Elliptic Curve Public Key Cryptosystems

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.

Contenu

Foreword. Preface. 1. Introduction to Public Key Cryptography. 2. Introduction to Elliptic Curves. 3. Isomorphism Classes of Elliptic Curves over Finite Fields. 4. The Discrete Logarithm Problem. 5. The Elliptic Curve Logarithm Problem. 6. Implementation of Elliptic Curve Cryptosystems. 7. Counting Points on Elliptic Curves over F2m. Bibliography. Index.