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1. Arithmetic Progressions on Huff Curves
Topic: Math
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. ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908329

2. Evolutionary Construction of de Bruijn Sequences
Topic: Math
Published: 7/20/2012
Author: Meltem Sonmez Turan
Abstract: A binary de Bruijn sequence of order $n$ is a cyclic sequence of period $2^n$, in which each $n$-bit pattern appears exactly once. These sequences are commonly used in applications such as stream cipher design, pseudo-random number generation, 3-D pa ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=909087

3. Applied and Computational Mathematics Division. Summary of Activities for Fiscal Year 2011
Series: NIST Interagency/Internal Report (NISTIR)
Report Number: 7856
Topic: Math
Published: 5/18/2012
Author: Ronald F Boisvert
Abstract: This report summarizes the technical work of the Applied and Computational Sciences Division of NIST’s Information Technology Laboratory.Part I (Overview) provides a high-level overview of the Division’s activities, including highlights of technical ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=910776

4. Isomorphism classes of Edwards and twisted Edwards curves over finite fields
Topic: Math
Published: 5/18/2012
Authors: Dustin Moody, Reza Farashahi, Hongfeng Wu
Abstract: 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 ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908630

5. Improved Indifferentiability Security Bound for the JH Mode
Topic: Math
Published: 3/22/2012
Authors: Dustin Moody, Souradyuti Paul, Daniel Coy Smith
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 indifferentiability security bound of the JH mode has so far remained remarkably lo ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=910702

6. An Evaluation of Local Shape Descriptors for 3D Shape Retrieval
Series: NIST Interagency/Internal Report (NISTIR)
Report Number: 7812
Topic: Math
Published: 3/8/2012
Author: Sarah Y. Tang
Abstract: 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 t ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=909219

7. Families of elliptic curves with rational 3-torsion
Topic: Math
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 ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=909543

8. Fourier, Gauss, Fraunhofer, Porod and the Shape from Moments Problem
Topic: Math
Published: 1/17/2012
Author: Gregg M Gallatin
Abstract: 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 Gau ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=909668

9. Counting the Leaves of Trees
Topic: Math
Published: 12/19/2011
Authors: Brian Dale Cloteaux, Luis A. Valentin
Abstract: A number of important combinatorial counting problems can be reformulated into the problem of counting the number of leaf nodes on a tree. Since the basic leaf-counting problem is #P-complete, there is strong evidence that no polynomial time algorith ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908869

10. Linear Algebra and Sequential Importance Ssampling for Network Reliability
Topic: Math
Published: 12/11/2011
Authors: David G. Harris, Francis Sullivan, Isabel M Beichl
Abstract: The reliability polynomial of a graph gives the probability that a graph is connected as a function of the probability that each edge is connected. The coefficients of the reliability polynomial count the number of connected subgraphs of various size ...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=909109