Elliptic Curves in Montgomery Form with B=1 and Their Low Order Torsion

Richard Moloney; Gary McGuire; Michael Markowitz

Paper 2009/213 Original: eprint.iacr.org/2009/213 ↗

Elliptic Curves in Montgomery Form with B=1 and Their Low Order Torsion

Richard Moloney

Gary McGuire

Michael Markowitz

Abstract

In this note we first characterize the class of Montgomery curves with B=1 by the simplicity of their transformation into short Weierstrass form and explicitly determine their torsion points of order 2 and 4. We then consider two ``verifiably random'' elliptic curves in the SECG standards and show that they are B=1 Montgomery curves that can also be simply transformed into Edwards form over their ground fields.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2009-11-26: last updated; 2009-05-26: published
Short URL: https://ia.cr/2009/213
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2009/213,
      author = {Richard Moloney and Gary McGuire and Michael Markowitz},
      title = {Elliptic Curves in Montgomery Form with B=1 and Their Low Order Torsion},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/213},
      year = {2009},
      url = {https://eprint.iacr.org/2009/213}
}