Elliptic curves

Number theory and cryptography

Lawrence C. Washington

440 pages, parution le 24/06/2003

Ajouter à une liste

Indisponible

Résumé

Presents the mathematics and applications of elliptic curves at an accessible level
Include applications of elliptic curves to cryptography, factorization, and primality testing
Covers attacks on the discrete log problem for supersigular and anomalous curves
Discusses the Weil pairing and the Tate-Lichtenbaum pairing and their cryptographic applications
Addresses elliptic curves over finite fields, the rationals, and the complex numbers
Outlines the work of Wiles andRibet on Fermat's last theorem
Summarizes the requisite abstract algebra topics in an appendix

Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to senior undergraduate or beginning graduate students.

Assuming only a modest background in elementary number theory, groups, and fields, Elliptic Curves: Number Theory and Cryptography introduces both the cryptographic and number theoretic sides of elliptic curves, interweaving the theory of elliptic curves with their applications. The author introduces elliptic curves over finite fields early in the treatment, leading readers directly to the intriguing cryptographic applications, but the book is structured so that readers can explore the number theoretic aspects independently if desired.

By side-stepping algebraic geometry in favor an approach based on basic formulas, this book clearly demonstrates how elliptic curves are used and opens the doors to higher-level studies. Elliptic Curves offers a solid introduction to the mathematics and applications of elliptic curves that well prepares its readers to tackle more advanced problems in cryptography and number theory.

Introduction
The basic theory
Torsion points
Elliptic curves over finite fields
The discrete logarithm problem
Elliptic curve cryptography
Other applications
Elliptic curves over Q
Elliptic curves over C
Complex multiplication
Divisors
Zeta functions
Fermat's last theorem

Appendices
References
Index

L'auteur - Lawrence C. Washington

University of Maryland, College Park, Maryland, USA

Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Lawrence C. Washington
Parution	24/06/2003
Nb. de pages	440
Format	16 x 24
Couverture	Relié
Poids	740g
Intérieur	Noir et Blanc
EAN13	9781584883654
ISBN13	978-1-58488-365-4