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Algebraic Geometry for Coding Theory and Cryptography

IPAM, Los Angeles, CA, February 2016

  • Conference proceedings
  • © 2017

Overview

Editors:
  1. Everett W. Howe

    1. Center for Communications Research, San Diego, USA

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  2. Kristin E. Lauter

    1. Microsoft Research, One Microsoft Way, Redmond, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Judy L. Walker

    1. Department of Mathematics, University of Nebraska-Lincoln, Lincoln, USA

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  • Addresses new problems in coding theory and cryptography using algebraic geometry
  • Presents recent cross-disciplinary research from the February 2016 conference at IPAM

Part of the book series: Association for Women in Mathematics Series (AWMS, volume 9)

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Table of contents (5 papers)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Representations of the Multicast Network Problem

    • Sarah E. Anderson, Wael Halbawi, Nathan Kaplan, Hiram H. López, Felice Manganiello, Emina Soljanin et al.
    Pages 1-23

  3. Hypersurfaces in Weighted Projective Spaces Over Finite Fields with Applications to Coding Theory

    • Yves Aubry, Wouter Castryck, Sudhir R. Ghorpade, Gilles Lachaud, Michael E. O’Sullivan, Samrith Ram
    Pages 25-61

  4. Isogenies for Point Counting on Genus Two Hyperelliptic Curves with Maximal Real Multiplication

    • Sean Ballentine, Aurore Guillevic, Elisa Lorenzo García, Chloe Martindale, Maike Massierer, Benjamin Smith et al.
    Pages 63-94

  5. Locally Recoverable Codes from Algebraic Curves and Surfaces

    • Alexander Barg, Kathryn Haymaker, Everett W. Howe, Gretchen L. Matthews, Anthony Várilly-Alvarado
    Pages 95-127

  6. Variations of the McEliece Cryptosystem

    • Jessalyn Bolkema, Heide Gluesing-Luerssen, Christine A. Kelley, Kristin E. Lauter, Beth Malmskog, Joachim Rosenthal
    Pages 129-150
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Keywords

About this book

Covering topics in algebraic geometry, coding theory, and cryptography, this volume presents interdisciplinary group research completed for the February 2016 conference at the Institute for Pure and Applied Mathematics (IPAM) in cooperation with the Association for Women in Mathematics (AWM). The conference gathered research communities across disciplines to share ideas and problems in their fields and formed small research groups made up of graduate students, postdoctoral researchers, junior faculty, and group leaders who designed and led the projects. Peer reviewed and revised, each of this volume's five papers achieves the conference’s goal of using algebraic geometry to address a problem in either coding theory or cryptography. Proposed variants of the McEliece cryptosystem based on different constructions of codes, constructions of locally recoverable codes from algebraic curves and surfaces, and algebraic approaches to the multicast network coding problem are only some of the topics covered in this volume. Researchers and graduate-level students interested in the interactions between algebraic geometry and both coding theory and cryptography will find this volume valuable.

Editors and Affiliations

  • Center for Communications Research, San Diego, USA

    Everett W. Howe

  • Microsoft Research, One Microsoft Way, Redmond, USA

    Kristin E. Lauter

  • Department of Mathematics, University of Nebraska-Lincoln, Lincoln, USA

    Judy L. Walker

Bibliographic Information

  • Book Title: Algebraic Geometry for Coding Theory and Cryptography

  • Book Subtitle: IPAM, Los Angeles, CA, February 2016

  • Editors: Everett W. Howe, Kristin E. Lauter, Judy L. Walker

  • Series Title: Association for Women in Mathematics Series

  • DOI: https://doi.org/10.1007/978-3-319-63931-4

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2017

  • Hardcover ISBN: 978-3-319-63930-7Published: 16 November 2017

  • Softcover ISBN: 978-3-319-87675-7Published: 24 August 2018

  • eBook ISBN: 978-3-319-63931-4Published: 15 November 2017

  • Series ISSN: 2364-5733

  • Series E-ISSN: 2364-5741

  • Edition Number: 1

  • Number of Pages: XV, 150

  • Number of Illustrations: 6 b/w illustrations, 2 illustrations in colour

  • Topics: Algebraic Geometry, Mathematical Applications in Computer Science, Cryptology

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