Secure Elliptic Curves in Cryptography

  • Victor Gayoso MartínezEmail author
  • Lorena González-Manzano
  • Agustín Martín Muñoz


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 using 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 chapter presents the different types of elliptic curves used in Cryptography together with the best-known procedure for generating secure elliptic curves, Brainpool. The contribution is completed with the examination of the latest proposals regarding secure elliptic curves analyzed by the SafeCurves initiative.



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


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Victor Gayoso Martínez
    • 1
    Email author
  • Lorena González-Manzano
    • 2
  • Agustín Martín Muñoz
    • 1
  1. 1.Institute of Physical and Information Technologies (ITEFI)Spanish National Research Council (CSIC)MadridSpain
  2. 2.Computer Security Lab (COSEC)Universidad Carlos III de MadridLeganés, MadridSpain

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