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You searched on: Author: dustin moody Sorted by: title

Displaying records 1 to 10 of 19 records.
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1. An Asymptotically Optimal Structural Attack on the ABC Multivariate Encryption Scheme
Published: 10/3/2014
Authors: Dustin Moody, Ray A Perlner, Daniel C Smith-Tone
Abstract: Historically, multivariate public key cryptography has been less than successful at offering encryption schemes which are both secure and efficient. At PQCRYPTO '13 in Limoges, Tao, Diene, Tang, and Ding introduced a promising new multivariate e ...

2. Analogues of Vélu's formulas for Isogenies on Alternate Models of Elliptic Curves
Published: 9/9/2015
Authors: Dustin Moody, Daniel Shumow
Abstract: Isogenies are the morphisms between elliptic curves, and are accordingly a topic of interest in the subject. As such, they have been well-studied, and have been used in several cryptographic applications. Vélu's formulas show how to explicitly ...

3. Arithmetic Progressions on Edwards Curves
Published: 2/8/2011
Author: Dustin Moody
Abstract: We look at arithmetic progressions on elliptic curves known as Edwards curves. By an arithmetic progression on an elliptic curve, we mean that the x-coordinates of a sequence of rational points on the curve form an arithmetic progression. Previous ...

4. Arithmetic Progressions on Huff Curves
Published: 7/23/2012
Author: Dustin Moody
Abstract: 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. ...

5. Character sums determined by low degree isogenies of elliptic curves
Published: 7/25/2013
Authors: Dustin Moody, Christopher Rasmussen
Abstract: 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 <= 8.

6. Class Numbers via 3-Isogenies and Elliptic Surfaces
Published: 11/6/2012
Authors: Cam McLeman, Dustin Moody
Abstract: 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(\sqrt{p}). In this sense, this provides a higher-d ...

7. Division Polynomials for Jacobi Quartic Curves
Published: 6/13/2011
Author: Dustin Moody
Abstract: In this paper we fi nd division polynomials for Jacobi quartics. These curves are an alternate model for elliptic curves to the more common Weierstrass equation. Division polynomials for Weierstrass curves are well known, and the division polynomials ...

8. Elliptic Curves arising from Brahmagupta Quadrilaterals
Published: 8/1/2014
Authors: Farzali Izadi, Foad Khoshnam, Dustin Moody, Arman Zargar
Abstract: 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 ...

9. Families of Elliptic Curves with Rational 3-torsion
Published: 1/30/2012
Authors: Dustin Moody, Hongfeng Wu
Abstract: In this paper we look at three families of elliptic curves with rational 3-torsion over a finite field. These families include Hessian curves, twisted Hessian curves, and a new family we call generalized DIK curves. We find the number of Fq-isogeny ...

10. Improved Indifferentiability Security Bound for the JH Mode
Published: 3/22/2012
Authors: Dustin Moody, Souradyuti Paul, Daniel C Smith-Tone
Abstract: The JH hash function is one of the five fi nalists of the ongoing NIST SHA3 hash function competition. Despite several earlier attempts, and years of analysis, the indi fferentiability security bound of the JH mode has so far remained remarkably lo ...

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  • SP 250-XX: Calibration Services
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