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Topic Area: Math

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1. Applied and Computational Mathematics Division Applied and Computational Mathematics Division: Summary of Activities for Fiscal Year 2012
Series: NIST Interagency/Internal Report (NISTIR)
Report Number: 7931
Topic: Math
Published: 5/9/2013
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 tech ...
http://nist.gov/manuscript-publication-search.cfm?pub_id=913423

2. HAZARDOUS CONTINUATION BACKWARD IN TIME IN NONLINEAR PARABOLIC EQUATIONS AND AN EXPERIMENT IN DEBLURRING NONLINEARLY BLURRED IMAGERY
Series: Journal of Research (NIST JRES)
Report Number: 118.010
Topic: Math
Published: 4/25/2013
Author: Alfred S Carasso
Abstract: Identifying sources of ground water pollution, and deblurring nanoscale imagery, as well as astronomical galaxy images, often involves the numerical computation of parabolic equations backward in time. However, very little computational experien ...
http://nist.gov/manuscript-publication-search.cfm?pub_id=912357

3. Alternative methods of latent fingerprint enhancement and metrics for comparing them
Series: NIST Interagency/Internal Report (NISTIR)
Report Number: 7910
Topic: Math
Published: 1/14/2013
Author: Alfred S Carasso
Abstract: Digital enhancements of latent fingerprints using Photoshop processing is the preferred methodology among law enforcement forensic experts. This report explores alternative enhancement methods that are independent of Photoshop, relying instead o ...
http://nist.gov/manuscript-publication-search.cfm?pub_id=912758

4. Class Numbers via 3-Isogenies and Elliptic Surfaces
Topic: Math
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 ...
http://nist.gov/manuscript-publication-search.cfm?pub_id=911885

5. Reduction Formulae for Products of Theta Functions
Series: Journal of Research (NIST JRES)
Report Number: 117.017
Topic: Math
Published: 11/6/2012
Author: Peter L. Walker
Abstract: In four cases it is already known that the product of two distinct Jacobian theta functions having the same variable z and the same nome q is a multiple of a single Jacobian theta function, with the multiple independent of z. The main purpose of t ...
http://nist.gov/manuscript-publication-search.cfm?pub_id=911334

6. 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://nist.gov/manuscript-publication-search.cfm?pub_id=908329

7. 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://nist.gov/manuscript-publication-search.cfm?pub_id=909087

8. 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://nist.gov/manuscript-publication-search.cfm?pub_id=910776

9. Isomorphism Classes of Edwards Curves over Finite Fields
Topic: Math
Published: 5/18/2012
Authors: Reza Farashahi, Dustin Moody, 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://nist.gov/manuscript-publication-search.cfm?pub_id=908630

10. Adaptive Preimage Resistance Analysis Revisited: Requirements, Subtleties and Implications
Topic: Math
Published: 4/16/2012
Authors: Dong H. Chang, Moti Yung
Abstract: In the last few years, the need to design new cryptographic hash functions has led to the intense study of when desired hash multi-properties are preserved or assured under compositions and domain extensions. In this area, it is important to identify ...
http://nist.gov/manuscript-publication-search.cfm?pub_id=906235