This book introduces the basic concepts of information and communication security by providing the appropriate mathematical elements to prove or break the security of cryptographic schemes. It is the transcript of a course held by the author at the Communication Systems Division of the ¿cole Polytechnique F¿d¿rale de Lausanne. It covers the main topics of cryptology, including symmetric and public-key cryptography, cryptographic protocols, design, cryptanalysis, and implementation of cryptosystems.

The book contains 12 chapters: The first, “Prehistory of Cryptography,” treats the foundations of conventional cryptography and the Shannon concepts regarding secrecy. Chapter 2, “Conventional Cryptography,” considers the main symmetric cryptographic protocols--data encryption standard (DES) and advanced encryption standard (AES); DES modes of operation; some applications (like Unix passwords); stream ciphers; and some basic types of attacks (such as brute force and meet-in-the-middle attacks). Chapter 3 is dedicated to some conventional cryptographic primitives that assure the integrity, authentication, and randomness of messages (hashing, message authentication code, and pseudorandom generators).

Chapter 4 investigates the main attack methods against symmetric cryptographic protocols: linear and differential cryptanalysis, security models, and Markov ciphers. It also considers some ways to strengthen security and to estimate the resistance against attacks. Chapter 5 presents several security protocols that use conventional cryptography: passwords, challenge-response protocols, one-time passwords, key distribution, authentication chains, and wireless communication (the global system for mobile communications (GSM) and the Bluetooth networks).

Chapters 6, 7, and 8 cover the mathematical background used in the construction and analysis of cryptographic schemes: linear algebra (including elliptic curves over finite fields), number theory (primality and factorization and the discrete logarithm problem), and some elements of complexity theory (with a sketch of Turing machines). Unfortunately, the mathematics of probabilities and statistics are poorly covered in this book.

Chapter 9 continues the presentation of cryptographic protocols with public key cryptography; the main schemes are presented, including Diffie-Hellman, RSA, and El Gamal. Unfortunately, nothing about elliptic curve cryptographic algorithms is mentioned. Chapter 10 is dedicated to digital signature schemes. Chapter 11 describes other cryptographic protocols. It provides a summary introduction to zero knowledge and secret sharing schemes. Some special digital signatures are also considered. The last chapter provides a bridge between cryptography and communication security. Some known examples of cryptographic applications (certificates, secure sockets layer, secure shell, and pretty good privacy protocols) are presented.

Each chapter contains a section with exercises that do not require an extensive background in mathematics, since the most important notions are introduced and discussed in many of the exercises. This book is designed for upper-level undergraduate and graduate-level students in computer science. It is also suitable for researchers and practitioners in industry.