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Elliptic curves. Number theory and cryptography. 2nd ed. (English) Zbl 1200.11043

Boca Raton, FL: Chapman and Hall/CRC (ISBN 978-1-4200-7146-7/hbk). xviii, 513 p. (2008).
See the review of the first edition in Zbl 1034.11037.
With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves. New to the Second Edition are chapters on
– isogenies and hyperelliptic curves,
– a discussion of alternative coordinate systems, such as projective, Jacobian, and Edwards coordinates, along with related computational issues,
– a more complete treatment of the Weil and Tate–Lichtenbaum pairings,
– Doud’s analytic method for computing torsion on elliptic curves over \(\mathbb Q\),
– an explanation of how to perform calculations with elliptic curves in several popular computer algebra systems.

MSC:

11G20 Curves over finite and local fields
11G05 Elliptic curves over global fields
11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
14G50 Applications to coding theory and cryptography of arithmetic geometry
94A60 Cryptography
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
11G50 Heights
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)

Citations:

Zbl 1034.11037

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Online Encyclopedia of Integer Sequences:

a(n) is the first term of the n-th proper elliptic 6-cycle.