Understanding Cryptography: A Textbook for Students and Practitioners

Cover
Half Title page
Title page
Copyright page
Dedication
Foreword
Preface
Acknowledgements
Table of Contents
Chapter 1 Introduction to Cryptography and Data Security
1.1 Overview of Cryptology (and This Book)
1.2 Symmetric Cryptography
1.2.1 Basics
1.2.2 Simple Symmetric Encryption: The Substitution Cipher
1.3 Cryptanalysis
1.3.1 General Thoughts on Breaking Cryptosystems
1.3.2 How Many Key Bits Are Enough?
1.4 Modular Arithmetic and More Historical Ciphers
1.4.1 Modular Arithmetic
1.4.2 Integer Rings
1.4.3 Shift Cipher (or Caesar Cipher)
1.4.4 Affine Cipher
1.5 Discussion and Further Reading
1.6 Lessons Learned
Problems
Chapter 2 Stream Ciphers
2.1 Introduction
2.1.1 Stream Ciphers vs. Block Ciphers
2.1.2 Encryption and Decryption with Stream Ciphers
2.2 Random Numbers and an Unbreakable Stream Cipher
2.2.1 Random Number Generators
2.2.2 The One-Time Pad
2.2.3 Towards Practical Stream Ciphers
2.3 Shift Register-Based Stream Ciphers
2.3.1 Linear Feedback Shift Registers (LFSR)
2.3.2 Known-Plaintext Attack Against Single LFSRs
2.3.3 Trivium
2.4 Discussion and Further Reading
2.5 Lessons Learned
Problems
Chapter 3 The Data Encryption Standard (DES) and Alternatives
3.1 Introduction to DES
3.1.1 Confusion and Diffusion
3.2 Overview of the DES Algorithm
3.3 Internal Structure of DES
3.3.1 Initial and Final Permutation
3.3.2 The f -Function
3.3.3 Key Schedule
3.4 Decryption
3.5 Security of DES
3.5.1 Exhaustive Key Search
3.5.2 Analytical Attacks
3.6 Implementation in Software and Hardware
3.7 DES Alternatives
3.7.1 The Advanced Encryption Standard (AES) and the AESFinalist Ciphers
3.7.2 Triple DES (3DES) and DESX
3.7.3 Lightweight Cipher PRESENT
3.8 Discussion and Further Reading
3.9 Lessons Learned
Problems
Chapter 4 The Advanced Encryption Standard (AES)
4.1 Introduction
4.2 Overview of the AES Algorithm
4.3 Some Mathematics: A Brief Introduction to Galois Fields
4.3.1 Existence of Finite Fields
4.3.2 Prime Fields
4.3.3 Extension Fields GF(2m)
4.3.4 Addition and Subtraction in GF(2m)
4.3.5 Multiplication in GF(2m)
4.3.6 Inversion in GF(2m)
4.4 Internal Structure of AES
4.4.1 Byte Substitution Layer
4.4.2 Diffusion Layer
4.4.3 Key Addition Layer
4.4.4 Key Schedule
4.5 Decryption
4.6 Implementation in Software and Hardware
4.7 Discussion and Further Reading
4.8 Lessons Learned
Problems
Chapter 5 More About Block Ciphers
5.1 Encryption with Block Ciphers: Modes of Operation
5.1.1 Electronic Codebook Mode (ECB)
5.1.2 Cipher Block Chaining Mode (CBC)
5.1.3 Output Feedback Mode (OFB)
5.1.4 Cipher Feedback Mode (CFB)
5.1.5 Counter Mode (CTR)
5.1.6 Galois Counter Mode (GCM)
5.2 Exhaustive Key Search Revisited
5.3 Increasing the Security of Block Ciphers
5.3.1 Double Encryption and Meet-in-the-Middle Attack
5.3.2 Triple Encryption
5.3.3 Key Whitening
5.4 Discussion and Further Reading
5.5 Lessons Learned
Problems
Chapter 6 Introduction to Public-Key Cryptography
6.1 Symmetric vs. Asymmetric Cryptography
6.2 Practical Aspects of Public-Key Cryptography
6.2.2 The Remaining Problem: Authenticity of Public Keys
6.2.3 Important Public-Key Algorithms
6.2.4 Key Lengths and Security Levels
6.3 Essential Number Theory for Public-Key Algorithms
6.3.1 Euclidean Algorithm
6.3.2 Extended Euclidean Algorithm
6.3.3 Euler’s Phi Function
6.3.4 Fermat’s Little Theorem and Euler’s Theorem
6.4 Discussion and Further Reading
6.5 Lessons Learned
Problems
Chapter 7 The RSA Cryptosystem
7.1 Introduction
7.2 Encryption and Decryption
7.3 Key Generation and Proof of Correctness
7.4 Encryption and Decryption: Fast Exponentiation
7.5 Speed-up Techniques for RSA
7.5.1 Fast Encryption with Short Public Exponents
7.5.2 Fast Decryption with the Chinese Remainder Theorem
7.6 Finding Large Primes
7.6.1 How Common Are Primes?
7.6.2 Primality Tests
7.7 RSA in Practice: Padding
7.8 Attacks
7.9 Implementation in Software and Hardware
7.10 Discussion and Further Reading
7.11 Lessons Learned
Problems
Chapter 8 Public-Key Cryptosystems Based on the Discrete Logarithm Problem
8.1 Diffie–Hellman Key Exchange
8.2 Some Algebra
8.2.1 Groups
8.2.2 Cyclic Groups
8.2.3 Subgroups
8.3 The Discrete Logarithm Problem
8.3.1 The Discrete Logarithm Problem in Prime Fields
8.3.2 The Generalized Discrete Logarithm Problem
8.3.3 Attacks Against the Discrete Logarithm Problem
8.4 Security of the Diffie–Hellman Key Exchange
8.5 The Elgamal Encryption Scheme
8.5.1 From Diffie–Hellman Key Exchange to Elgamal Encryption
8.5.2 The Elgamal Protocol
8.5.3 Computational Aspects
8.5.4 Security
8.6 Discussion and Further Reading
8.7 Lessons Learned
Problems
Chapter 9 Elliptic Curve Cryptosystems
9.1 How to Compute with Elliptic Curves
9.1.1 Definition of Elliptic Curves
9.1.2 Group Operations on Elliptic Curves
9.2 Building a Discrete Logarithm Problem with Elliptic Curves
9.3 Diffie–Hellman Key Exchange with Elliptic Curves
9.4 Security
9.5 Implementation in Software and Hardware
9.6 Discussion and Further Reading
9.7 Lessons Learned
Problems
Chapter 10 Digital Signatures
10.1 Introduction
10.1.1 Odd Colors for Cars, or: Why Symmetric Cryptography Is Not Sufficient
10.1.2 Principles of Digital Signatures
10.1.3 Security Services
10.2 The RSA Signature Scheme
10.2.1 Schoolbook RSA Digital Signature
10.2.2 Computational Aspects
10.2.3 Security
10.3 The Elgamal Digital Signature Scheme
10.3.1 Schoolbook Elgamal Digital Signature
10.3.2 Computational Aspects
10.3.3 Security
10.4 The Digital Signature Algorithm (DSA)
10.4.1 The DSA Algorithm
10.4.2 Computational Aspects
10.4.3 Security
10.5 The Elliptic Curve Digital Signature Algorithm (ECDSA)
10.5.1 The ECDSA Algorithm
10.5.2 Computational Aspects
10.5.3 Security
10.6 Discussion and Further Reading
10.7 Lessons Learned
Problems
Chapter 11 Hash Functions
11.1 Motivation: Signing Long Messages
11.2 Security Requirements of Hash Functions
11.2.1 Preimage Resistance or One-Wayness
11.2.2 Second Preimage Resistance or Weak Collision Resistance
11.2.3 Collision Resistance and the Birthday Attack
11.3 Overview of Hash Algorithms
11.3.1 Dedicated Hash Functions: The MD4 Family
11.3.2 Hash Functions from Block Ciphers
11.4 The Secure Hash Algorithm SHA-1
11.4.1 Preprocessing
11.4.2 Hash Computation
11.4.3 Implementation
11.5 Discussion and Further Reading
11.6 Lessons Learned
Problems
Chapter 12 Message Authentication Codes (MACs)
12.1 Principles of Message Authentication Codes
12.2 MACs from Hash Functions: HMAC
12.3 MACs from Block Ciphers: CBC-MAC
12.4 Galois Counter Message Authentication Code (GMAC)
12.5 Discussion and Further Reading
12.6 Lessons Learned
Problems
Chapter 13 Key Establishment
13.1 Introduction
13.1.1 Some Terminology
13.1.2 Key Freshness and Key Derivation
13.1.3 The n2 Key Distribution Problem
13.2 Key Establishment Using Symmetric-Key Techniques
13.2.1 Key Establishment with a Key Distribution Center
13.2.2 Kerberos
13.2.3 Remaining Problems with Symmetric-Key Distribution
13.3 Key Establishment Using Asymmetric Techniques
13.3.1 Man-in-the-Middle Attack
13.3.2 Certificates
13.3.3 Public-Key Infrastructures (PKI) and CAs
13.4 Discussion and Further Reading
13.5 Lessons Learned
Problems
References
Index