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