Paper 2017/212
Montgomery curves and their arithmetic: The case of large characteristic fields
Craig Costello and Benjamin Smith
Abstract
Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstra's ECM factorization algorithm. Since then, his curves and the algorithms associated with them have become foundational in the implementation of elliptic curve cryptosystems. This article surveys the theory and cryptographic applications of Montgomery curves over non-binary finite fields, including Montgomery's x-only arithmetic and Ladder algorithm, x-only Diffie--Hellman, y-coordinate recovery, and 2-dimensional and Euclidean differential addition chains such as Montgomery's PRAC algorithm.
Metadata
- Available format(s)
-
PDF
- Publication info
- Published elsewhere. Journal of Cryptographic Engineering
- Keywords
- Montgomery curveMontgomery ladderelliptic curve cryptographyscalar multiplication
- Contact author(s)
-
craigco @ microsoft com
smith @ lix polytechnique fr - History
- 2017-11-14: revised
- 2017-03-02: received
- See all versions
- Short URL
- https://ia.cr/2017/212
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2017/212,
author = {Craig Costello and Benjamin Smith},
title = {Montgomery curves and their arithmetic: The case of large characteristic fields},
howpublished = {Cryptology {ePrint} Archive, Paper 2017/212},
year = {2017},
url = {https://eprint.iacr.org/2017/212}
}
