Double-and-Add with Relative Jacobian Coordinates

Björn Fay

Paper 2014/1014

Double-and-Add with Relative Jacobian Coordinates

Björn Fay

Abstract

One of the most efficient ways to implement a scalar multiplication on elliptic curves with precomputed points is to use mixed coordinates (affine and Jacobian). We show how to relax these preconditions by introducing relative Jacobian coordinates and give an algorithm to compute a scalar multiplication where the precomputed points can be given in Jacobian coordinates. We also show that this new approach is compatible with Meloni’s trick, which was already used in other papers to reduce the number of multiplications needed for a double-and-add step to 18 field multiplications.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint. MINOR revision.
Keywords: elliptic curve relative Jacobian coordinates co-Z coordinates scalar multiplication double-and-add precomputed points
Contact author(s): mail @ bfay de
History: 2014-12-26: received
Short URL: https://ia.cr/2014/1014
License: CC BY

BibTeX

@misc{cryptoeprint:2014/1014,
      author = {Björn Fay},
      title = {Double-and-Add with Relative Jacobian Coordinates},
      howpublished = {Cryptology {ePrint} Archive, Paper 2014/1014},
      year = {2014},
      url = {https://eprint.iacr.org/2014/1014}
}