Modular Arithmetic, Groups, Finite Fields and Probability -- Elliptic Curves -- Historical Ciphers -- The Enigma Machine -- Information Theoretic Security -- Historical Stream Ciphers -- Modern Stream Ciphers -- Block Ciphers -- Symmetric Key Distribution -- Hash Functions and Message Authentication Codes -- Basic Public Key Encryption Algorithms -- Primality Testing and Factoring -- Discrete Logarithms -- Key Exchange and Signature Schemes -- Implementation Issues -- Obtaining Authentic Public Keys -- Attacks on Public Key Schemes -- Definitions of Security -- Complexity Theoretic Approaches -- Provable Security: With Random Oracles -- Hybrid Encryption -- Provable Security: Without Random Oracles -- Secret Sharing Schemes -- Commitments and Oblivious Transfer -- Zero-Knowledge Proofs -- Secure Multiparty Computation.

In this introductory textbook the author explains the key topics in cryptography. He takes a modern approach, where defining what is meant by "secure" is as important as creating something that achieves that goal, and security definitions are central to the discussion throughout. The author balances a largely non-rigorous style {u2014} many proofs are sketched only {u2014} with appropriate formality and depth. For example, he uses the terminology of groups and finite fields so that the reader can understand both the latest academic research and "real-world" documents such as application programming interface descriptions and cryptographic standards. The text employs colour to distinguish between public and private information, and all chapters include summaries and suggestions for further reading. This is a suitable textbook for advanced undergraduate and graduate students in computer science, mathematics and engineering, and for self-study by professionals in information security. While the appendix summarizes most of the basic algebra and notation required, it is assumed that the reader has a basic knowledge of discrete mathematics, probability, and elementary calculus