Elliptic Curves: Number Theory and Cryptography
Elliptic Curves: Number Theory and Cryptography (Discrete Mathematics and Its Applications) Lawrence C. Washington,
Publisher: Chapman & Hall/CRC
ISBN: 1584883650
Edition: Hardcover; 2003-05-01
Summary:
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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