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Search Publications by: Dustin Moody (Fed)

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Displaying 76 - 90 of 90

Class Numbers via 3-Isogenies and Elliptic Surfaces

November 6, 2012
Author(s)
Cam McLeman, Dustin Moody
We show that a character sum attached to a family of 3-isogenies defi ned on the fibers of a certain elliptic surface over Fp relates to the class number of the quadratic imaginary number field Q(\sqrtp}). In this sense, this provides a higher-dimensional

Arithmetic Progressions on Huff Curves

July 23, 2012
Author(s)
Dustin Moody
We look at arithmetic progressions on elliptic curves known as Huff curves. By an arithmetic progression on an elliptic curve, we mean that either the x or y-coordinates of a sequence of rational points on the curve form an arithmetic progression. Previous

Isomorphism Classes of Edwards Curves over Finite Fields

May 18, 2012
Author(s)
Reza Farashahi, Dustin Moody, Hongfeng Wu
Edwards curves are a new model for elliptic curves, which have attracted notice in cryptography. We give exact formulas for the number of F_q-isomorphism classes of Edwards curves and twisted Edwards curves. This answers a question recently asked by R

Improved Indifferentiability Security Bound for the JH Mode

March 22, 2012
Author(s)
Dustin Moody, Souradyuti Paul, Daniel C. Smith-Tone
The JH hash function is one of the five fi nalists of the ongoing NIST SHA3 hash function competition. Despite several earlier attempts, and years of analysis, the indi fferentiability security bound of the JH mode has so far remained remarkably low, only

Families of Elliptic Curves with Rational 3-torsion

January 30, 2012
Author(s)
Dustin Moody, Hongfeng Wu
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

Division Polynomials for Jacobi Quartic Curves

June 13, 2011
Author(s)
Dustin Moody
In this paper we fi nd division polynomials for Jacobi quartics. These curves are an alternate model for elliptic curves to the more common Weierstrass equation. Division polynomials for Weierstrass curves are well known, and the division polynomials we fi

Arithmetic Progressions on Edwards Curves

February 8, 2011
Author(s)
Dustin Moody
We look at arithmetic progressions on elliptic curves known as Edwards curves. By an arithmetic progression on an elliptic curve, we mean that the x-coordinates of a sequence of rational points on the curve form an arithmetic progression. Previous work has
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