Download E-books Algebraic Geometry in Coding Theory and Cryptography PDF

By Harald Niederreiter

This textbook equips graduate scholars and complicated undergraduates with the mandatory theoretical instruments for using algebraic geometry to info concept, and it covers fundamental purposes in coding idea and cryptography. Harald Niederreiter and Chaoping Xing give you the first exact dialogue of the interaction among nonsingular projective curves and algebraic functionality fields over finite fields. This interaction is key to investigate within the box at the present time, but formerly no different textbook has featured whole proofs of it. Niederreiter and Xing hide classical functions like algebraic-geometry codes and elliptic-curve cryptosystems in addition to fabric now not handled by way of different books, together with function-field codes, electronic nets, code-based public-key cryptosystems, and frameproof codes. Combining a scientific improvement of conception with a vast collection of real-world functions, this is often the main complete but obtainable creation to the sector available.

  • Introduces graduate scholars and complicated undergraduates to the principles of algebraic geometry for purposes to info idea
  • Provides the 1st precise dialogue of the interaction among projective curves and algebraic functionality fields over finite fields
  • Includes purposes to coding conception and cryptography
  • Covers the newest advances in algebraic-geometry codes
  • Features purposes to cryptography no longer handled in different books

Show description

Read or Download Algebraic Geometry in Coding Theory and Cryptography PDF

Best Algebraic Geometry books

The Many Facets of Geometry: A Tribute to Nigel Hitchin (Oxford Science Publications)

Few humans have proved extra influential within the box of differential and algebraic geometry, and in exhibiting how this hyperlinks with mathematical physics, than Nigel Hitchin. Oxford University's Savilian Professor of Geometry has made basic contributions in parts as various as: spin geometry, instanton and monopole equations, twistor conception, symplectic geometry of moduli areas, integrables structures, Higgs bundles, Einstein metrics, hyperkähler geometry, Frobenius manifolds, Painlevé equations, distinctive Lagrangian geometry and replicate symmetry, conception of grebes, and plenty of extra.

The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics)

First textbook-level account of uncomplicated examples and strategies during this quarter. appropriate for self-study via a reader who is aware a bit commutative algebra and algebraic geometry already. David Eisenbud is a widely known mathematician and present president of the yank Mathematical Society, in addition to a winning Springer writer.

Measure, Topology, and Fractal Geometry (Undergraduate Texts in Mathematics)

In keeping with a direction given to gifted high-school scholars at Ohio college in 1988, this booklet is basically a sophisticated undergraduate textbook concerning the arithmetic of fractal geometry. It properly bridges the space among conventional books on topology/analysis and extra really expert treatises on fractal geometry.

Higher-Dimensional Algebraic Geometry (Universitext)

The type conception of algebraic types is the focal point of this publication. This very lively zone of study remains to be constructing, yet an awesome volume of data has collected during the last 20 years. The authors aim is to supply an simply available creation to the topic. The ebook starts off with preparatory and traditional definitions and effects, then strikes directly to talk about numerous facets of the geometry of gentle projective types with many rational curves, and finishes in taking the 1st steps in the direction of Moris minimum version software of class of algebraic types through proving the cone and contraction theorems.

Additional resources for Algebraic Geometry in Coding Theory and Cryptography

Show sample text content

Rated 4.34 of 5 – based on 35 votes