiv, Ukraine

    A. V. Bessalov & O. V. Tsygankova

Authors
  1. A. V. Bessalov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. V. Tsygankova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Bessalov.

Additional information

Original Russian Text © A.V. Bessalov, O.V. Tsygankova, 2015, published in Problemy Peredachi Informatsii, 2015, Vol. 51, No. 4, pp. 92–98.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bessalov, A.V., Tsygankova, O.V. Interrelation of families of points of high order on the Edwards curve over a prime field. Probl Inf Transm 51, 391–397 (2015). https://doi.org/10.1134/S0032946015040080

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0032946015040080

Keywords

Search

Navigation