The Advanced Encryption Standard (AES), elliptic curve DSA, the secure hash algorithm…these and other major advances made in recent years precipitated this comprehensive revision of the standard-setting text and reference, Cryptography: Theory and Practice. Now more tightly focused on the core areas, it contains many additional topics as well as thoroughly updated treatments of topics presented in the first edition. There is increased emphasis on general concepts, but the outstanding features that first made this a bestseller all remain, including its mathematical rigor, numerous examples, pseudocode descriptions of algorithms, and clear, precise explanations. Highlights of the Second Edition: Explains the latest Federal Information Processing Standards, including the Advanced Encryption Standard (AES), the Secure Hash Algorithm (SHA-1), and the Elliptic Curve Digital Signature Algorithm (ECDSA) Uses substitution-permutation networks to introduce block cipher design and analysis concepts Explains both linear and differential cryptanalysis Presents the Random Oracle model for hash functions Addresses semantic security of RSA and Optional Asymmetric Encryption Padding Discusses Wiener's attack on low decryption exponent RSA Overwhelmingly popular and relied upon in its first edition, now, more than ever, Cryptography: Theory and Practice provides an introduction to the field ideal for upper-level students in both mathematics and computer science. More highlights of the Second Edition: Provably secure signature schemes: Full Domain Hash Universal hash families Expanded treatment of message authentication codes More discussions on elliptic curves Lower bounds for the complexity of generic algorithms for the discrete logarithm problem Expanded treatment of factoring algorithms Security definitions for signature schemes

Table of Contents:
CLASSICAL CRYPTOGRAPHY Introduction: Some Simple Cryptosystems The Shift Cipher The Substitution Cipher The Affine Cipher The Vigenère Cipher The Hill Cipher The Permutation Cipher Stream Ciphers Cryptanalysis Cryptanalysis of the Affine Cipher Cryptanalysis of the Substitution Cipher Cryptanalysis of the Vigenère Cipher Cryptanalysis of the Hill Cipher Cryptanalysis of the LFSR Stream Cipher Exercises SHANNON'S THEORY Introduction Elementary Probability Theory Perfect Secrecy Entropy Huffman Encodings Properties of Entropy Spurious Keys and Unicity Distance Product Cryptosystems Exercises BLOCK CIPHERS AND THE ADVANCED ENCRYPTION STANDARD Introduction Substitution-Permutation Networks Linear Cryptanalysis The Piling-Up Lemma Linear Aproximations of S-Boxes A Linear Attack on an SPN Differential Cryptanalysis The Data Encryption Standard Description of DES Analysis of DES The Advanced Encryption Standard Description of AES Discussion and Analysis of AES Modes of Operation Exercises CRYPTOGRAPHIC HASH FUNCTIONS Hash Functions and Data Integrity Security of Hash Functions The Random Oracle Model Algorithms in the Random Oracle Model Comparison of Security Criteria Iterated Hash Functions The Merkle-Damgard Construction The Secure Hash Algorithm Message Authentication Codes Nested MACs and HMAC CBC-MAC Unconditionally Secure MACs Strongly Universal Hash Families Optimality of Deception Probabilities Exercises THE RSA CRYPTOSYSTEM AND FACTORING INTEGERS Introduction to Public-Key Cryptography More Number Theory The Euclidean Algorithm The Chinese Remainder Theorem Other Useful Facts The RSA Cryptosystem Implementing RSA Primality Testing Square Roots Modulo n Factoring Algorithms The Pollard p - 1 Algorithm The Pollard Rho Algorithm Dixon's Random Squares Algorithm Factoring Algorithms in Practice Other Attacks on RSA Computing f(n) The Decryption Exponent Wiener's Low Decryption Exponent Attack The Rabin Cryptosystem Security of the Rabin Cryptosystem Semantic Security of RSA Partial Information Concerning Plaintext Bits Optimal Asymmetric Encryption Padding Exercises PUBLIC-KEY CRYPTOGRAPHY BASED ON THE DISCRETE LOGARITHM PROBLEM The ElGamalCryptosystem Algorithms for the Discrete Logarithm Problem Shanks' Algorithm The Pollard Rho Discrete Logarithm Algorithm The Pohlig-Hellman Algorithm The Index Calculus Method Lower Bounds on the Complexity of Generic Algorithms Finite Fields Elliptic Curves Elliptic Curves over the Reals Elliptic Curves Modulo a Prime Properties of Elliptic Curves Point Compression and the ECIES Computing Point Multiples on Elliptic Curves Discrete Logarithm Algorithms in Practice Security of ElGamal Systems Bit Security of Discrete Logarithms Semantic Security of ElGamal Systems The Diffie-Hellman Problems Exercises SIGNATURE SCHEMES Introduction Security Requirements for Signature Schemes Signatures and Hash Function The ElGamal Signature Scheme Security of the ElGamal Signature Scheme Variants of the ElGamal Signature Scheme The Schnorr Signature Scheme The Digital Signature Algorithm The Elliptic Curve DSA Provably Secure Signature Schemes One-Time Signatures Full Domain Hash Undeniable Signatures Fail-Stop Signatures Exercises BIBLIOGRAPHY CRYPTOSYSTEM INDEX ALGORITHMS INDEX PROBLEM INDEX INDEX Each chapter also contains a section of Notes and References