- 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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We study various properties of the family of elliptic curves x+ 1/x+y+ 1/y+t = 0, which is isomorphic to the Weierstrass curve E_t: Y^2=X(X^2+(t^2/4-2)X+1)

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Elliptic curves are typically defined by Weierstrass equations. Given a kernel, the well-known V Velu's formula shows how to explicitly write down an isogeny

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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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In 2013, Tao et al. introduced the ABC Simple Matrix Scheme for Encryption, a multivariate public key encryption scheme. The scheme boasts great efficiency in

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This article introduces the NIST Post-Quantum Cryptography standardization process. We highlight the challenges, discuss the mathematical problems in the

Created July 30, 2019, Updated June 15, 2021