Elliptic Curves: Number Theory and Cryptography, Second Edition

Lawrence C. Washington

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April 3, 2008 by Chapman and Hall/CRC
Reference - 536 Pages - 20 B/W Illustrations
ISBN 9781420071467 - CAT# C7146
Series: Discrete Mathematics and Its Applications

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Features

  • Explores how elliptic curves are used in cryptography and number theory
  • Requires no background in algebraic geometry
  • Discusses both the Weil and Tate–Lichtenbaum pairings
  • Covers elliptic curve cryptosystems, such as pairing-based encryption
  • Introduces three popular packages (Pari, Magma, and Sage) for computing with elliptic curves
  • Summary

    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.