Paper 2008/194

Endomorphisms for faster elliptic curve cryptography on a large class of curves

Steven D. Galbraith, Xibin Lin, and Michael Scott


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 quadratic extensions and demonstrate that these results can be applied to the GLV method. Our implementation runs in between 0.70 and 0.84 the time of the previous best methods for elliptic curve point multiplication on curves without small class number complex multiplication. Further speedups are possible when using more special curves.

Note: Full Version of Eurocrypt 2009 paper

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Eurocrypt 2009
elliptic curvespoint multiplicationGLV methodIsogenies
Contact author(s)
mike @ computing dcu ie
2009-10-29: last of 4 revisions
2008-05-03: received
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      author = {Steven D.  Galbraith and Xibin Lin and Michael Scott},
      title = {Endomorphisms for faster elliptic curve cryptography on a large class of curves},
      howpublished = {Cryptology ePrint Archive, Paper 2008/194},
      year = {2008},
      note = {\url{}},
      url = {}
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