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Besides giving readers the techniques for solving polynomial equations and congruences, "An Introduction to Mathematical Thinking" provides preparation for understanding more advanced topics in Linear and Modern Algebra, as well as Calculus. This book introduces proofs and mathematical thinking while teaching basic algebraic skills involving number systems, including the integers and complex numbers. Ample questions at the end of each chapter provide opportunities for learning and practice; the "Exercises" are routine applications of the material in the chapter, while the "Problems" require more ingenuity, ranging from easy to nearly impossible. Topics covered in this comprehensive introduction range from logic and proofs, integers and diophantine equations, congruences, induction and binomial theorem, rational and real numbers, and functions and bijections to cryptography, complex numbers, and polynomial equations. With its comprehensive appendices, this book is an excellent desk reference for mathematicians and those involved in computer science.
After two decades of research and development, elliptic curve cryptography now has widespread exposure and acceptance. Industry, banking, and government standards are in place to facilitate extensive deployment of this efficient public-key mechanism. Anchored by a comprehensive treatment of the practical aspects
of elliptic curve cryptography (ECC), this guide explains the basic
mathematics, describes state-of-the-art implementation methods, and
presents standardized protocols for public-key encryption, digital
signatures, and key establishment. In addition, the book addresses
some issues that arise in software and hardware implementation, as
well as side-channel attacks and countermeasures. Readers receive
the theoretical fundamentals as an underpinning for a wealth of
practical and accessible knowledge about efficient
application. * Breadth of coverage and unified, integrated approach to elliptic curve cryptosystems * Describes important industry and government protocols, such as
the FIPS 186-2 standard from the U.S. National Institute for
Standards and Technology * Provides full exposition on techniques for efficiently
implementing finite-field and elliptic curve arithmetic
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