- 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 review the current status of efforts to develop and deploy post-quantum cryptography on the Internet. Then we suggest specific ways in which quantum

Author(s)

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This Recommendation specifies the set of elliptic curves recommended for U.S. Government use. In addition to the previously recommended Weierstrass curves

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This standard specifies a suite of algorithms that can be used to generate a digital signature. Digital signatures are used to detect unauthorized modifications

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If large-scale quantum computers are ever built, they will compromise the security of many commonly used cryptographic algorithms. In response, the National

Author(s)

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

Created July 30, 2019, Updated December 8, 2022