Journal of Cryptology

, Volume 24, Issue 3, pp 446–469

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

Authors

    • Mathematics DepartmentAuckland University
  • Xibin Lin
    • School of Mathematics and Computational ScienceSun Yat-Sen University
  • Michael Scott
    • School of ComputingDublin City University
Article

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

Abstract

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