An Introduction to Mathematical Cryptography

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, anddigital 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

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.