Paper 2014/027

Twisting Edwards curves with isogenies

Mike Hamburg

Abstract

Edwards’ elliptic curve form is popular in modern cryptographic implementations thanks to their fast, strongly unified addition formulas. Twisted Edwards curves with a = −1 are slightly faster, but their addition formulas are not complete over Fp where p ≡ 3 (mod 4). In this short note, we propose that designers specify Edwards curves, but implement scalar multiplications and the like using an isogenous twisted Edwards curve.

Metadata
Available format(s)
PDF
Category
Implementation
Publication info
Preprint. MINOR revision.
Keywords
twisted Edwards curvesisogeny
Contact author(s)
mike @ shiftleft org
History
2014-01-10: received
Short URL
https://ia.cr/2014/027
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2014/027,
      author = {Mike Hamburg},
      title = {Twisting Edwards curves with isogenies},
      howpublished = {Cryptology ePrint Archive, Paper 2014/027},
      year = {2014},
      note = {\url{https://eprint.iacr.org/2014/027}},
      url = {https://eprint.iacr.org/2014/027}
}
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