Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves

  • Steven D. Galbraith
  • Xibin Lin
  • Michael Scott
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5479)


Efficiently computable homomorphisms allow elliptic curve point multiplication to be accelerated using the Gallant-Lambert- Vanstone (GLV) method. We extend results of Iijima, Matsuo, Chao and Tsujii which give such homomorphisms for a large class of elliptic curves by working over \({\mathbb F}_{p^2}\) and demonstrate that these results can be applied to the GLV method.

In general we expect our method to require about 0.75 the time of previous best methods (except for subfield curves, for which Frobenius expansions can be used). We give detailed implementation results which show that the method runs in between 0.70 and 0.84 the time of the previous best methods for elliptic curve point multiplication on general curves.


elliptic curves point multiplication GLV method isogenies 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Steven D. Galbraith
    • 1
  • Xibin Lin
    • 2
  • Michael Scott
    • 3
  1. 1.Mathematics Department, Royal HollowayUniversity of London, EghamSurreyUnited Kingdom
  2. 2.School of Mathematics and Computational ScienceSun Yat-Sen UniversityGuangzhouP.R. China
  3. 3.School of ComputingDublin City University, BallymunDublin 9Ireland

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