U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Search Publications by: Dustin Moody (Fed)

Search Title, Abstract, Conference, Citation, Keyword or Author
Displaying 26 - 50 of 55

Securing Tomorrow's Information through Post-Quantum Cryptography

February 27, 2018
Author(s)
Dustin Moody, 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 problems that are difficult or intractable for conventional computers. If large-scale quantum

Heron Quadrilaterals via Elliptic Curves

August 5, 2017
Author(s)
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 elliptic curves of the form y^2=x^3+\alpha x^2-n^2 x. This correspondence generalizes the notions

Geometric Progressions on Elliptic Curves

June 13, 2017
Author(s)
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 curves and general quartics curves. By a geometric progression on an elliptic curve, we mean

Arithmetic Progressions on Conics

December 27, 2016
Author(s)
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 whose x-coordinates are in arithmetic progression. We revisit arithmetic progressions on the

High Rank Elliptic Curves with Torsion Z/4Z induced by Kihara's Curves

October 5, 2016
Author(s)
Foad Khoshnam, Dustin Moody
Working over the field Q(t), Kihara constructed an elliptic curve with torsion group Z/4Z and five independent rational points, showing the rank is at least five. Following his approach, we give a new infinite family of elliptic curves with torsion group Z

Key Recovery Attack on Cubic Simple Matrix Encryption

August 11, 2016
Author(s)
Ray Perlner, Dustin Moody, Daniel 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 Matrix family of encryption schemes which utilize the structure of a large matrix algebra to

Report on Post-Quantum Cryptography

April 28, 2016
Author(s)
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 problems that are difficult or intractable for conventional computers. If large-scale quantum

Vulnerabilities of "McEliece in the World of Escher"

March 3, 2016
Author(s)
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 pattern based on "generalized error sets." The general approach was referred to as "McEliece in

Improved Indifferentiability Security Bound for the JH Mode

February 15, 2015
Author(s)
Dustin Moody, Daniel C. Smith-Tone, Souradyuti Paul
Indifferentiability 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 was one of the

Report on Pairing-based Cryptography

February 3, 2015
Author(s)
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 pairing-based cryptography schemes currently published in research literature and standardized in

Elliptic Curves arising from Brahmagupta Quadrilaterals

August 1, 2014
Author(s)
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 Brahmagupta, introduced by K. R. S. Sastry, by means of elliptic curves. Motivated by these

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

September 18, 2013
Author(s)
Dustin Moody, Arman S. Zargar
In this article, we study the quartic Diophantine equation x^4+y^4-2z^4-2w^4=0. We find non-trivial integer solutions. Furthermore, we show that when a solution has been found, a series of other solutions can be derived. We do so using two different

Character sums determined by low degree isogenies of elliptic curves

July 25, 2013
Author(s)
Dustin Moody, Christopher Rasmussen
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

Class Numbers via 3-Isogenies and Elliptic Surfaces

November 6, 2012
Author(s)
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 quadratic imaginary number field Q(\sqrtp}). In this sense, this provides a higher-dimensional

Arithmetic Progressions on Huff Curves

July 23, 2012
Author(s)
Dustin Moody
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. Previous

Isomorphism Classes of Edwards Curves over Finite Fields

May 18, 2012
Author(s)
Reza Farashahi, Dustin Moody, Hongfeng Wu
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 by R