Modern Cryptography: Applied Mathematics for Encryption and Information Security

Introduction
Contents
About the Author
Abbreviations
Chapter 1: History of Cryptography to the 1800s
	Introduction
	In This Chapter We Will Cover the Following
	Why Study Cryptography?
	What Is Cryptography?
	Substitution Ciphers
		The Caesar Cipher
			Mathematical Notation of the Caesar Cipher
		Atbash Cipher
		Affine Ciphers
			ROT 13
		Homophonic Substitution
			The Great Cipher
			Copiale Cipher
		Polybius Cipher
			Ancient Cryptography in Modern Wars
		Null Cipher
		Multi-alphabet Substitution
			Tabula Recta
			Vigenère
			The Beaufort Cipher
		Devices
			Scytale Cipher
			Alberti Cipher Disk
			The Jefferson Disk
		Phaistos Disc
		Phryctoriae
		Book Ciphers
			Beale Ciphers
			Dorabella Cipher
			Babington Plot Ciphers
	Transposition Ciphers
		Reverse Order
		Rail Fence Cipher
		Geometric Shape Cipher
		Columnar Cipher
			Myskowski Variation
	Combinations
	D’Agapeyeff Cipher
	Conclusions
	Test Your Knowledge
	References
Chapter 2: History of Cryptography from the 1800s
	Introduction
	In This Chapter We Will Cover the Following
	Playfair
	Two-Square Cipher
	Four-Square Cipher
	Hill Cipher
	ADFGVX
	Bifid
	The Gronsfeld Cipher
	The Vernam Cipher
	Edgar Allan Poe
	Cryptography Comes of Age
		Enigma
			Enigma Variations
			Alan Turing
		Kryha
		SIGABA
		Lorenz Cipher
		Navajo Code Talkers
		VIC Cipher
		IFF Systems
		The NSA: The Early Years
	Conclusions
	Test Your Knowledge
	References
Chapter 3: Basic Information Theory
	Introduction
	In This Chapter We Will Cover
	The Information Age
	Claude Shannon
		Theorem 1: Shannon’s Source Coding Theorem
		Theorem 2: Noisy Channel Theorem
	Concepts
		Information Entropy
		Quantifying Information
		Confusion and Diffusion
		Avalanche
		Hamming Distance
		Hamming Weight
		Kerckhoffs’s Principle/Shannon’s Maxim
	Information Diversity
	Scientific and Mathematical Theories
		What Is a Mathematical Theory?
		The Scientific Process
		A Scientific Theory
			A Look at Successful Scientific Theories
	Binary Math
		Converting
		Binary Operations
			Binary AND
			Binary OR
			Binary XOR
	Conclusions
	Test Your Knowledge
	References
Chapter 4: Essential Number Theory and Discrete Math
	Introduction
	In This Chapter We Will Cover
	Number Systems
		Natural Numbers
		Integers
		Rational Numbers
		Irrational Numbers
		Real Numbers
		Complex Numbers
		Transcendental Numbers
	Prime Numbers
		Finding Prime Numbers
			Mersenne Prime
			Fermat Prime
			Eratosthenes Sieve
			Other Sieves
			Lucas-Lehmer Test
		Relatively Prime
	Important Operations
		Divisibility Theorems
		Summation
		Logarithms
			Natural Logarithm
			Discrete Logarithm
		Modulus Operations
			Congruence
			Congruence Classes
	Famous Number Theorists and Their Contributions
		Fibonacci
		Fermat
		Euler
		Goldbach
	Discrete Mathematics
		Set Theory
		Logic
			Propositional Logic
			Building Logical Constructs
			Truth Tables
		Combinatorics
			Permutations
	Conclusions
	Test Your Knowledge
	References
Chapter 5: Essential Algebra
	Introduction
	In This Chapter We Will Cover
	Groups, Rings, and Fields
		Groups
			Abelian Group
			Cyclic Group
		Rings
		Fields
			Galois Fields
	Diophantine Equations
	Linear Algebra
		Matrix Addition and Multiplication
		Matrix Transposition
		Submatrix
		Identity Matrix
		Determinants
		Eigenvalues and Eigenvectors
		Vector Spaces
	Algorithms
		Basic Algorithms
		Sorting Algorithms
			Quick Sort
			Bubble Sort
			Euclidean Algorithm
			Designing Algorithms
	Conclusions
	Test Your Knowledge
	References
Chapter 6: Feistel Networks
	Introduction
	Cryptographic Keys
	Feistel Function
		Unbalanced Feistel
	Pseudo-Hadamard Transform
	MDS Matrix
	Lucifer
	DES
		3DES
	s-box and p-box
	DEAL
	MacGuffin
	GOST
	Blowfish
	Twofish
	Skipjack
	CAST
	FEAL
	MARS
	TEA
		XTEA
	LOKI97
	Camellia
	ICE
	Simon
	IDEA
	MISTY1
	KASUMI
	MAGENTA
	Speck
	Symmetric Methods
		ECB
		CBC
		PCBC
		CFB
		Galois/Counter Mode
	Conclusions
	Test Your Knowledge
	References
Chapter 7: Substitution-Permutation Networks
	Introduction
	In This Chapter We Will Cover
	Replacing DES
	AES
		Rijndael Steps
		Rijndael Outline
			Initial Round
			Rounds
			Final Round
		Rijndael s-box
		Rijndael Key Schedule
			The Operations
			The Actual Key Schedule
	Serpent
		Serpent s-boxes
		Serpent Key Schedule
		The Serpent Algorithm
	Square
	SHARK
	SAFER
		The Round Function
		Key Schedule
	KHAZAD
	NESSIE
	Stream Ciphers
		LFSR
		RC4
			RC4 Key Schedule Algorithm
		FISH
			PIKE
		eSTREAM
			SNOW
			Rabbit
			HC-128
			MICKEY
			A5
			Phelix
		Salsa20
	One-Time Pad
	Conclusions
	Test Your Knowledge
	References
Chapter 8: s-box Design
	Introduction
	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
			Strict Avalanche Criterion
			Balance
			Bit Independence Criterion
	Approaches to s-box Design
	DES s-box
		The Actual s-boxes for DES
	The Rijndael s-box
		The Irreducible Polynomial
		Multiplicative Inverse
		Affine Transformation
		Generating the s-box
			An Example
		Changing the Rijndael s-box
	s-box Variations
		Key-Dependent s-boxes
		Chaos-Driven s-boxes
	Conclusions
	Test Your Knowledge
	References
Chapter 9: Cryptographic Hashes
	Introduction
	In This Chapter We Will Cover
	What Is a Cryptographic Hash?
	How Are Cryptographic Hashes Used?
		Message Integrity
		Password Storage
		Forensic Integrity
	Merkle-Damgard
	Specific Algorithms
		Checksums
			Longitudinal Parity Check
			Fletcher Checksum
		MD5
		SHA
			SHA-1
			SHA-2
			SHA-3
		RIPEMD
		Tiger
		HAVAL
		NTLM
			NTLM v1
			NTLMv2
		Whirlpool
		Skein
		FSB
		GOST
		BLAKE
		Grøstl
		SWIFFT
	MAC and HMAC
	Key Derivation Functions
	Conclusions
	Test Your Knowledge
	References
Chapter 10: Asymmetric Algorithms
	Introduction
	In This Chapter We Will Cover the Following
	What Is Asymmetric Cryptography?
	Indistinguishability
	RSA
		RSA Example 1
		RSA Example 2
		Factoring RSA Keys
	The Rabin Cryptosystem
	Diffie–Hellman
	ElGamal
	MQV
	YAK
	Forward Secrecy
	Optimal Asymmetric Encryption Padding
	Cramer–Shoup
	Applications
		Key Exchange
		Digital Signatures
			Digital Signature Algorithm
		Digital Certificates
		SSL/TLS
	Homomorphic Encryption
	Conclusions
	Test Your Knowledge
	References
Chapter 11: Elliptic Curve Cryptography
	Introduction
	In This Chapter, We Will Cover the Following
	General Overview
		Basic Operations on Elliptic Curves
	The Algorithm
	ECC Variations
		ECC Diffie-Hellman
	ECC DSA
	Conclusions
	Test Your Knowledge
	References
Chapter 12: Random Number Generators
	Introduction
	In This Chapter We Will Cover
	What Makes a Good PRNG?
		Desirable Properties of Pseudorandom Numbers
		Tests of Randomness
			1-D Test
			Equidistribution
			Runs Test
			Test for Longest Run of 1s
			Poker Test
			Statistical Tests
				Chi-Squared Test
		Standards for PRNG
	Specific Algorithms
		Mid-Square
		Linear Congruential Generator
			Lagged Fibonacci Generators
			Lehmer Algorithm
		Mersenne Twister
		Blum Blum Shub
		Yarrow
		Fortuna
		DUAL_EC_DRBG
	The Marsaglia CD ROM
	Improving PRNGs
		Shuffling
		Cryptographic Hash
	Conclusions
	Test Your Knowledge
	References
Chapter 13: SSL/TLS
	Introduction
	In This Chapter We Will Cover
	Digital Signatures
		Direct Signature
		Arbitrated Digital Signature
			Blind Signatures
	Digital Certificates
		X.509
			Specific Types of X.509 Certificates
		PGP
		Alternate Certificate Types
	Public Key Infrastructure X.509
	SSL and TLS
		History
		The Handshake Step by Step
			Handshake Initiation
		Applications of SSL/TLS
			OpenSSL
			VoIP
			Email
			Web Servers
				Apache Web Server
				IIS
	Conclusions
	Test Your Knowledge
	References
Chapter 14: Virtual Private Networks, Authentication, and Wireless Security
	Introduction
	In This Chapter We Will Cover
	Concepts
	Authentication
		CHAP
		EAP
			LEAP
			EAP-TLS
			PEAP
			EAP-POTP
		Kerberos
		SESAME
		NTLM
	PPTP
		PPTP Authentication
		PPTP Encryption
	L2TP
	IPSec
		IKE Phase 1
			Main Mode
			Aggressive Mode
		IKE Phase 2
	VPN Gateways and Concentrators
	SSL/TLS
	Other Secure Communications
		SSH
		Wi-Fi Encryption
			WEP
			WPA
			WPA2
			WPA3
	Conclusions
	Test Your Knowledge
	References
Chapter 15: Military Applications
	Introduction
	In This Chapter We Will Cover
	NSA and Cryptography
		Security Classifications
		NSA Cryptographic Standards
			Type 1 Products
				HAIPE-IS
				HAVE QUICK
				SINCGARS
			Type 2 Products
				Fortezza Plus
				Fishbowl
			Type 3 and 4 Products
			Suite A
				SAVILLE
				BATON
		FIREFLY
			Suite B
		The Modern Role of the NSA
		Secure Phones
	US Cryptography Laws and Regulations
	How Do Other Nations Handle Cryptography?
		International Regulations and Agreements
			COCOM and Wassenaar
			Specific Governments
	Cryptography and Malware
		Weaponized Malware
		Cyber Warfare
	TOR
		TOR Technical Details
	Conclusions
	Test Your Knowledge
	References
Chapter 16: Steganography
	Introduction
	In This Chapter We Will Cover
	What Is Steganography?
	Historical Steganography
	Methods and Tools
		Classes of Steganography
			Discrete Cosine Transform
			Steganophony
			Video Steganography
		Tools
			Quick Stego/QuickCrypto
			InvisibleSecrets
			MP3 Stego
			OpenStego
			DeepSound
			Other Tools
	Current Use of Steganography
	Steganalysis
	Distributed Steganography
		Total Blocks and Block Order
	Conclusions
	Test Your Knowledge
	References
Chapter 17: Cryptanalysis
	Introduction
	In This Chapter We Will Cover
	Classic Methods
		Frequency Analysis
		Kasiski
	Modern Methods
		Linear Cryptanalysis
		Differential Cryptanalysis
			Higher-Order Differential Cryptanalysis
			Truncated Differential Cryptanalysis
			Impossible Differential Cryptanalysis
		Integral Cryptanalysis
		Mod-n Cryptanalysis
	Asymmetric Cryptanalysis
	General Rules for Cryptanalysis
	Rainbow Tables
	The Birthday Paradox
	Other Methods
		Other Passwords
		Related Data
		Spyware
	Resources
	Conclusions
	Test Your Knowledge
	References
Chapter 18: Cryptographic Backdoors
	Introduction
	In This Chapter We Will Cover
	What Are Cryptographic Backdoors?
	General Concepts
		Output Indistinguishability
		Confidentiality
		Ability to Compromise the Backdoor
	Specific Examples
		Dual_EC_DRBG
		Details
		RSA Backdoor
		Compromising a Hashing Algorithm
	The Prevalence of Backdoors
		Governmental Approach
		Private Citizen/Group Approach
	Countermeasures
	Conclusions
	Test Your Knowledge
	References
Chapter 19: Quantum Computing and Cryptography
	Introduction
	What This Means for Cryptography
	What Is a Quantum Computer?
		Quantum Physics Basics
		Physical Qubits
	Possible Quantum-Resistant Cryptographic Algorithms
	Conclusions
	Test Your Knowledge
	References
Chapter 20: Lattice-Based Cryptography
	Introduction
	Lattice-Based Mathematical Problems
		Shortest Integer Problem
			Shortest Vector Problem
		Closest Vector Problem
	Cryptographic Algorithms
		NTRU
		GGH
		Peikert’s Ring
		Solving Lattice Problems
		Lenstra-Lenstra-Lovász (LLL)
	Conclusions
	Test Your Knowledge
	References
Chapter 21: More Approaches to Quantum-Resistant Cryptography
	Introduction
	Multivariate Cryptography
		Mathematics
		Matsumoto-Imai
		Hidden Field Equations
		Multivariate Quadratic Digital Signature (MQDSS)
		SFLASH
		SWIFFT
		Lamport Signature
	Code-Based Cryptography
		McEliece
		Niederreiter Cryptosystem
	Supersingular Isogeny Key Exchange
		Elliptic Curves
		SIDH
	Conclusions
	Test Your Knowledge
	References
Index