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Paper: Skew-Frobenius map on twisted Edwards curve

Authors:
Mingqiang Wang
Xiaoyun Wang
Tao Zhan
Yuliang Zheng
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URL: http://eprint.iacr.org/2010/005
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Abstract: In this paper, we consider the Frobenius endomorphism on twisted Edwards curve and give the characteristic polynomial of the map. Applying the Frobenius endomorphism on twisted Edwards curve, we construct a skew-Frobenius map defined on the quadratic twist of an twisted Edwards curve. Our results show that the Frobenius endomorphism on twisted Edwards curve and the skew-Frobenius endomorphism on quadratic twist of an twisted Edwards curve can be exploited to devise fast point multiplication algorithm that do not use any point doubling. As an application, the GLV method can be used for speeding up point multiplication on twisted Edwards curve.
BibTeX
@misc{eprint-2010-22906,
  title={Skew-Frobenius map on twisted  Edwards curve},
  booktitle={IACR Eprint archive},
  keywords={implementation /},
  url={http://eprint.iacr.org/2010/005},
  note={ mqwang71@hotmail.com 14615 received 6 Jan 2010},
  author={Mingqiang  Wang and Xiaoyun Wang and Tao Zhan and Yuliang Zheng},
  year=2010
}