Algebraic Geometry in Coding Theory and Cryptography by Harald Niederreiter (PDF)

Description

This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Algebraic geometry is a beautiful subject and have found nice applications in many areas of mathematics/CS.Coding theory and Cryptography are two such areas.There are many great books available on each of these areas. They focus either on Coding theory, or on Cryptography.This book however, builds on keeping algebraic geometry in the first place.It isolates out the relevant algebraic structures needed for Coding and Cryptography and then furnish the way the application-areas use these algebraic-geometric structures.The text is clear for most of the parts. If it lacks one thing, it is some amount of motivational discourse, and hence appears rather tarse and a bit directionless at times. What helped me at that point is to quickly glean over the theorems in a sequence and spare a moment to tie them together to get an overview. Once the overview is obtained, reading through the content is relatively painless. It is written lucidly, but some familiarity with Abstract algebra, especially Fields, extensions etc., would help a smoother reading.

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