An Introduction to Mathematical Cryptography

Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman

Springer-Verlag – Undergraduate Texts in Mathematics
ISBN: 978-1-4939-1710-5 – 2nd ed. – © 2014 – 538 + xv pages
Math. Subj. Class: Primary 94A60; Secondary 11T71, 14G50
Available from Amazon and direct from Springer.

An Introduction to Mathematical Cryptography is an advanced undergraduate/beginning graduate-level text that provides a self-contained introduction to modern cryptography, with an emphasis on 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:

Additional topics, including hash functions, pseudorandom number generators, zero-knowledge proofs, quantum computation, and DES/AES, are briefly described in the final chapter. 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.


  1. An Introduction to Cryptography
  2. Discrete Logarithms and Diffie-Hellman
  3. Integer Factorization and RSA
  4. Probability Theory and Information Theory
  5. Elliptic Curves and Cryptography
  6. Lattices and Cryptography
  7. Digital Signatures
  8. Additional Topics in Cryptology

Click on the links for the following material.

     List of Errata — 1st Edition
     List of Errata — 2nd Edition

Contact Information

No book is ever free from error or incapable of being improved. We would be delighted to receive comments, positive or negative, and corrections from our readers. You can send mail to us at

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