Paper 2009/213

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

Richard Moloney, Gary McGuire, and 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
Published elsewhere. Unknown where it was published
Keywords
elliptic curve cryptosystem
Contact author(s)
gary mcguire @ ucd ie
History
2009-11-26: revised
2009-05-26: received
See all versions
Short URL
https://ia.cr/2009/213
License
Creative Commons Attribution
CC BY

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},
      note = {\url{https://eprint.iacr.org/2009/213}},
      url = {https://eprint.iacr.org/2009/213}
}
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