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Publication Citation: Families of Elliptic Curves with Rational 3-torsion

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Author(s): Dustin Moody; Hongfeng Wu;
Title: Families of Elliptic Curves with Rational 3-torsion
Published: January 30, 2012
Abstract: In this paper we look at three families of elliptic curves with rational 3-torsion over a finite field. These families include Hessian curves, twisted Hessian curves, and a new family we call generalized DIK curves. We find the number of Fq-isogeny classes of each family, as well as the number of Fq-isomorphism classes of the generalized DIK curves. We also include some formulas for efficient computation on these curves, improving upon known results. In particular, we find better formulas for doubling and addition on the original tripling-oriented DIK curves and also for addition and tripling on elliptic curves with j-invariant 0.
Citation: Journal of Mathematical Cryptology
Volume: 5
Issue: 3-4
Pages: pp. 225 - 246
Keywords: Elliptic curves, Hessian curves, cryptography
Research Areas: Math
DOI: http://dx.doi.org/10.1515/jmc-2011-0013  (Note: May link to a non-U.S. Government webpage)
PDF version: PDF Document Click here to retrieve PDF version of paper (386KB)