Cryptography in the Information Society

Length: 273 pages
Edition: 1
Language: English
Publisher: World Scientific Pub Co Inc
Publication Date: 2020-12-02
ISBN-10: 9811226156
ISBN-13: 9789811226151
Sales Rank: #0 (See Top 100 Books)

This textbook describes the main techniques and features of contemporary cryptography, but does so using secondary school mathematics so that the concepts discussed can be understood by non-mathematicians. The topics addressed include block ciphers, stream ciphers, public key encryption, digital signatures, cryptographic protocols, elliptic curve cryptography, theoretical security, blockchain and cryptocurrencies, issues concerning random numbers, and steganography. The key results discussed in each chapter are mathematically proven, and the methods are described in sufficient detail to enable their computational implementation. Exercises are provided.

Cover
Halftitle
Series Editors
Title
Copyright
Preface
Acknowledgments
Contents
1. Introduction
    Problems and Exercises
2. Public Key Cryptosystems
    2.1 Prehistory and Main Ideas
    2.2 The First Public-Key System — Diffie–Hellman 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
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
4. Digital Signatures
    4.1 RSA Digital Signature
    4.2 ElGamal Digital Signature
    4.3 Digital Signature Standards
    Problems and Exercises
    Themes for Labs
5. Cryptographic Protocols
    5.1 Introduction
    5.2 Mental Poker
    5.3 Zero Knowledge Proofs
        5.3.1 Graph Coloring Problem
        5.3.2 Hamiltonian Cycle Problem
    5.4 Digital Cash
    5.5 Mutual Identification with Key Establishment
    Problems and Exercises
    Themes for Labs
6. Elliptic Curve Cryptosystems
    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 an Elliptic Curve
    6.7 Using Standard Curves
    Problems and Exercises
    Themes for Labs
7. Theoretical Security of Cryptosystems
    7.1 Introduction
    7.2 Theory of Perfect Secrecy
    7.3 The One-Time Pad Cipher
    7.4 Elements of Information Theory
    7.5 Robustness of the One-Time Pad Under Small Deviations of the Key from Randomness
    7.6 Running-Key Ciphers
    7.7 Unicity Distance for Secret Key Cipher
    7.8 Ideal Cryptosystems
    Problems and Exercises
8. Modern Secret Key Ciphers and Hash Functions
    8.1 Introduction
    8.2 Block Ciphers
        8.2.1 The Magma Cipher
        8.2.2 The RC6 Cipher
        8.2.3 The Rijndael (AES) Cipher
        8.2.4 The Kuznyechik (Grasshopper) 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
        8.4.4 The HC-128 Algorithm
    8.5 Cryptographic Hash Functions
9. Cryptocurrencies and the Blockchain
    9.1 Introduction
    9.2 Proof-of-work and the Hashcash
    9.3 Time-Stamping of Documents
    9.4 The Blockchain
    9.5 Bitcoin and Cryptocurrencies
        9.5.1 Transactions and Bitcoins
        9.5.2 Ledger Maintenance and Mining Bitcoins
        9.5.3 Stability of the Bitcoin System
10. Random Numbers in Cryptography
    10.1 Introduction
    10.2 Refining Physical Random Number Generators
    10.3 Pseudo-Random Number Generators
    10.4 Statistical Tests for Random and Pseudo-Random Number Generators
    10.5 Distinguishing Attack on Stream Ciphers
    10.6 Statistical Attack on Block Ciphers
11. Steganography
    11.1 Purpose of Steganography
    11.2 Basic Methods of Data Embedding
    11.3 Optimal Embedding under Given Level of Distortion
        11.3.1 Problem Setting
        11.3.2 Stegosystem Based on Linear Hash Functions
        11.3.3 Linear Hash Functions over Binary Fields
        11.3.4 Potential Capacity of Stegosystems Based on Linear Hash Functions
        11.3.5 Methods of Constructing Stegosystems Based on Linear Hash Functions
    11.4 Asymptotically Optimal Perfect Stegosystems
Answers to Problems and Exercises
Bibliography
Index