A complete set of addition laws\\for incomplete Edwards curves

Daniel J.  Bernstein; Tanja Lange

Paper 2009/580

A complete set of addition laws\\for incomplete Edwards curves

Daniel J. Bernstein and Tanja Lange

Abstract

Edwards curves were the first curves shown to have a complete addition law. However, the completeness of the addition law depends on the curve parameters and even a complete Edwards curve becomes incomplete over a quadratic field extension. This paper covers arbitrary Edwards curves and gives a set of two addition laws that for any pair of input points P1, P2 produce the sum P1+P2.

Note: Fixed 2 typos.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. to appear in J. Number Theory
Keywords: Elliptic curves Edwards curves complete addition law points at infinity.
Contact author(s): tanja @ hyperelliptic org
History: 2010-10-06: revised; 2009-12-01: received; See all versions
Short URL: https://ia.cr/2009/580
License: CC BY

BibTeX

@misc{cryptoeprint:2009/580,
      author = {Daniel J.  Bernstein and Tanja Lange},
      title = {A complete set of addition laws\\for incomplete Edwards curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/580},
      year = {2009},
      url = {https://eprint.iacr.org/2009/580}
}