Advertisement

An Introduction to Mathematical Cryptography

  • Jeffrey Hoffstein
  • Jill Pipher
  • Joseph H. Silverman

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman
    Pages 1-59
  3. Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman
    Pages 61-115
  4. Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman
    Pages 117-191
  5. Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman
    Pages 193-205
  6. Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman
    Pages 207-298
  7. Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman
    Pages 299-371
  8. Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman
    Pages 373-470
  9. Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman
    Pages 471-501
  10. Back Matter
    Pages 503-538

About this book

Introduction

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 DiffieHellmann 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.

Keywords

coding theory digital signatures discrete logarithms elliptic curves information theory lattices and cryptography probability theory

Authors and affiliations

  • Jeffrey Hoffstein
    • 1
  • Jill Pipher
    • 2
  • Joseph H. Silverman
    • 3
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA
  3. 3.Department of MathematicsBrown UniversityProvidenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-1711-2
  • Copyright Information Springer Science+Business Media New York 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-1710-5
  • Online ISBN 978-1-4939-1711-2
  • Series Print ISSN 0172-6056
  • Series Online ISSN 2197-5604
  • Buy this book on publisher's site