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

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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.

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References

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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
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  2. O. V. Tsygankova
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Correspondence to A. V. Bessalov.

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

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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

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

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