An Introduction to Mathematical Cryptography / Edition 1

An Introduction to Mathematical Cryptography / Edition 1

by Jeffrey Hoffstein, J.H. Silverman, Jill Pipher
     
 

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;

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Overview

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.

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Product Details

ISBN-13:
9780387779935
Publisher:
Springer New York
Publication date:
02/18/2010
Series:
Undergraduate Texts in Mathematics Series
Edition description:
2008
Pages:
524
Product dimensions:
6.40(w) x 9.30(h) x 1.20(d)

Table of Contents

1 An Introduction to Cryptography 1

2 Discrete Logarithms and Diffie-Hellman 53

3 Integer Factorization and RSA 113

4 Combinatorics, Probability, and Information Theory 189

5 Elliptic Curves and Cryptography 279

6 Lattices and Cryptography 349

7 Digital Signatures 437

8 Additional Topics in Cryptography 465

List of Notation 489

References 493

Index 501

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