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Search Publications by Dustin Moody

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Displaying 1 - 25 of 32

Elliptic Curves Arising from Triangular Numbers

Abhishek Juyal, Shiv D. Kumar, Dustin Moody
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

Status Report on the First Round of the NIST Post-Quantum Cryptography Standardization Process

Gorjan Alagic, Jacob M. Alperin-Sheriff, Daniel C. Apon, David A. Cooper, Quynh H. Dang, Carl A. Miller, Dustin Moody, Rene C. Peralta, Ray A. Perlner, Angela Y. Robinson, Daniel C. Smith-Tone, Yi-Kai Liu
The National Institute of Standards and Technology is in the process of selecting one or more public-key cryptographic algorithms through a public competition

Heron Quadrilaterals via Elliptic Curves

Farzali Izadi, Foad Khoshnam, Dustin Moody
A Heron quadrilateral is a cyclic quadrilateral with rational area. In this work, we establish a correspondence between Heron quadrilaterals and a family of

Geometric Progressions on Elliptic Curves

Abdoul Aziz Ciss, Dustin Moody
In this paper, we look at long geometric progressions on different model of elliptic curves, namely Weierstrass curves, Edwards and twisted Edwards curves, Huff

Arithmetic Progressions on Conics

Abdoul Aziz Ciss, Dustin Moody
In this paper, we look at long arithmetic progressions on conics. By an arithmetic progression on a curve, we mean the existence of rational points on the curve

Key Recovery Attack on Cubic Simple Matrix Encryption

Ray A. Perlner, Dustin Moody, Daniel C. Smith-Tone
In the last few years multivariate public key cryptography has experienced an infusion of new ideas for encryption. Among these new strategies is the ABC Simple

Report on Post-Quantum Cryptography

Lidong Chen, Stephen P. Jordan, Yi-Kai Liu, Dustin Moody, Rene C. Peralta, Ray A. Perlner, Daniel C. Smith-Tone
In recent years, there has been a substantial amount of research on quantum computers - machines that exploit quantum mechanical phenomena to solve mathematical

Vulnerabilities of "McEliece in the World of Escher"

Dustin Moody, Ray A. Perlner
Recently, Gligoroski et al. proposed code-based encryption and signature schemes using list decoding, blockwise triangular private keys, and a nonuniform error

Report on Pairing-based Cryptography

Dustin Moody, Rene C. Peralta, Ray A. Perlner, Andrew R. Regenscheid, Allen L. Roginsky, Lidong Chen
This report summarizes study results on pairing-based cryptography. The main purpose of the study is to form NIST’s position on standardizing and recommending

Elliptic Curves arising from Brahmagupta Quadrilaterals

Farzali Izadi, Foad Khoshnam, Dustin Moody, Arman Zargar
A Brahmagupta quadrilateral is a cyclic quadrilateral whose sides, diagonals, and area are all integer values. In this article, we characterize the notions of

On integer solutions of x^4+y^4-2z^4-2w^4=0

Dustin Moody, Arman S. Zargar
In this article, we study the quartic Diophantine nist-equation x^4+y^4-2z^4-2w^4=0. We find non-trivial integer solutions. Furthermore, we show that when a

Class Numbers via 3-Isogenies and Elliptic Surfaces

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