Contents -- Preface -- Chapter 1 Introduction -- Problems and Exercises -- Chapter 2 Public Key Cryptosystems -- 2.1 Prehistory and Main Ideas -- 2.2 The First Public Key System - DiffieHellman Key Agreement -- 2.3 The Elements of Number Theory -- 2.4 Shamir Cipher -- 2.5 ElGamal Encryption -- 2.6 RSA Encryption and Trapdoor Functions -- Problems and Exercises -- Themes for Labs -- Chapter 3 Solving Discrete Logarithm Problem -- 3.1 Problem Setting -- 3.2 The Baby-step Giant-step Algorithm -- 3.3 Index Calculus Algorithm -- Problems and Exercises -- Themes for Labs -- Chapter 4 Digital Signatures -- 4.1 RSA Digital Signature -- 4.2 ElGamal Digital Signature -- 4.3 Digital Signature Standards -- Problems and Exercises -- Themes for Labs -- Chapter 5 Cryptographic Protocols -- 5.1 Mental Poker -- 5.2 Zero Knowledge Proofs -- 5.2.1 Graph Colouring Problem -- 5.2.2 Hamiltonian Cycle Problem -- 5.3 Digital Cash -- 5.4 Mutual Identification with Key Establishment -- Problems and Exercises -- Themes for Labs -- Chapter 6 Elliptic Curve Crypt osys t ems -- 6.1 Introduction -- 6.2 Mathematical Foundations -- 6.3 Choosing Curve Parameters -- 6.4 Constructing Cryptosystems -- 6.4.1 Elliptic Curve ElGamal Encryption -- 6.4.2 Elliptic Curve Digital Signature Algorithm -- 6.5 Efficient Implementation of Operations -- 6.6 Counting Points on Elliptic Curve -- 6.7 Using Standard Curves -- Problems and Exercises -- Themes for Labs -- Chapter 7 Theoretical Security of Cryptosystems -- 7.1 Introduction -- 7.2 Theory of Perfect Secrecy -- 7.3 Vernam Cipher -- 7.4 Elements of Information Theory -- 7.5 Unicity Distance for Secret Key Cipher -- 7.6 Ideal Cryptosystems -- Problems and Exercises -- Chapter 8 Modern Secret Key Ciphers -- 8.1 Introduction -- 8.2 Block Ciphers -- 8.2.1 The GOST 28147-89 Block Cipher -- 8.2.2 The RC5 and RC6 Ciphers.

8.2.3 The Rijndael (AES) Cipher -- 8.3 Main Modes of Operation of Block Ciphers -- 8.3.1 ECB Mode -- 8.3.2 CBC Mode -- 8.4 Stream Ciphers -- 8.4.1 The OFB Block Cipher Mode -- 8.4.2 The CTR Block Cipher Mode -- 8.4.3 The RC4 Algorithm -- 8.5 Cryptographic Hash Functions -- Chapter 9 Random Numbers in Cryptography -- 9.1 Introduction -- 9.2 Refining Physical Random Number Generators -- 9.3 Pseudo-Random Number Generators -- 9.4 Statistical Tests for Random and Pseudo-Random Number Generators -- 9.5 Statistical Attack to Block Ciphers -- Answers to Problems and Exercises -- Bibliography -- Author Index -- Subject Index.