Elliptic Curves: Number Theory and Cryptography (Discrete Mathematics and Its Applications)
by: Lawrence C. Washington
Details
# Hardcover: 440 pages
# Publisher: Chapman & Hall/CRC; 1 edition (May 28, 2003)
# Language: English
# ISBN-10: 1584883650
# ISBN-13: 978-1584883654
Description
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.
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A Classical Introduction to Modern Number Theory (GTM) - 2nd Edition
by: Kenneth Ireland Michael Rosen
Details
# Publisher: Springer
# Number Of Pages: 389
# Edition: 2nd edition (1990)
# Pages: 389 ordered pages (401 total pages for ebook) and (412 total page for the hard cover)!
Series: GTM (84)
# Sales Rank: 381488
# ISBN / ASIN: 038797329X
# EAN: 9780387973296
# Binding: Hardcover
# Manufacturer: Springer
# Studio: Springer
# Average Rating: 5
# Total Reviews: 6
Description
Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.
http://ifile.it/rbxfnv/gtm084.djvu
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Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Encyclopaedia of Mathematical Sciences)
by: Yu.I. Manin Alexei A. Panchishkin
Details
# Hardcover: 514 pages
# Publisher: Springer; 2nd edition (April 5, 2007)
# Language: English
# ISBN-10: 3540203648
# ISBN-13: 978-3540203643
Description
Introduction to Modern Number Theory surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions.
This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects.
http://ifile.it/fuwq9c/introduction_to_modern_number_theory.pdf
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