Algebraic Geometry for Coding Theory and Cryptography

IPAM, Los Angeles, CA, February 2016

  • Everett W. Howe
  • Kristin E. Lauter
  • Judy L. Walker
Conference proceedings

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

Table of contents

  1. Front Matter
    Pages i-xv
  2. Sarah E. Anderson, Wael Halbawi, Nathan Kaplan, Hiram H. López, Felice Manganiello, Emina Soljanin et al.
    Pages 1-23
  3. Yves Aubry, Wouter Castryck, Sudhir R. Ghorpade, Gilles Lachaud, Michael E. O’Sullivan, Samrith Ram
    Pages 25-61
  4. Sean Ballentine, Aurore Guillevic, Elisa Lorenzo García, Chloe Martindale, Maike Massierer, Benjamin Smith et al.
    Pages 63-94
  5. Alexander Barg, Kathryn Haymaker, Everett W. Howe, Gretchen L. Matthews, Anthony Várilly-Alvarado
    Pages 95-127
  6. Jessalyn Bolkema, Heide Gluesing-Luerssen, Christine A. Kelley, Kristin E. Lauter, Beth Malmskog, Joachim Rosenthal
    Pages 129-150

About these proceedings

Introduction

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.

Keywords

Algebraic geometry network-constrained generator matrices isogenies for genus-2 curves pairing-based cryptography coding theory trace-zero subgroups codes with locality constraints affine and projective algebraic sets Frobenius conjugates elliptic and hyperelliptic curves public key cryptography post-quantum cryptography modular polynomials

Editors and affiliations

  • Everett W. Howe
    • 1
  • Kristin E. Lauter
    • 2
  • Judy L. Walker
    • 3
  1. 1.Center for Communications ResearchSan DiegoUSA
  2. 2.Microsoft ResearchOne Microsoft WayRedmondUSA
  3. 3.Department of MathematicsUniversity of Nebraska-LincolnLincolnUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-63931-4
  • Copyright Information The Author(s) and the Association for Women in Mathematics 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-63930-7
  • Online ISBN 978-3-319-63931-4
  • Series Print ISSN 2364-5733
  • Series Online ISSN 2364-5741
  • About this book