Prime Numbers pp 285-351 | Cite as

Elliptic Curve Arithmetic

  • Richard Crandall
  • Carl Pomerance


The history of what are called elliptic curves goes back well more than a century. Originally developed for classical analysis, elliptic curves have found their way into abstract and computational number theory, and now sit squarely as a primary tool. Like the prime numbers themselves, elliptic curves have the wonderful aspects of elegance, complexity, and power. Elliptic curves are not only celebrated algebraic constructs; they also provide considerable leverage in regard to prime number and factorization studies. Elliptic curve applications even go beyond these domains; for example, they have an increasingly popular role in modern cryptography, as we discuss in Section 8.1.3.


Elliptic Curve Elliptic Curf Class Number Elliptic Multiplication Curve Order 
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Copyright information

© Springer-Verlag, New York, Inc. 2001

Authors and Affiliations

  • Richard Crandall
    • 1
  • Carl Pomerance
    • 2
  1. 1.Center for Advanced ComputationPortlandUSA
  2. 2.Department of MathematicsDartmouth UniversityHanoverUSA

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