ThecreationofpublickeycryptographybyDi?eandHellmanin1976andthe
subsequent invention of the RSA public key cryptosystem by Rivest,
Shamir, and Adleman in 1978 are watershed events in the long history of
secret c- munications. It is hard to overestimate the importance of
public key cr- tosystems and their associated digital signature schemes
in the modern world of computers and the Internet. This book provides an
introduction to the theory of public key cryptography and to the
mathematical ideas underlying that theory. 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 su?cient detail so that this book provides a
self-contained course for the beginning student. The only prerequisite
is a ?rst 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.
Amongthemanyfacetsofmoderncryptography, thisbookchoosestoc- centrate
primarily on public key cryptosystems and digital signature schemes.
This allows for an in-depth development of the necessary mathematics -
quired for both the construction of these schemes and an analysis of
their security. The reader who masters the material in this book will
not only be well prepared for further study in cryptography, but will
have acquired a real understanding of the underlying mathematical
principles on which modern cryptography is based
