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Elliptic Curves: Number Theory and Cryptography, Second Edition (Discrete Mathematics and Its Applications) - Hardcover

Book 10 of 67: Discrete Mathematics and Its Applications

Washington, Lawrence C.

 
9781420071467: Elliptic Curves: Number Theory and Cryptography, Second Edition (Discrete Mathematics and Its Applications)
Hardcover
ISBN 10: 1420071467 ISBN 13: 9781420071467
Publisher: Chapman and Hall/CRC, 2008

Synopsis

Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves.

New to the Second Edition

  • Chapters on isogenies and hyperelliptic curves
  • A discussion of alternative coordinate systems, such as projective, Jacobian, and Edwards coordinates, along with related computational issues
  • A more complete treatment of the Weil and Tate–Lichtenbaum pairings
  • Doud’s analytic method for computing torsion on elliptic curves over Q
  • An explanation of how to perform calculations with elliptic curves in several popular computer algebra systems

    • Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermat’s Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices.

    "synopsis" may belong to another edition of this title.

    About the Author

    Lawrence C. Washington

    From the Back Cover

    Like its bestselling predecessor, this second edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. It now includes new chapters on isogenies and hyperelliptic curves, a more complete treatment of the Tate-Lichtenbaum pairing, alternative coordinate systems and related computational issues, and Doud's analytic method for computing torsion on elliptic curves over Q. This edition also discusses how to perform computations with elliptic curves in several popular computer algebra systems. Basic exercises appear at the end of each chapter.

    "About this title" may belong to another edition of this title.

    Publisher
    Chapman and Hall/CRC
    Publication date
    2008
    Language
    English
    ISBN 10 
    1420071467
    ISBN 13 
    9781420071467
    Binding
    Hardcover
    Edition number
    2
    Number of pages
    532