Cryptography and Cryptology

Cryptography is one of the most active areas in current mathematics research and applications. This book focuses on cryptography along with two related areas: the study of probabilistic proof systems, and the theory of computational pseudorandomness. Following a common theme that explores the interplay between randomness and computation, the important notions in each field are covered, as well as novel ideas and insights.

This book presents a comprehensive examination of cryptography - the representation of messages in code and its transformation from a national security tool to a key component of the global information superhighway.

As paper-based communication and transaction mechanisms are replaced by automated ones, traditional forms of security such as photographs and handwritten signatures are becoming outdated. Most security experts believe that digital certificates offer the best technology for safeguarding electronic communications. They are already widely used for authenticating and encrypting email and software, and eventually will be built into any device or piece of software that must be able to communicate securely.

This book examines multiple aspects of public-key cryptography. It covers the theory of provably secure public-key cryptography and the implementation of exponentiation and multi-exponentiation. An introduction to provable security is provided.