Differential Addition in generalized Edwards Coordinates

Benjamin Justus; Daniel Loebenberger

Paper 2009/523

Differential Addition in generalized Edwards Coordinates

Benjamin Justus and Daniel Loebenberger

Abstract

We use two parametrizations of points on elliptic curves in generalized Edwards form x^2 + y^2 = c^2 (1+d x^2 y^2) that omit the x-coordinate. The first parametrization leads to a differential addition formula that can be computed using 6M + 4S, a doubling formula using 1M+4S and a tripling formula using 4M + 7S. The second one yields a differential addition formula that can be computed using 5M+2S and a doubling formula using 5S. All formulas apply also for the case c <> 1 and arbitrary curve parameter d. This generalizes formulas from the literature for the special case c = 1. For both parametrizations the formula for recovering the missing X-coordinate is also provided.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): daniel @ bit uni-bonn de
History: 2010-03-04: revised; 2009-11-02: received; See all versions
Short URL: https://ia.cr/2009/523
License: CC BY

BibTeX

@misc{cryptoeprint:2009/523,
      author = {Benjamin Justus and Daniel Loebenberger},
      title = {Differential Addition in generalized Edwards Coordinates},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/523},
      year = {2009},
      url = {https://eprint.iacr.org/2009/523}
}