Efficient arithmetic on elliptic curves using a mixed Edwards-Montgomery representation

Wouter Castryck; Steven Galbraith; Reza Rezaeian Farashahi

Paper 2008/218

Efficient arithmetic on elliptic curves using a mixed Edwards-Montgomery representation

Wouter Castryck, Steven Galbraith, and Reza Rezaeian Farashahi

Abstract

From the viewpoint of x-coordinate-only arithmetic on elliptic curves, switching between the Edwards model and the Montgomery model is quasi cost-free. We use this observation to speed up Montgomery's algorithm, reducing the complexity of a doubling step from 2M + 2S to 1M + 3S for suitably chosen curve parameters.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): wouter castryck @ gmail com
History: 2008-06-03: last of 2 revisions; 2008-05-23: received; See all versions
Short URL: https://ia.cr/2008/218
License: CC BY

BibTeX

@misc{cryptoeprint:2008/218,
      author = {Wouter Castryck and Steven Galbraith and Reza Rezaeian Farashahi},
      title = {Efficient arithmetic on elliptic curves using a mixed Edwards-Montgomery representation},
      howpublished = {Cryptology ePrint Archive, Paper 2008/218},
      year = {2008},
      note = {\url{https://eprint.iacr.org/2008/218}},
      url = {https://eprint.iacr.org/2008/218}
}