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1. Arithmetic Progressions on Edwards Curves
Published: 2/8/2011
Author: Dustin Moody
Abstract: 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 ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=907596

2. Arithmetic Progressions on Huff Curves
Published: 7/23/2012
Author: Dustin Moody
Abstract: 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. ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908329

3. Character sums determined by low degree isogenies of elliptic curves
Published: 7/25/2013
Authors: Dustin Moody, Christopher Rasmussen
Abstract: We look at certain character sums determined by isogenies on elliptic curves over finite fields. We prove a congruence condition for character sums attached to arbitrary cyclic isogenies, and produce explicit formulas for isogenies of degree m <= 8.
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=909562

4. Class Numbers via 3-Isogenies and Elliptic Surfaces
Published: 11/6/2012
Authors: Cam McLeman, Dustin Moody
Abstract: 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(\sqrt{p}). In this sense, this provides a higher-d ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=911885

5. Division Polynomials for Jacobi Quartic Curves
Published: 6/13/2011
Author: Dustin Moody
Abstract: 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 ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908330

6. Families of Elliptic Curves with Rational 3-torsion
Published: 1/30/2012
Authors: Dustin Moody, Hongfeng Wu
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 ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=909543

7. Improved Indifferentiability Security Bound for the JH Mode
Published: 3/22/2012
Authors: Dustin Moody, Souradyuti Paul, Daniel C Smith-Tone
Abstract: 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 lo ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=910702

8. Improved Indifferentiability Security Bound for the JH Mode
Published: 5/16/2012
Authors: Dustin Moody, Daniel C Smith-Tone, Souradyuti Paul
Abstract: Indi fferentiability security of a hash mode of operation guarantees the mode's resistance against all generic attacks. It is also useful to establish the security of protocols that use hash functions as random functions. The JH hash function is one ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=911448

9. Indifferentiability Security of the Fast Widepipe Hash: Breaking the Birthday Barrier
Published: 12/2/2012
Authors: Dustin Moody, Daniel C Smith-Tone, Souradyuti Paul
Abstract: A hash function secure in the indi fferentiability framework is able to resist all generic attacks. Such hash functions also play a crucial role in the security of the protocols that use hash functions as random functions. The rate of a hash mode is ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=911449

10. Isomorphism Classes of Edwards Curves over Finite Fields
Published: 5/18/2012
Authors: Reza Farashahi, Dustin Moody, Hongfeng Wu
Abstract: 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 ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908630



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