Algebraic Geometry for Coding Theory and Cryptography

IPAM, Los Angeles, CA, February 2016

Everett W. Howe, Kristin E. Lauter, Judy L. Walker (Herausgeber)

Buch | Hardcover

XV, 150 Seiten

2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-63930-7 (ISBN)

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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.

1. Representations of the Multicast Network Problem.- 2. Hypersurfaces in weighted projective spaces over finite fields with applications to coding theory.- 3. Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication.- 4. Locally recoverable codes from algebraic curves and surfaces.- 5. Variations of the McEliece Cryptosystem.

Erscheinungsdatum	11.01.2018
Reihe/Serie	Association for Women in Mathematics Series
Zusatzinfo	XV, 150 p. 8 illus., 2 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	421 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	affine and projective algebraic sets • Algebraic Geometry • codes with locality constraints • coding theory • data encryption • elliptic and hyperelliptic curves • Frobenius conjugates • isogenies for genus-2 curves • Mathematical Applications in Computer Science • Mathematical Modelling • Mathematics • mathematics and statistics • modular polynomials • network-constrained generator matrices • pairing-based cryptography • post-quantum cryptography • Public Key Cryptography • trace-zero subgroups
ISBN-10	3-319-63930-7 / 3319639307
ISBN-13	978-3-319-63930-7 / 9783319639307
Zustand	Neuware