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An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics)

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An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: * classical cryptographic constructions, such as Diffie-Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; * fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; * an in-depth treatment of important recent cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. This book is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.

Synopsis:

An Introduction to Mathematical Cryptography provides an introduction to public key cryptography and underlying mathematics that is required for the subject. Each of the eight chapters expands on a specific area of mathematical cryptography and provides an extensive list of exercises. It is a suitable text for advanced students in pure and applied mathematics and computer science, or the book may be used as a self-study. This book also provides a self-contained treatment of mathematical cryptography for the reader with limited mathematical background.

About the Author

Dr. Jeffrey Hoffstein has been a professor at Brown University since 1989 and has been a  visiting professor and tenured professor at several other universities since 1978. His research areas are number theory, automorphic forms, and cryptography. He has authored more than 50 publications. Dr. Jill Pipher has been a professor at Brown Univesity since 1989. She has been an invited lecturer and has received numerous awards and honors. Her research areas are harmonic analysis, elliptic PDE, and cryptography. She has authored over 40 publications. Dr. Joseph Silverman has been a professor at Brown University 1988. He served as the Chair of the Brown Mathematics department from 2001-2004. He has received numerous fellowships, grants and awards and is a frequently invited lecturer. His research areas are number theory, arithmetic geometry, elliptic curves, dynamical systems and cryptography. He has authored more than120 publications and has had more than 20 doctoral students.

Table of Contents

An Introduction to Cryptography.- Discrete Logarithms and Diffie-Hellman.- Integer Factorization and RSA.- Probability Theory and Information Theory.- Elliptic Curves and Cryptography.- Lattices and Cryptography.- Digital Signatures.- Additional Topics in Cryptology.

Product Details

ISBN:
9780387779935
Author:
Hoffstein, Jeffrey
Publisher:
Springer
Author:
Silverman, J. H.
Author:
Pipher, Jill
Author:
Silverman, Joseph H.
Subject:
Number Theory
Subject:
Computer Science
Subject:
Security - General
Subject:
Coding theory
Subject:
Digital signatures
Subject:
discrete logarithms
Subject:
elliptic curves
Subject:
Information Theory
Subject:
lattices and cryptography
Subject:
Probability Theory.
Subject:
Data Structures, Cryptology and Information Theory
Subject:
Data encryption.
Subject:
Information and Communication, Circuits
Subject:
Order, Lattices, Ordered Algebraic Structures <P>Detailed introduction to elliptic curves and how they re used in cryptography, including the “hot” recent topic of elliptic curve pairing-based cryptography</P> <P>Detailed introduction to lattices and
Subject:
Mathematics-Number Theory
Subject:
Order, Lattices, Ordered Algebraic Structures
Copyright:
Edition Description:
Book
Series:
Undergraduate Texts in Mathematics
Publication Date:
20080812
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
540
Dimensions:
235 x 155 mm 2060 gr

Related Subjects

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Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Number Theory

An Introduction to Mathematical Cryptography (Undergraduate Texts in Mathematics) New Hardcover
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$61.25 In Stock
Product details 540 pages Springer - English 9780387779935 Reviews:
"Synopsis" by , An Introduction to Mathematical Cryptography provides an introduction to public key cryptography and underlying mathematics that is required for the subject. Each of the eight chapters expands on a specific area of mathematical cryptography and provides an extensive list of exercises. It is a suitable text for advanced students in pure and applied mathematics and computer science, or the book may be used as a self-study. This book also provides a self-contained treatment of mathematical cryptography for the reader with limited mathematical background.
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