Mathematics of Public Key Cryptography

Front Cover
Cambridge University Press, Mar 15, 2012 - Computers - 615 pages
Public key cryptography is a major interdisciplinary subject with many real-world applications, such as digital signatures. A strong background in the mathematics underlying public key cryptography is essential for a deep understanding of the subject, and this book provides exactly that for students and researchers in mathematics, computer science and electrical engineering. Carefully written to communicate the major ideas and techniques of public key cryptography to a wide readership, this text is enlivened throughout with historical remarks and insightful perspectives on the development of the subject. Numerous examples, proofs and exercises make it suitable as a textbook for an advanced course, as well as for self-study. For more experienced researchers it serves as a convenient reference for many important topics: the Pollard algorithms, Maurer reduction, isogenies, algebraic tori, hyperelliptic curves and many more.
 

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Contents

1 Introduction
1
Part I Background
11
Part II Algebraic groups
59
Part III Exponentiation factoring and discrete logarithms
213
Part IV Lattices
335
Part V Cryptography related todiscrete logarithms
403
Part VI Cryptography related tointeger factorisation
483
VII Advanced topics in elliptic and hyperelliptic curves
513
Appendix A Background mathematics
564
References
579
Author index
603
Subject index
608
Copyright

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About the author (2012)

Steven D. Galbraith is a leading international authority on the mathematics of public key cryptography. He is an Associate Professor in the Department of Mathematics at the University of Auckland.

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