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

Authors:
Steven D. Galbraith
Xibin Lin
Michael Scott
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URL: http://eprint.iacr.org/2008/194
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Abstract: 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.
BibTeX
@misc{eprint-2008-17871,
  title={Endomorphisms for faster elliptic curve cryptography on a large class of curves},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / elliptic curves, point multiplication, GLV method, Isogenies},
  url={http://eprint.iacr.org/2008/194},
  note={ mike@computing.dcu.ie 14120 received 2 May 2008, last revised 29 Aug 2008},
  author={Steven D. Galbraith and Xibin Lin and Michael Scott},
  year=2008
}