Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves. New to the Second Edition 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 Q An explanation of how to perform calculations with elliptic curves in several popular computer algebra systems Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermat's Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices.
Author
Lawrence Clinton Washington (born 1951, Vermont) is an American mathematician, who specializes in number theory. Washington studied at Johns Hopkins University, where in 1971 he received his B.A. and masters degree. In 1974 he earned his PhD at Princeton University under Kenkichi Iwasawa with thesis Class numbers and Z_p extensions.[1] He then became an assistant professor at Stanford University and from 1977 at the University of Maryland, where he became in 1981 an associate professor and in 1986 a professor. He held visiting positions at several institutions, including IHES (1980/81), Max-Planck-Institut für Mathematik (1984), the Institute for Advanced Study (1996), and MSRI (1986/87), as well as at the University of Perugia, Nankai University and the State University of Campinas. Washington wrote a standard work on cyclotomic fields. He also worked on p-adic L-functions. He wrote a treatise with Allan Adler on their discovery of a connection between higher-dimensional analogues of magic squares and p-adic L-functions.[2] Washington has done important work on Iwasawa theory, Cohen-Lenstra heuristics, and elliptic curves and their applications to cryptography. In Iwasawa theory he proved with Bruce Ferrero in 1979 a conjecture of Kenkichi Iwasawa, that the \mu-invariant vanishes for cyclotomic Zp-extensions of abelian number fields (Theorem of Ferrero-Washington).[3] In 1979–1981 he was a Sloan Fellow. (from Wikipedia)
