## Cryptology ePrint Archive: Report 2009/213

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

Richard Moloney and 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.

Category / Keywords: public-key cryptography / elliptic curve cryptosystem

Date: received 16 May 2009, last revised 26 Nov 2009

Contact author: gary mcguire at ucd ie

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2009/213

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