An Introduction to Mathematical Cryptography

  • J.H. Silverman
  • Jill Pipher
  • Jeffrey Hoffstein

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

Table of contents

  1. Front Matter
    Pages 1-14
  2. Jeffrey Hoffstein
    Pages 1-58
  3. Jeffrey Hoffstein
    Pages 1-54
  4. Jeffrey Hoffstein
    Pages 1-75
  5. Jeffrey Hoffstein
    Pages 1-70
  6. Jeffrey Hoffstein
    Pages 1-87
  7. Jeffrey Hoffstein
    Pages 1-27
  8. Jeffrey Hoffstein
    Pages 1-23
  9. Back Matter
    Pages 1-35

About this book


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.


AES Crib DES Number theory algorithms cryptography cryptology information information theory

Authors and affiliations

  • J.H. Silverman
  • Jill Pipher
  • Jeffrey Hoffstein

There are no affiliations available

Bibliographic information

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