Skew-Frobenius map on twisted  Edwards curve

Mingqiang  Wang; Xiaoyun Wang; Tao Zhan; Yuliang Zheng

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Paper 2010/005

Skew-Frobenius map on twisted Edwards curve

Mingqiang Wang, Xiaoyun Wang, Tao Zhan, and Yuliang Zheng

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.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): mqwang71 @ hotmail com
History: 2010-01-07: received
Short URL: https://ia.cr/2010/005
License: CC BY

BibTeX

@misc{cryptoeprint:2010/005,
      author = {Mingqiang  Wang and Xiaoyun Wang and Tao Zhan and Yuliang Zheng},
      title = {Skew-Frobenius map on twisted  Edwards curve},
      howpublished = {Cryptology ePrint Archive, Paper 2010/005},
      year = {2010},
      note = {\url{https://eprint.iacr.org/2010/005}},
      url = {https://eprint.iacr.org/2010/005}
}