Twisting Edwards curves with isogenies

Mike Hamburg

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 curves isogeny
Contact author(s): mike @ shiftleft org
History: 2014-01-10: received
Short URL: https://ia.cr/2014/027
License: 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},
      url = {https://eprint.iacr.org/2014/027}
}