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A study on the performance of secure elliptic curves for cryptographic purposes

Edwards curves
elliptic curve cryptography
java
Montgomery curves
point arithmetic
Weierstrass curves
R. Durán Díaz, V. Gayoso Martínez, L. Hernández Encinas, and A. Martín Muñoz
International Joint Conference SOCO'16-CISIS'16-ICEUTE'16 - Advances in Intelligent Systems and Computing 527, 658-667 San Sebastián (Spain), october 19-21, 2016
http://dx.doi.org/10.1007/978-3-319-47364-2_64

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 securer 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.

Acknowledgements

This work has been supported by the European Union FEDER funds distributed through Ministerio de Econom´ıa 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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