Journal of Cryptology

, Volume 24, Issue 3, pp 446–469

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


DOI: 10.1007/s00145-010-9065-y

Cite this article as:
Galbraith, S.D., Lin, X. & Scott, M. J Cryptol (2011) 24: 446. doi:10.1007/s00145-010-9065-y


Efficiently computable homomorphisms allow elliptic curve point multiplication to be accelerated using the Gallant–Lambert–Vanstone (GLV) method. Iijima, Matsuo, Chao and Tsujii gave such homomorphisms for a large class of elliptic curves by working over \({\mathbb{F}}_{p^{2}}\). We extend their results and demonstrate that they 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 0.83 the time of the previous best methods for elliptic curve point multiplication on general curves.

Key words

Elliptic curvesPoint multiplicationGLV methodMultiexponentiationIsogenies

Copyright information

© International Association for Cryptologic Research 2010

Authors and Affiliations

  • Steven D. Galbraith
    • 1
  • Xibin Lin
    • 2
  • Michael Scott
    • 3
  1. 1.Mathematics DepartmentAuckland UniversityAucklandNew Zealand
  2. 2.School of Mathematics and Computational ScienceSun Yat-Sen UniversityGuangzhouP.R. China
  3. 3.School of ComputingDublin City UniversityDublin 9Ireland