### 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.

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

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},
note = {\url{https://eprint.iacr.org/2006/220}},
url = {https://eprint.iacr.org/2006/220}
}

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