Multi-Dimensional Montgomery Ladders for Elliptic Curves

Daniel R.  L.  Brown

Paper 2006/220

Multi-Dimensional Montgomery Ladders for Elliptic Curves

Daniel R. L. Brown

Abstract

Montgomery's ladder algorithm for elliptic curve scalar multiplication uses only the x-coordinates of points. Avoiding calculation of the y-coordinates saves time for certain curves. Montgomery introduced his method to accelerate Lenstra's elliptic curve method for integer factoring. Bernstein extended Montgomery's ladder algorithm by computing integer combinations of two points, thus accelerating signature verification over certain curves. This paper modifies and extends Bernstein's algorithm to integer combinations of two or more points.

Note: To be updated.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Keywords: ECC Montgomery ladder
Contact author(s): dbrown @ certicom com
History: 2006-06-30: revised; 2006-06-30: received; See all versions
Short URL: https://ia.cr/2006/220
License: CC BY

BibTeX

@misc{cryptoeprint:2006/220,
      author = {Daniel R.  L.  Brown},
      title = {Multi-Dimensional Montgomery Ladders for Elliptic Curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/220},
      year = {2006},
      url = {https://eprint.iacr.org/2006/220}
}