- Elliptic Curves,
- Cryptography,
- Pairings, and
- Computational Number Theory.

C. Rasmussen, D. Moody, Character sums determined by low degree isogenies of elliptic curves, to appear in Rocky Mountain J. Math (2013).

D. Moody, A. Zargar, On Integer solutions of x

^{4}+y^{4}-2z^{4}-2w^{4}=0, No. Theory and Discrete Math. 19 (1), pp. 37-43 (2013).- C. McLeman, D. Moody, Class numbers via 3-isogenies and elliptic surfaces, Int. J. Number Theory, 9 (01), pp. 125-137 (2012).
- R. Farashahi, D. Moody, H. Wu, Isomorphism classes of Edwards curves over finite fields, Finite Fields Appl. 18 (3), pp. 597-612 (2012).
- D. Moody, S. Paul, D. Smith-Tone, Improved indifferentiability security bound for the JH mode, proceedings of NIST's 3rd SHA-3 Candidate Conference, (2012).
- D. Moody, H. Wu, Families of elliptic curves with rational 3-torsion , J. Math. Cryptol. 5 (3-4), pp. 225-246 (2011).
- D. Moody, Computing isogeny volcanoes of composite degree, App. Math. Comp. 218 (9), pp. 5249-5258 (2011).
- D. Moody, Mean value formulas for twisted Edwards curves, J. Comb. Number Theory, 3 (2), pp. 103-112 (2011).
- D. Moody, Arithmetic progressions on Huff curves, Ann. Math. Inform. 38, pp. 111-116 (2011).
- D. Moody, Division polynomials for Jacobi quartic curves, proceedings of ISSAC (2011).
- D. Moody, Using 5-isogenies to quintuple points on elliptic curves, Inform. Process. Lett., 111 (7), pp. 314-317 (2011).
- D. Moody. Arithmetic progressions on Edwards curves, J. Integer Seq. (14) Article 11.1.7, (2011).
- D. Moody. The Diffie-Hellman problem and generalization of Verheul�s theorem, Des. Codes Cryptogr. (52) pp 381--392 (2009).
- D. Moody. The Diffie-Hellman problem and generalization of Verheul�s theorem, PhD dissertation (2008).
- D. Moody. The Beurling-Selberg extremal function, BYU Master�s Project (2003).

D. Moody, D. Shumow. Isogenies on Edwards and Huff curves, (submitted 2011)

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, Amadou Tall

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Abhishek Juyal, Shiv D. Kumar,

We study the Legendre family of elliptic curves E_t : y^2 = x(x − 1)(x − ∆t), parametrized by triangular numbers ∆t = t(t + 1)/2. We prove that the rank of E_t

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The National Institute of Standards and Technology is in the process of selecting one or more public-key cryptographic algorithms through a public competition

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, Larry Feldman, Gregory A. Witte

In recent years, there has been a substantial amount of research on quantum computers - machines that exploit quantum mechanical phenomena to solve mathematical

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A Heron quadrilateral is a cyclic quadrilateral with rational area. In this work, we establish a correspondence between Heron quadrilaterals and a family of

Created July 30, 2019