An Introduction to Mathematical Cryptography

Hoffstein, Pipher, Silverman | ISBN 978-0-387-77993-5

Pdf | 533 pgs | 8 mb

The security of communications and commerce in a digital age relies on the modern incarnation of the ancient art of codes and ciphers. Underlying the birth of modern cryptography is a great deal of fascinating mathematics, some of which has been developed for cryptographic applications, but much of which is taken from the classical mathematical canon. The principal goal of this book is to introduce the reader to a variety of mathematical topics while simultaneously integrating the mathematics into a description of modern public key cryptography.

Public key cryptography draws on many areas of mathematics, including number theory, abstract algebra, probability, and information theory. Each of these topics is introduced and developed in sufficient detail so that this book provides a self-contained course for the beginning student. The only prerequisite is a first course in linear algebra. On the other hand, students with stronger mathematical backgrounds can move directly to cryptographic applications and still have time for advanced topics such as elliptic curve pairings and lattice-reduction algorithms.

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