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International Workshop on Soft Computing Models in Industrial and Environmental Applications

Computational Intelligence in Security for Information Systems Conference

International Conference on EUropean Transnational Education

SOCO 2016, CISIS 2016, ICEUTE 2016: International Joint Conference SOCO’16-CISIS’16-ICEUTE’16 pp 658–667Cite as

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

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Part of the book series: Advances in Intelligent Systems and Computing ((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.

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References

  1. Koblitz, N.: Elliptic curve cryptosytems. Math. Comput. 48(177), 203–209 (1987)

    Article  MATH  Google Scholar 

  2. Miller, V.S.: Use of elliptic curves in cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 417–426. Springer, Heidelberg (1986). doi:10.1007/3-540-39799-X_31

    Chapter  Google Scholar 

  3. American National Standards Institute: Public Key Cryptography for the Financial Services Industry: Key Agreement and Key Transport Using Elliptic Curve Cryptography. ANSI X9.63 (2001)

    Google Scholar 

  4. IEEE: Standard specifications for public key cryptography. Institute of Electrical and Electronics Engineers, IEEE 1363 (2000)

    Google Scholar 

  5. National Institute of Standard and Technology: Digital Signature Standard (DSS). NIST FIPS 186-4 (2009). http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf

  6. Brainpool: ECC Brainpool standard curves and curve generation, version 1.0 (2005). http://www.ecc-brainpool.org/download/Domain-parameters.pdf

  7. Lochter, M., Merkle, J.: Elliptic Curve Cryptography (ECC) Brainpool standard curves and curve generation. Request for comments (RFC 5639), Internet Engineering Task Force (2010)

    Google Scholar 

  8. Bernstein, D.J., Lange, T.: SafeCurves (2014). http://safecurves.cr.yp.to/

  9. Menezes, A.J.: Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publishers, Boston (1993)

    Book  MATH  Google Scholar 

  10. Cohen, H., Frey, G.: Handbook of Elliptic and Hyperelliptic Curve Cryptography. Discrete Mathematics and its Applications. Chapman & Hall/CRC, Boca Raton (2006)

    MATH  Google Scholar 

  11. Bernstein, D.J.: Curve25519: new Diffie-Hellman speed records. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958, pp. 207–228. Springer, Heidelberg (2006). doi:10.1007/11745853_14

    Chapter  Google Scholar 

  12. National Security Agency: NSA Suite B cryptography (2009). http://www.nsa.gov/ia/programs/suiteb_cryptography/index.shtml

  13. Bundesamt für Sicherheit in der Informationstechnik: Elliptic curve cryptography. BSI TR-03111 version 2.0. (2012). https://www.bsi.bund.de/SharedDocs/Downloads/EN/BSI/Publications/TechGuidelines/TR03111/BSI-TR-03111_pdf.pdf?__blob=publicationFile

  14. Bernstein, D.J., Lange, T.: Explicit-formulas database (2016). https://hyperelliptic.org/EFD/

  15. Edwards, H.M.: A normal form for elliptic curves. Bull. Am. Math. Soc. 44, 393–422 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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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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Authors and Affiliations

  1. Department of Automatics, University of Alcalá, Madrid, Spain

    Raúl Durán Díaz

  2. Institute of Physical and Information Technologies (ITEFI), Spanish National Research Council (CSIC), Madrid, Spain

    Victor Gayoso Martínez, Luis Hernández Encinas & Agustin Martín Muñoz

Authors
  1. Raúl Durán Díaz
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  2. Victor Gayoso Martínez
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  3. Luis Hernández Encinas
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  4. Agustin Martín Muñoz
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Corresponding author

Correspondence to Victor Gayoso Martínez .

Editor information

Editors and Affiliations

  1. Computational Intelligence Group, University of the Basque Country (UPV/EHU), San Sebastian, Spain

    Manuel Graña

  2. University of the Basque Country, Vitoria, Spain

    José Manuel López-Guede

  3. Computational Intelligence Group, University of the Basque Country (UPV/EHU), San Sebastian, Spain

    Oier Etxaniz

  4. Department of Civil Engineering, University of Burgos, Burgos, Spain

    Álvaro Herrero

  5. University of Salamanca, Salamanca, Spain

    Héctor Quintián

  6. University of Salamanca, Salamanca, Spain

    Emilio Corchado

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Durán Díaz, R., Gayoso Martínez, V., Hernández Encinas, L., Martín Muñoz, A. (2017). A Study on the Performance of Secure Elliptic Curves for Cryptographic Purposes. In: Graña, M., López-Guede, J.M., Etxaniz, O., Herrero, Á., Quintián, H., Corchado, E. (eds) International Joint Conference SOCO’16-CISIS’16-ICEUTE’16. SOCO CISIS ICEUTE 2016 2016 2016. Advances in Intelligent Systems and Computing, vol 527. Springer, Cham. https://doi.org/10.1007/978-3-319-47364-2_64

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  • DOI: https://doi.org/10.1007/978-3-319-47364-2_64

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47363-5

  • Online ISBN: 978-3-319-47364-2

  • eBook Packages: EngineeringEngineering (R0)

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