Montgomery curves and the Montgomery ladder

Daniel J.  Bernstein; Tanja Lange

Paper 2017/293

Montgomery curves and the Montgomery ladder

Daniel J. Bernstein and Tanja Lange

Abstract

The Montgomery ladder is a remarkably simple method of computing scalar multiples of points on a broad class of elliptic curves. This article surveys a wide range of topics related to the Montgomery ladder, both from the historical perspective of Weierstrass curves and from the modern perspective of Edwards curves. New material includes a full proof of a complete constant-time ladder algorithm suitable for cryptographic applications.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. "Topics in Computational Number Theory inspired by Peter L. Montgomery", edited by Joppe W. Bos and Arjen K. Lenstra, to appear
Keywords: Montgomery curves Montgomery ladder Edwards curves
Contact author(s): authorcontact-montladder @ box cr yp to
History: 2017-04-03: received
Short URL: https://ia.cr/2017/293
License: CC BY

BibTeX

@misc{cryptoeprint:2017/293,
      author = {Daniel J.  Bernstein and Tanja Lange},
      title = {Montgomery curves and the Montgomery ladder},
      howpublished = {Cryptology {ePrint} Archive, Paper 2017/293},
      year = {2017},
      url = {https://eprint.iacr.org/2017/293}
}