An Introduction to Mathematical Cryptography / by Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman.

Format:

Book

Author/Creator:

Hoffstein, Jeffrey, author.

Pipher, Jill, author.

Silverman, Joseph H., 1955- author.

Contributor:

SpringerLink (Online service)

Series:

Undergraduate texts in mathematics 0172-6056

Undergraduate Texts in Mathematics, 0172-6056

Language:

English

Subjects (All):

Number theory.

Data structures (Computer science).

Data encryption (Computer science).

Information theory.

Algebra.

Ordered algebraic structures.

Number Theory.

Data Structures and Information Theory.

Cryptology.

Information and Communication, Circuits.

Order, Lattices, Ordered Algebraic Structures.

Local Subjects:

Number Theory.

Data Structures and Information Theory.

Cryptology.

Information and Communication, Circuits.

Order, Lattices, Ordered Algebraic Structures.

Physical Description:

1 online resource (XVII, 538 pages 32 illustrations).

Edition:

Second edition 2014.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 2014.

System Details:

text file PDF

Summary:

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. This text provides 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. 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 cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.

Contents:

Preface

Introduction

1 An Introduction to Cryptography

2 Discrete Logarithms and Diffie-Hellman

3 Integer Factorization and RSA

4 Digital Signatures

5 Combinatorics, Probability, and Information Theory

6 Elliptic Curves and Cryptography

7 Lattices and Cryptography

8 Additional Topics in Cryptography

List of Notation

References

Index.

Other Format:

Printed edition:

ISBN:

9781493917112

Access Restriction:

Restricted for use by site license.