Algebraic geometry in coding theory and cryptography

Includes index

Includes bibliography (p. 249-256) and references

1. Finite fields and function fields 2. Algebraic varieties 3. Algebraic curves 4. Rational places 5. Applications to coding theory 6. Applications to cryptography.Frontmatter Contents Preface 1. Finite Fields and Function Fields 2. Algebraic Varieties 3. Algebraic Curves 4. Rational Places 5. Applications to Coding Theory 6. Applications to Cryptography

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.