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A Study on the Performance of Secure Elliptic Curves for Cryptographic Purposes

  • Raúl Durán Díaz
  • Victor Gayoso MartínezEmail author
  • Luis Hernández Encinas
  • Agustin Martín Muñoz
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 527)

Abstract

Elliptic Curve Cryptography (ECC) is a branch of public-key cryptography based on the arithmetic of elliptic curves. In the short life of ECC, most standards have proposed curves defined over prime finite fields satisfying the curve equation in the short Weierstrass form. However, some researchers have started to propose as a more secure alternative the use of Edwards and Montgomery elliptic curves, which could have an impact in current ECC deployments. This contribution evaluates the performance of the three types of elliptic curves using some of the examples provided by the initiative SafeCurves and a Java implementation developed by the authors, which allows us to offer some conclusions about this topic.

Keywords

Edwards curves Elliptic curve cryptography Java Montgomery curves Point arithmetic Weierstrass curves 

Notes

Acknowledgements

This work has been supported by the European Union FEDER funds distributed through Ministerio de Economía y Competitividad (Spain) under the project TIN2014-55325-C2-1-R (ProCriCiS), and through Comunidad de Madrid (Spain) under the project S2013/ICE-3095-CM (CIBERDINE).

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© Springer International Publishing AG 2017

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (http://creativecommons.org/licenses/by-nc/2.5/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Authors and Affiliations

  • Raúl Durán Díaz
    • 1
  • Victor Gayoso Martínez
    • 2
    Email author
  • Luis Hernández Encinas
    • 2
  • Agustin Martín Muñoz
    • 2
  1. 1.Department of AutomaticsUniversity of AlcaláMadridSpain
  2. 2.Institute of Physical and Information Technologies (ITEFI)Spanish National Research Council (CSIC)MadridSpain

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