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Algebraic Geometry in Coding Theory and Cryptography
Harald Niederreiter & Chaoping Xing

Hardcover | 2009 | $57.50/ £39.95 | ISBN: 9780691102887
272 pp. | 6 x 9 | SHOPPING CART

eBook | ISBN: 9781400831302 |
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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


"Coding theory has a rapidly growing corpus of knowledge, and now appears explicitly in several classifications in the MSC. [This] book . . . is certainly an important addition to the literature in this area and a serious candidate for becoming one of the standard textbooks in related courses."--Cicero Carvalho, Mathematical Reviews


"This is a beautifully written volume that gives the necessary background to read the research literature on coding and cryptography based on concepts from curves in algebraic geometries. Both of the authors are outstanding researchers, well known for the clarity and depth of their contributions. This work is a valuable and welcome addition to the literature on coding and cryptography."--Ian F. Blake, University of British Columbia

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    File created: 5/10/2015

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