Cryptography, Information Theory, and Error-Correction: A Handbook for the 21st Century, 2nd Edition

by Aiden A. Bruen, James M. McQuillan, Mario A. Forcinito

Length: 688 pages
Edition: 2
Language: English
Publisher: Wiley
Publication Date: 2021-07-21
ISBN-10: 1119582423
ISBN-13: 9781119582427
Sales Rank: #6072779 (See Top 100 Books)

CRYPTOGRAPHY, INFORMATION THEORY, AND ERROR-CORRECTION

A rich examination of the technologies supporting secure digital information transfers from respected leaders in the field

As technology continues to evolve Cryptography, Information Theory, and Error-Correction: A Handbook for the 21^ST Century is an indispensable resource for anyone interested in the secure exchange of financial information. Identity theft, cybercrime, and other security issues have taken center stage as information becomes easier to access. Three disciplines offer solutions to these digital challenges: cryptography, information theory, and error-correction, all of which are addressed in this book.

This book is geared toward a broad audience. It is an excellent reference for both graduate and undergraduate students of mathematics, computer science, cybersecurity, and engineering. It is also an authoritative overview for professionals working at financial institutions, law firms, and governments who need up-to-date information to make critical decisions. The book’s discussions will be of interest to those involved in blockchains as well as those working in companies developing and applying security for new products, like self-driving cars. With its reader-friendly style and interdisciplinary emphasis this book serves as both an ideal teaching text and a tool for self-learning for IT professionals, statisticians, mathematicians, computer scientists, electrical engineers, and entrepreneurs.

Six new chapters cover current topics like Internet of Things security, new identities in information theory, blockchains, cryptocurrency, compression, cloud computing and storage.  Increased security and applicable research in elliptic curve cryptography are also featured. The book also:

Shares vital, new research in the field of information theory
Provides quantum cryptography updates
Includes over 350 worked examples and problems for greater understanding of ideas.

Cryptography, Information Theory, and Error-Correction guides readers in their understanding of reliable tools that can be used to store or transmit digital information safely.

Cover
Table of Contents
Series Page
Title Page
Copyright
Dedications
Preface to the Second Edition
    WELCOME, New Co‐author
    Intended Readership, Connections Between the Areas
    Problems with Solutions
    Style
    Possible Courses
    What's New
    Hardcover and eBook
Acknowledgments for the Second Edition
Book Website
About the Authors
Part I: Mainly Cryptography
    Chapter 1: Historical Introduction and the Life and Work of Claude E. Shannon
        1.1 Historical Background
        1.2 Brief Biography of Claude E. Shannon
        1.3 Career
        1.4 Personal – Professional
        1.5 Scientific Legacy
        1.6 The Data Encryption Standard Code, DES, 1977–2005
        1.7 Post‐Shannon Developments
        Notes
    Chapter 2: Classical Ciphers and Their Cryptanalysis
        2.1 Introduction
        2.2 The Caesar Cipher
        2.3 The Scytale Cipher
        2.4 The Vigenère Cipher
        2.5 Frequency Analysis
        2.6 Breaking the Vigenère Cipher, Babbage–Kasiski
        2.7 The Enigma Machine and Its Mathematics
        2.8 Modern Enciphering Systems
        2.9 Problems
        2.10 Solutions
    Chapter 3: RSA, Key Searches, TLS, and Encrypting Email
        3.1 The Basic Idea of Cryptography
        3.2 Public Key Cryptography and RSA on a Calculator
        3.3 The General RSA Algorithm
        3.4 Public Key Versus Symmetric Key
        3.5 Attacks, Security, Catch‐22 of Cryptography
        3.6 Summary of Encryption
        3.7 The Diffie–Hellman Key Exchange
        3.8 Intruder‐in‐the‐Middle Attack on the Diffie–Hellman (or Elliptic Curve) Key‐Exchange
        3.9 TLS (Transport Layer Security)
        3.10 PGP and GPG
        3.11 Problems
        3.12 Solutions
        Notes
    Chapter 4: The Fundamentals of Modern Cryptography
        4.1 Encryption Revisited
        4.2 Block Ciphers, Shannon's Confusion and Diffusion
        4.3 Perfect Secrecy, Stream Ciphers, One‐Time Pad
        4.4 Hash Functions
        4.5 Message Integrity Using Symmetric Cryptography
        4.6 General Public Key Cryptosystems
        4.7 Digital Signatures
        4.8 Modifying Encrypted Data and Homomorphic Encryption
        4.9 Quantum Encryption Using Polarized Photons
        4.10 Quantum Encryption Using Entanglement
        4.11 Quantum Key Distribution is Not a Silver Bullet
        4.12 Postquantum Cryptography
        4.13 Key Management and Kerberos
        4.14 Problems
        4.15 Solutions
    Chapter 5: Modes of Operation for AES and Symmetric Algorithms
        5.1 Modes of Operation
        5.2 The Advanced Encryption Standard Code
        5.3 Overview of AES
    Chapter 6: Elliptic Curve Cryptography (ECC)
        6.1 Abelian Integrals, Fields, Groups
        6.2 Curves, Cryptography
        6.3 The Hasse Theorem, and an Example
        6.4 More Examples
        6.5 The Group Law on Elliptic Curves
        6.6 Key Exchange with Elliptic Curves
        6.7 Elliptic Curves mod n
        6.8 Encoding Plain Text
        6.9 Security of ECC
        6.10 More Geometry of Cubic Curves
        6.11 Cubic Curves and Arcs
        6.12 Homogeneous Coordinates
        6.13 Fermat's Last Theorem, Elliptic Curves, Gerhard Frey
        6.14 A Modification of the Standard Version of Elliptic Curve Cryptography
        6.15 Problems
        6.16 Solutions
    Chapter 7: General and Mathematical Attacks in Cryptography
        7.1 Cryptanalysis
        7.2 Soft Attacks
        7.3 Brute‐Force Attacks
        7.4 Man‐in‐the‐Middle Attacks
        7.5 Relay Attacks, Car Key Fobs
        7.6 Known Plain Text Attacks
        7.7 Known Cipher Text Attacks
        7.8 Chosen Plain Text Attacks
        7.9 Chosen Cipher Text Attacks, Digital Signatures
        7.10 Replay Attacks
        7.11 Birthday Attacks
        7.12 Birthday Attack on Digital Signatures
        7.13 Birthday Attack on the Discrete Log Problem
        7.14 Attacks on RSA
        7.15 Attacks on RSA using Low‐Exponents
        7.16 Timing Attack
        7.17 Differential Cryptanalysis
        7.18 Attacks Utilizing Preprocessing
        7.19 Cold Boot Attacks on Encryption Keys
        7.20 Implementation Errors and Unforeseen States
        7.21 Tracking. Bluetooth, WiFi, and Your Smart Phone
        7.22 Keep Up with the Latest Attacks (If You Can)
        Notes
    Chapter 8: Practical Issues in Modern Cryptography and Communications
        8.1 Introduction
        8.2 Hot Issues
        8.3 Authentication
        8.4 User Anonymity
        8.5 E‐commerce
        8.6 E‐government
        8.7 Key Lengths
        8.8 Digital Rights
        8.9 Wireless Networks
        8.10 Communication Protocols
        Notes
Part II: Mainly Information Theory
    Chapter 9: Information Theory and its Applications
        9.1 Axioms, Physics, Computation
        9.2 Entropy
        9.3 Information Gained, Cryptography
        9.4 Practical Applications of Information Theory
        9.5 Information Theory and Physics
        9.6 Axiomatics of Information Theory
        9.7 Number Bases, Erdös and the Hand of God
        9.8 Weighing Problems and Your MBA
        9.9 Shannon Bits, the Big Picture
    Chapter 10: Random Variables and Entropy
        10.1 Random Variables
        10.2 Mathematics of Entropy
        10.3 Calculating Entropy
        10.4 Conditional Probability
        10.5 Bernoulli Trials
        10.6 Typical Sequences
        10.7 Law of Large Numbers
        10.8 Joint and Conditional Entropy
        10.9 Applications of Entropy
        10.10 Calculation of Mutual Information
        10.11 Mutual Information and Channels
        10.12 The Entropy of X + Y
        10.13 Subadditivity of the Function –x log x
        10.14 Entropy and Cryptography
        10.15 Problems
        10.16 Solutions
    Chapter 11: Source Coding, Redundancy
        11.1 Introduction, Source Extensions
        11.2 Encodings, Kraft, McMillan
        11.3 Block Coding, the Oracle, Yes–No Questions
        11.4 Optimal Codes
        11.5 Huffman Coding
        11.6 Optimality of Huffman Coding
        11.7 Data Compression, Redundancy
        11.8 Problems
        11.9 Solutions
    Chapter 12: Channels, Capacity, the Fundamental Theorem
        12.1 Abstract Channels
        12.2 More Specific Channels
        12.3 New Channels from Old, Cascades
        12.4 Input Probability, Channel Capacity
        12.5 Capacity for General Binary Channels, Entropy
        12.6 Hamming Distance
        12.7 Improving Reliability of a Binary Symmetric Channel
        12.8 Error Correction, Error Reduction, Good Redundancy
        12.9 The Fundamental Theorem of Information Theory
        12.10 Proving the Fundamental Theorem
        12.11 Summary, the Big Picture
        12.12 Postscript: The Capacity of the Binary Symmetric Channel
        12.13 Problems
        12.14 Solutions
    Chapter 13: Signals, Sampling, Coding Gain, Shannon's Information Capacity Theorem
        13.1 Continuous Signals, Shannon's Sampling Theorem
        13.2 The Band‐Limited Capacity Theorem
        13.3 The Coding Gain
    Chapter 14: Ergodic and Markov Sources, Language Entropy
        14.1 General and Stationary Sources
        14.2 Ergodic Sources
        14.3 Markov Chains and Markov Sources
        14.4 Irreducible Markov Sources, Adjoint Source
        14.5 Cascades and the Data Processing Theorem
        14.6 The Redundancy of Languages
        14.7 Problems
        14.8 Solutions
    Chapter 15: Perfect Secrecy: The New Paradigm
        15.1 Symmetric Key Cryptosystems
        15.2 Perfect Secrecy and Equiprobable Keys
        15.3 Perfect Secrecy and Latin Squares
        15.4 The Abstract Approach to Perfect Secrecy
        15.5 Cryptography, Information Theory, Shannon
        15.6 Unique Message from Ciphertext, Unicity
        15.7 Problems
        15.8 Solutions
    Chapter 16: Shift Registers (LFSR) and Stream Ciphers
        16.1 Vernam Cipher, Psuedo‐Random Key
        16.2 Construction of Feedback Shift Registers
        16.3 Periodicity
        16.4 Maximal Periods, Pseudo‐Random Sequences
        16.5 Determining the Output from 2m Bits
        16.6 The Tap Polynomial and the Period
        16.7 Short Linear Feedback Shift Registers and the Berlekamp‐Massey Algorithm
        16.8 Problems
        16.9 Solutions
    Chapter 17: Compression and Applications
        17.1 Introduction, Applications
        17.2 The Memory Hierarchy of a Computer
        17.3 Memory Compression
        17.4 Lempel–Ziv Coding
        17.5 The WKdm Algorithms
        17.6 Main Memory – to Compress or Not to Compress
        17.7 Problems
        17.8 Solutions
Part III: Mainly Error‐Correction
    Chapter 18: Error‐Correction, Hadamard, and Bruen–Ott
        18.1 General Ideas of Error Correction
        18.2 Error Detection, Error Correction
        18.3 A Formula for Correction and Detection
        18.4 Hadamard Matrices
        18.5 Mariner, Hadamard, and Reed–Muller
        18.6 Reed–Muller Codes
        18.7 Block Designs
        18.8 The Rank of Incidence Matrices
        18.9 The Main Coding Theory Problem, Bounds
        18.10 Update on the Reed–Muller Codes: The Proof of an Old Conjecture
        18.11 Problems
        18.12 Solutions
    Chapter 19: Finite Fields, Modular Arithmetic, Linear Algebra, and Number Theory
        19.1 Modular Arithmetic
        19.2 A Little Linear Algebra
        19.3 Applications to RSA
        19.4 Primitive Roots for Primes and Diffie–Hellman
        19.5 The Extended Euclidean Algorithm
        19.6 Proof that the RSA Algorithm Works
        19.7 Constructing Finite Fields
        19.8 Pollard's p-1 Factoring Algorithm
        19.9 Latin Squares
        19.10 Computational Complexity, Turing Machines, Quantum Computing
        19.11 Problems
        19.12 Solutions
        Note
    Chapter 20: Introduction to Linear Codes
        20.1 Repetition Codes and Parity Checks
        20.2 Details of Linear Codes
        20.3 Parity Checks, the Syndrome, and Weights
        20.4 Hamming Codes, an Inequality
        20.5 Perfect Codes, Errors, and the BSC
        20.6 Generalizations of Binary Hamming Codes
        20.7 The Football Pools Problem, Extended Hamming Codes
        20.8 Golay Codes
        20.9 McEliece Cryptosystem
        20.10 Historical Remarks
        20.11 Problems
        20.12 Solutions
    Chapter 21: Cyclic Linear Codes, Shift Registers, and CRC
        21.1 Cyclic Linear Codes
        21.2 Generators for Cyclic Codes
        21.3 The Dual Code
        21.4 Linear Feedback Shift Registers and Codes
        21.5 Finding the Period of a LFSR
        21.6 Cyclic Redundancy Check (CRC)
        21.7 Problems
        21.8 Solutions
    Chapter 22: Reed‐Solomon and MDS Codes, and the Main Linear Coding Theory Problem (LCTP)
        22.1 Cyclic Linear Codes and Vandermonde
        22.2 The Singleton Bound for Linear Codes
        22.3 Reed–Solomon Codes
        22.4 Reed‐Solomon Codes and the Fourier Transform Approach
        22.5 Correcting Burst Errors, Interleaving
        22.6 Decoding Reed‐Solomon Codes, Ramanujan, and Berlekamp–Massey
        22.7 An Algorithm for Decoding and an Example
        22.8 Long MDS Codes and a Partial Solution of a 60 Year‐Old Problem
        22.9 Problems
        22.10 Solutions
    Chapter 23: MDS Codes, Secret Sharing, and Invariant Theory
        23.1 Some Facts Concerning MDS Codes
        23.2 The Case k = 2, Bruck Nets
        23.3 Upper Bounds on MDS Codes, Bruck–Ryser
        23.4 MDS Codes and Secret Sharing Schemes
        23.5 MacWilliams Identities, Invariant Theory
        23.6 Codes, Planes, and Blocking Sets
        23.7 Long Binary Linear Codes of Minimum Weight at Least 4
        23.8 An Inverse Problem and a Basic Question in Linear Algebra
    Chapter 24: Key Reconciliation, Linear Codes, and New Algorithms
        24.1 Symmetric and Public Key Cryptography
        24.2 General Background
        24.3 The Secret Key and the Reconciliation Algorithm
        24.4 Equality of Remnant Keys: The Halting Criterion
        24.5 Linear Codes: The Checking Hash Function
        24.6 Convergence and Length of Keys
        24.7 Main Results
        24.8 Some Details on the Random Permutation
        24.9 The Case Where Eve Has Nonzero Initial Information
        24.10 Hash Functions Using Block Designs
        24.11 Concluding Remarks
        Note
    Chapter 25: New Identities for the Shannon Function with Applications
        25.1 Extensions of a Binary Symmetric Channel
        25.2 A Basic Entropy Equality
        25.3 The New Identities
        25.4 Applications to Cryptography and a Shannon‐Type Limit
        25.5 Problems
        25.6 Solutions
    Chapter 26: Blockchain and Bitcoin
        26.1 Ledgers, Blockchains
        26.2 Hash Functions, Cryptographic Hashes
        26.3 Digital Signatures
        26.4 Bitcoin and Cryptocurrencies
        26.5 The Append‐Only Network, Identities, Timestamp, Definition of a Bitcoin
        26.6 The Bitcoin Blockchain and Merkle Roots
        26.7 Mining, Proof‐of‐Work, Consensus
        26.8 Thwarting Double Spending
    Chapter 27: IoT, The Internet of Things
        27.1 Introduction
        27.2 Analog to Digital (A/D) Converters
        27.3 Programmable Logic Controller
        27.4 Embedded Operating Systems
        27.5 Evolution, From SCADA to the Internet of Things
        27.6 Everything is Fun and Games until Somebody Releases a Stuxnet
        27.7 Securing the IoT, a Mammoth Task
        27.8 Privacy and Security
        Notes
    Chapter 28: In the Cloud
        28.1 Introduction
        28.2 Distributed Systems
        28.3 Cloud Storage – Availability and Copyset Replication
        28.4 Homomorphic Encryption
        28.5 Cybersecurity
        28.6 Problems
        28.7 Solutions
    Chapter 29: Review Problems and Solutions
        29.1 Problems
        29.2 Solutions
Appendix A
    A.1 ASCII
Appendix B
    B.1 Shannon's Entropy Table
Glossary
References
Index
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