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Mathematics & Statistics

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Displaying 226 - 250 of 473

Randomized methods for rank-deficient linear systems

February 13, 2015
Author(s)
Josef Sifuentes, Zydrunas Gimbutas, Leslie Greengard
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without additional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the eigenvectors of a matrix

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

A Binomial Approximation Method for the Ising Model

May 21, 2014
Author(s)
Isabel M. Beichl, Amanda A. Streib, Noah S. Streib, Francis Sullivan
A large portion of the complexity inherent to the Ising model can be captures with a trivial amount of computation. in this work, we support this claim by defining an approximation to the partition function and other thermodynamic quantities of the Ising

An Empirical Comparison of Combinatorial and Random Testing

April 4, 2014
Author(s)
Raghu N. Kacker, David R. Kuhn
Some conflicting results have been reported on the comparison between t-way combinatorial testing and random testing. In this paper, we report a new study that applies t-way and random testing to the Siemens suite. In particular, we investigate the

An Empirical Comparison of Combinatorial and Random Testing

April 1, 2014
Author(s)
Laleh Ghandehari, Jacek Czerwonka, Yu Lei, Soheil Shafiee, Raghu N. Kacker, D. Richard Kuhn
Some conflicting results have been reported on the comparison between t-way combinatorial testing and random testing. In this paper, we report a new study that applies t-way and random testing to the Siemens suite. In particular, we investigate the

Estimating Fault Detection Effectiveness

April 1, 2014
Author(s)
David R. Kuhn, Raghu N. Kacker, Yu Lei
[Poster] A t-way covering array can detect t-way faults, however they generally include other combinations beyond t-way as well. For example, a particular test set of all 5-way combinations is shown capable of detecting all seeded faults in a test program

Adaptive Composite B-Spline Grid Generation for Interactive 3D Visualizations

January 22, 2014
Author(s)
Bonita V. Saunders, Qiming Wang, Brian Antonishek
We describe an adaptive grid generation technique based on the composition of tensor product B-spline mappings, T and Phi, where Phi maps the unit square onto itself and T maps the unit square onto the desired physical domain. Variational methods are used

Constrained Hierarchical Control of a Diffusion Equation

December 31, 2013
Author(s)
Anthony J. Kearsley
In this paper, we consider the approximate pointwise control of a linear parabolic system with multiple targets. The location of the pointwise controls are constrained and we assume hierarchy among the objectives, Optimality conditions are derived for a

Fault Localization Based on Failure-Inducing Combinations

November 7, 2013
Author(s)
Raghu N. Kacker
Combinatorial testing has been shown to be a very effective testing strategy. After a failure is detected, the next task is to identify the actual fault that causes the failure. In this paper, we present an approach to fault localization that leverages the

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

Four Measures of Nonlinearity

June 23, 2013
Author(s)
Joan Boyar, Magnus Find, Rene Peralta
Cryptographic applications, such as hashing, block ciphers and stream ciphers, make use of functions which are simple by some criteria (such as circuit implementations), yet hard to invert almost everywhere. A necessary condition for the latter property is
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