Elliptic Curve Public Key Cryptosystems

1. Front Matter

   Pages i-xiii

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2. Introduction to Public Key Cryptography

   • Alfred Menezes

   Pages 1-14

3. Introduction to Elliptic Curves

   • Alfred Menezes

   Pages 15-34

4. Isomorphism Classes of Elliptic Curves Over Finite Fields

   • Alfred Menezes

   Pages 35-48

5. The Discrete Logarithm Problem

   • Alfred Menezes

   Pages 49-59

6. The Elliptic Curve Logarithm Problem

   • Alfred Menezes

   Pages 61-81

7. Implementation of elliptic Curve cryptosystems

   • Alfred Menezes

   Pages 83-100

8. Counting Points on Elliptic Curves Over F2m

   • Alfred Menezes

   Pages 101-116

9. Back Matter

   Pages 117-128

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Elliptic curves have been intensively studied in algebraic geometry and number theory. In recent years they have been used in devising efficient algorithms for factoring integers and primality proving, and in the construction of public key cryptosystems.
Elliptic Curve Public Key Cryptosystems provides an up-to-date and self-contained treatment of elliptic curve-based public key cryptology. Elliptic curve cryptosystems potentially provide equivalent security to the existing public key schemes, but with shorter key lengths. Having short key lengths means smaller bandwidth and memory requirements and can be a crucial factor in some applications, for example the design of smart card systems. The book examines various issues which arise in the secure and efficient implementation of elliptic curve systems.
Elliptic Curve Public Key Cryptosystems is a valuable reference resource for researchers in academia, government and industry who are concerned with issues of data security. Because of the comprehensive treatment, the book is also suitable for use as a text for advanced courses on the subject.

• Potential
• algorithms
• cryptography
• cryptology
• geometry
• number theory
• information and communication, circuits

• Auburn University, USA

  Alfred Menezes

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