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Modern Cryptography: Applied Mathematics for Encryption and Information Security

Book Description

This comprehensive guide to modern data encryption makes cryptography accessible to information security professionals of all skill levels—with no math expertise required

Cryptography underpins today’s cyber-security; however, few information security professionals have a solid understanding of these encryption methods due to their complex mathematical makeup. Modern Cryptography: Applied Mathematics for Encryption and Information Security leads readers through all aspects of the field, providing a comprehensive overview of cryptography and practical instruction on the latest encryption methods.

The book begins with an overview of the evolution of cryptography and moves on to modern protocols with a discussion of hashes, cryptanalysis, and steganography. From there, seasoned security author Chuck Easttom provides readers with the complete picture—full explanations of real-world applications for cryptography along with detailed implementation instructions. Unlike similar titles on the topic, this reference assumes no mathematical expertise—the reader will be exposed to only the formulas and equations needed to master the art of cryptography.

  • Concisely explains complex formulas and equations and makes the math easy
  • Teaches even the information security novice critical encryption skills
  • Written by a globally-recognized security expert who has taught cryptography to various government and civilian groups and organizations around the world

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Dedication
  5. About the Author
  6. Contents at a Glance
  7. Contents
  8. Acknowledgments
  9. Introduction
  10. PART I Foundations
    1. CHAPTER 1 History of Cryptography to the 1800s
      1. Why Study Cryptography?
      2. What Is Cryptography?
      3. Substitution Ciphers
        1. The Caesar Cipher
        2. Atbash Cipher
        3. Affine Ciphers
        4. Homophonic Substitution
        5. Polybius Cipher
        6. Null Cipher
        7. Multi-Alphabet Substitution
        8. Devices
        9. Book Ciphers
      4. Transposition Ciphers
        1. Reverse Order
        2. Rail Fence Cipher
        3. Geometric Shape Cipher
        4. Columnar Cipher
      5. Combinations
      6. Conclusions
      7. Test Your Knowledge
        1. Answers
      8. Endnotes
    2. CHAPTER 2 History of Cryptography from the 1800s
      1. Cryptography Marches On
        1. Playfair Cipher
        2. Two-Square Cipher
        3. Four-Square Cipher
        4. Hill Cipher
        5. ADFGX and ADFGVX Ciphers
        6. Bifid Cipher
        7. Gronsfeld Cipher
        8. Vernam Cipher
      2. Cryptography Comes of Age
        1. Enigma
        2. SIGABA
        3. Lorenz Cipher
        4. IFF Systems
      3. The NSA: The Early Years
      4. Conclusions
      5. Test Your Knowledge
        1. Answers
      6. Endnotes
    3. CHAPTER 3 Basic Information Theory
      1. The Information Age
      2. Claude Shannon
        1. Theorem 1: Shannon’s Source Coding Theorem
        2. Theorem 2: Noisy Channel Theorem
      3. Core Concepts of Cryptography
        1. Information Entropy
        2. Quantifying Information
        3. Confusion and Diffusion
        4. Avalanche
        5. Hamming Distance
        6. Hamming Weight
        7. Kerckhoffs’s Principle/Shannon’s Maxim
      4. Scientific and Mathematical Theories
        1. What Is a Mathematical Theory?
        2. The Scientific Process
        3. A Scientific Theory
      5. Binary Math
        1. Converting
        2. Binary Operations
      6. Conclusions
      7. Test Your Knowledge
        1. Answers
      8. Endnotes
    4. CHAPTER 4 Essential Number Theory and Discrete Math
      1. Number Systems
        1. Natural Numbers
        2. Negative Numbers
        3. Rational and Irrational Numbers
        4. Real Numbers
        5. Imaginary Numbers
      2. Prime Numbers
        1. Finding Prime Numbers
      3. Relatively Prime, or Co-prime, Numbers
      4. Important Operations
        1. Divisibility Theorems
        2. Summation
        3. Logarithms
        4. Modulus Operations
      5. Famous Number Theorists and Their Contributions
        1. Fibonacci
        2. Fermat
        3. Euler
        4. Goldbach
      6. Discrete Mathematics
        1. Set Theory
        2. Logic
        3. Combinatorics
        4. Graph Theory
      7. Conclusions
      8. Test Your Knowledge
        1. Answers
      9. Endnote
    5. CHAPTER 5 Essential Algebra
      1. Abstract Algebraic Structures
        1. Groups
        2. Rings
        3. Fields
      2. Diophantine Equations
      3. Matrix Math
        1. Matrix Addition and Multiplication
        2. Matrix Transposition
        3. Submatrix
        4. Identity Matrix
      4. Algorithms
        1. Basic Algorithms
        2. Sorting Algorithms
        3. P vs. NP
      5. History Highlights
        1. Ancient Mediterranean Algebra
        2. Ancient Chinese Algebra
        3. Ancient Arabic Algebra
        4. Important Mathematicians
      6. Conclusions
      7. Test Your Knowledge
        1. Answers
      8. Endnote
  11. PART II Symmetric Ciphers and Hashes
    1. CHAPTER 6 Feistel Networks
      1. Cryptographic Keys
      2. Feistel Function
        1. Unbalanced Feistel
      3. Pseudo-Hadamard Transform
      4. MDS Matrix
      5. Lucifer
      6. DES
        1. 3DES
      7. S-Box and P-Box
      8. GOST
      9. Blowfish
      10. Twofish
      11. Skipjack
      12. CAST
      13. FEAL
      14. MARS
      15. TEA
      16. LOKI97
      17. Camellia
      18. ICE
      19. Simon
      20. Symmetric Methods
        1. ECB
        2. CBC
        3. PCBC
        4. CFB
      21. Conclusions
      22. Test Your Knowledge
        1. Answers
      23. Endnotes
    2. CHAPTER 7 Substitution-Permutation Networks
      1. Replacing DES
      2. Advanced Encryption Standard
        1. Rijndael Steps
        2. Rijndael Outline
        3. Rijndael S-Box
        4. Rijndael Key Schedule
      3. Serpent Algorithm
        1. Serpent S-Boxes and Key Schedule
        2. The Serpent Algorithm
      4. Square
      5. SHARK
      6. SAFER Ciphers
        1. The Round Function
        2. Key Schedule
      7. KHAZAD
      8. NESSIE
      9. Stream Ciphers
        1. LFSR
        2. RC4
        3. FISH
        4. eSTREAM
        5. A5
      10. One-Time Pad
      11. Conclusions
      12. Test Your Knowledge
        1. Answers
      13. Endnotes
    3. CHAPTER 8 S-Box Design
      1. Why Study S-Box Design?
        1. Critical to Block Ciphers
        2. Designing Ciphers
        3. Altering S-Boxes
      2. General Facts about S-Boxes
        1. Types of S-Boxes
        2. Design Considerations
      3. The DES S-Box
        1. The Actual S-Boxes for DES
      4. The Rijndael S-Box
        1. The Irreducible Polynomial
        2. Multiplicative Inverse
        3. Affine Transformation
        4. Generating the S-Box
        5. Changing the Rijndael S-Box
      5. Conclusions
      6. Test Your Knowledge
        1. Answers
      7. Endnotes
    4. CHAPTER 9 Cryptographic Hashes
      1. What Is a Cryptographic Hash?
      2. How Are Cryptographic Hashes Used?
        1. Message Integrity
        2. Password Storage
        3. Forensic Integrity
      3. Merkle-Damgård
      4. Specific Algorithms
        1. Checksums
        2. MD5
        3. SHA
        4. RIPEMD
        5. Tiger
        6. HAVAL
        7. Whirlpool
        8. Skein
        9. FSB
        10. GOST
      5. Attacks on Hashes
      6. Salt
      7. MAC and HMAC
      8. Conclusions
      9. Test Your Knowledge
        1. Answers
      10. Endnotes
  12. PART III Asymmetric Ciphers
    1. CHAPTER 10 Common Algorithms
      1. What Is Asymmetric Cryptography?
        1. RSA
      2. The Rabin Cryptosystem
      3. Diffie-Hellman
      4. ElGamal
      5. MQV
      6. Optimal Asymmetric Encryption Padding
      7. Cramer-Shoup
      8. Applications
        1. Key Exchange
        2. Digital Signatures
        3. Digital Certificates
        4. SSL/TLS
      9. Homomorphic Encryption
      10. Conclusions
      11. Test Your Knowledge
        1. Answers
      12. Endnote
    2. CHAPTER 11 Elliptic Curve Cryptography
      1. General Overview
        1. What Is an Elliptic Curve?
        2. Basic Operations on Elliptic Curves
      2. The Algorithm
      3. ECC Variations
        1. ECC Diffie-Hellman
        2. Elliptic Curve Digital Signature Algorithm
      4. Conclusions
      5. Test Your Knowledge
        1. Answers
      6. Endnotes
  13. PART IV Applications
    1. CHAPTER 12 Random Number Generators
      1. What Makes a Good PRNG?
        1. (Desirable) Properties of Pseudo-random Numbers
        2. Tests of Randomness
        3. Standards for PRNG
      2. Specific Algorithms
        1. Middle-Square Algorithm
        2. Linear Congruential Generator
        3. Mersenne Twister
        4. Blum Blum Shub
        5. Yarrow
        6. Fortuna
        7. Dual_EC_DRBG
      3. The Marsaglia CD-ROM
      4. Improving PRNGs
        1. Shuffling
        2. Cryptographic Hash
      5. Conclusions
      6. Test Your Knowledge
        1. Answers
      7. Endnotes
    2. CHAPTER 13 Secure Sockets Layer/Transport Layer Security Protocol
      1. Digital Signatures
        1. Direct Signature
        2. Arbitrated Digital Signature
      2. Digital Certificates
        1. X.509
        2. PGP
      3. Public-Key Infrastructure X.509
      4. SSL and TLS Protocol Basics
        1. History
        2. The Handshake Step-by-Step
        3. SSL/TLS Applications
      5. Conclusions
      6. Test Your Knowledge
        1. Answers
      7. Endnotes
    3. CHAPTER 14 Virtual Private Networks
      1. Authentication
        1. CHAP
        2. EAP
        3. Kerberos
        4. NTLM
      2. PPTP
        1. PPTP vs. PPP
        2. PPTP Authentication
        3. PPTP Encryption
      3. L2TP
      4. IPSec
        1. IKE Phase 1
        2. IKE Phase 2
      5. SSL/TLS
      6. Other Secure Communications
        1. SSH
        2. Wi-Fi Encryption
      7. Conclusions
      8. Test Your Knowledge
        1. Answers
      9. Endnotes
    4. CHAPTER 15 Military Applications
      1. NSA and Cryptography
        1. NSA Cryptographic Standards
        2. The Modern Role of the NSA
      2. U.S. Cryptography Laws and Regulations
      3. Cryptography in Other Nations
        1. International Regulations and Agreements
      4. Cryptography and Malware
        1. Weaponized Malware
        2. Cyber-Warfare
        3. TOR
      5. Conclusions
      6. Test Your Knowledge
        1. Answers
      7. Endnotes
    5. CHAPTER 16 Steganography
      1. Steganography Basics
      2. Steganography History
      3. Steganography Methods and Tools
        1. Steganographic Methods
        2. Steganographic Tools
      4. Current Uses of Steganography
      5. Steganalysis
      6. Distributed Steganography
        1. Total Blocks and Block Order
      7. Conclusions
      8. Test Your Knowledge
        1. Answers
      9. Endnotes
    6. CHAPTER 17 Cryptanalysis
      1. Classic Cryptanalysis Methods
        1. Frequency Analysis
        2. Kasiski Examination
      2. Modern Methods
        1. Linear Cryptanalysis
        2. Differential Cryptanalysis
        3. Integral Cryptanalysis
        4. Mod n Cryptanalysis
      3. Asymmetric Cryptanalysis and RSA
      4. General Rules for Cryptanalysis
      5. Rainbow Tables
      6. The Birthday Paradox
      7. Other Methods
        1. Other Passwords
        2. Related Data
        3. Spyware
        4. Side-Channel Attack
      8. Resources
      9. Conclusions
      10. Test Your Knowledge
        1. Answers
      11. Endnotes
    7. CHAPTER 18 Cryptographic Backdoors
      1. What Are Cryptographic Backdoors?
      2. General Properties
        1. Examples of Backdoors
      3. Other Ways to Compromise Cryptography
        1. Heartbleed Bug
        2. Key Escrow
      4. The Prevalence of Backdoors
        1. Governmental Approach
        2. Private Citizen/Group Approach
      5. Countermeasures
      6. Conclusions
      7. Test Your Knowledge
        1. Answers
      8. Endnotes
    8. CHAPTER 19 The Future of Cryptography
      1. Cryptography and the Cloud
        1. What Is the Cloud?
        2. Cryptography Options for the Cloud
      2. Homomorphic Cryptography
        1. RSA
        2. Goldwasser–Micali
        3. Paillier
      3. Quantum Cryptography
        1. What Is Quantum Mechanics?
        2. Quantum Key Distribution
        3. Breaking Quantum Code
      4. Conclusions
      5. Test Your Knowledge
        1. Answers
      6. Endnotes
  14. APPENDIX Implementing Cryptography
  15. Index