Cryptography

"It is by far the most suitable text for undergraduate and graduate courses on the subject in mathematics and computer science departments. Besides having breadth and scope in the choice of topics, many of them are dealt with in much more depth than what can be found elsewhere at this level . . . If you really want to learn some cryptography this is probably the best available text." - Peter Shiu, Department of Mathematical Sciences, Loughborough University, in The Mathematical Gazette, March 2007 ". . . the book is very well suited for a course in crypotography." - Bran van Asch, in Mathematical Reviews, 2007f

CLASSICAL CRYPTOGRAPHY Introduction: Some Simple Cryptosystems Cryptanalysis Notes Exercises SHANNON'S THEORY Introduction Elementary Probability Theory Perfect Secrecy Entropy Properties of Entropy Spurious Keys and Unicity Distance Product Cryptosystems Notes Exercises BLOCK CIPHERS AND THE ADVANCED ENCRYPTION STANDARD Introduction Substitution-Permutation Networks Linear Cryptanalysis Differential Cryptanalysis The Data Encryption Standard The Advanced Encryption Standard Modes of Operation Notes and References Exercises CRYPTOGRAPHIC HASH FUNCTIONS Hash Functions and Data Integrity Security of Hash Functions Iterated Hash Functions Message Authentication Codes Unconditionally Secure MACs Notes and References Exercises THE RSA CRYPTOSYSTEM AND FACTORING INTEGERS Introduction to Public-key Cryptography More Number Theory The RSA Cryptosystem Primality Testing Square Roots Modulo n Factoring Algorithms Other Attacks on RSA The Rabin Cryptosystem Semantic Security of RSA Notes and References Exercises PUBLIC-KEY CRYPTOGRAPHY AND DISCRETE LOGARITHMS The ElGamal Cryptosystem Algorithms for the Discrete Logarithm Problem Lower Bounds on the Complexity of Generic Algorithms Finite Fields Elliptic Curves Discrete Logarithm Algorithms in Practice Security of ElGamal Systems Notes and References Exercises SIGNATURE SCHEMES Introduction Security Requirements for Signature Schemes The ElGamal Signature Scheme Variants of the ElGamal Signature Scheme Provably Secure Signature Schemes Undeniable Signatures Fail-stop Signatures Notes and References Exercises PSEUDO-RANDOM NUMBER GENERATION Introduction and Examples Indistinguishability of Probability Distributions The Blum-Blum-Shub Generator Probabilistic Encryption Notes and References Exercises IDENTIFICATION SCHEMES AND ENTITY AUTHENTICATION Introduction Challenge-and-Response in the Secret-Key Setting Challenge-and-Response in the Public-Key Setting The Schnorr Identification Scheme The Okamoto Identification Scheme The Guillou-Quisquater Identification Scheme Notes and References Exercises KEY DISTRIBUTION Introduction Diffie-Hellman Key Predistribution Unconditionally Secure Key Predistribution Key Distribution Patterns Session Key Distribution Schemes Notes and References Exercises KEY AGREEMENT SCHEMES Introduction Diffie-Hellman Key Agreement MTI Key Agreement Schemes Key Agreement Using Self-Certifying Keys Encrypted Key Exchange Conference Key Agreement Schemes Notes and References Exercises PUBLIC-KEY INFRASTRUCTURE Introduction: What is a PKI? Certificates Trust Models The Future of PKI? Identity-Based Cryptography Notes and References Exercises SECRET SHARING SCHEMES Introduction: The Shamir Threshold Scheme Access Structures and General Secret Sharing Information Rate and Construction of Efficient Schemes Notes and References Exercises MULTICAST SECURITY AND COPYRIGHT PROTECTION Introduction to Multicast Security Broadcast Encryption Multicast Re-Keying Copyright Protection Tracing Illegally Redistributed Keys Notes and References Exercises FURTHER READING BIBLIOGRAPHY INDEX