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Mathematics & Statistics

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Displaying 476 - 500 of 872

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

Combinatorial Testing of ACTS: A Case Study

April 21, 2012
Author(s)
Mehra N. Borazjany, Linbin Yu, Yu Lei, Raghu N. Kacker, D. Richard Kuhn
In this paper we present a case study of applying combinatorial testing to test a combinatorial test generation tool called ACTS. The purpose of this study is two-fold. First, we want to gain experience and insights about how to apply combinatorial testing

Improved Indifferentiability Security Bound for the JH Mode

March 22, 2012
Author(s)
Dustin Moody, Souradyuti Paul, Daniel C. Smith-Tone
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 low, only

An Evaluation of Local Shape Descriptors for 3D Shape Retrieval

March 8, 2012
Author(s)
Sarah Y. Tang
As the usage of 3D models increases, so does the importance of developing accurate 3D shape retrieval algorithms. Most prominently, shape descriptors are used to describe the geometric and topological properties of objects and compared to determine two

Light a Single Candle: Studying Supernovae

March 1, 2012
Author(s)
Dianne M. O'Leary, Bert W. Rust
At peak luminosity, Type Ia supernovae can be even brighter than their parent galaxies, and their light curves display a very uniform and regular behavior. This makes them excellent candidates for a role as standard candles in measuring the distances to

Families of Elliptic Curves with Rational 3-torsion

January 30, 2012
Author(s)
Dustin Moody, Hongfeng Wu
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 classes

Fourier, Gauss, Fraunhofer, Porod and the Shape from Moments Problem

January 17, 2012
Author(s)
Gregg M. Gallatin
We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss' law and evaluated explicitly for polygons in two dimensions, polyhedra three dimensions, etc. We also show how this combination of Fourier and Gauss can