Practical Mathematical Cryptography provides a clear and accessible introduction to practical mathematical cryptography.
Cryptography, both as a science and as practice, lies at the intersection of mathematics and the science of computation, and the presentation emphasises the essential mathematical nature of the computations and arguments involved in cryptography.
Cryptography is also a practical science, and the book shows how modern cryptography solves important practical problems in the real world, developing the theory and practice of cryptography from the basics to secure messaging and voting.
The presentation provides a unified and consistent treatment of the most important cryptographic topics, from the initial design and analysis of basic cryptographic schemes towards applications.
Features
- Builds from theory toward practical applications
- Suitable as the main text for a mathematical cryptography course
- Focus on secure messaging and voting systems.
Author(s): Kristian Gjøsteen
Series: Chapman & Hall/CRC Cryptography and Network Security Series
Edition: 1
Publisher: Chapman and Hall/CRC
Year: 2022
Language: English
Tags: Cryptography; Symmetric Cryptography; Key Exchange; Diffie-Hellman Protocol; Public Key Encryption; Digital Signatures; Quantum Computation; Symmetric Cryptography
Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
CHAPTER 1: Symmetric Cryptography
1.1. DEFINITIONS
1.2. CONFIDENTIALITY AGAINST EAVESDROPPERS
1.3. INTEGRITY
1.4. CONFIDENTIALITY AND INTEGRITY
1.5. THE KEY DISTRIBUTION PROBLEM
CHAPTER 2: Key Exchange and Diffie-Hellman
2.1. THE DIFFIE-HELLMAN PROTOCOL
2.2. DISCRETE LOGARITHMS
2.3. PRIMALITY TESTING
2.4. FINITE FIELDS
2.5. ELLIPTIC CURVES
2.6. ACTIVE ATTACKS
CHAPTER 3: Public Key Encryption
3.1. DEFINITIONS
3.2. SCHEMES BASED ON DIFFIE-HELLMAN
3.3. RSA
3.4. FACTORING INTEGERS
3.5. LATTICES
3.6. LATTICE-BASED CRYPTOSYSTEMS
3.7. LATTICE ALGORITHMS
3.8. THE PUBLIC KEY INFRASTRUCTURE PROBLEM
CHAPTER 4: Digital Signatures
4.1. DEFINITIONS
4.2. HASH FUNCTIONS
4.3. RSA SIGNATURES
4.4. SCHNORR SIGNATURES
4.5. HASH-BASED SIGNATURES
4.6. SECURING DIFFIE-HELLMAN
4.7. THE PUBLIC KEY INFRASTRUCTURE PROBLEM
CHAPTER 5: Factoring Using Quantum Computers
5.1. BACKGROUND
5.2. QUANTUM COMPUTATION
5.3. FACTORING USING A QUANTUM COMPUTER
CHAPTER 6: Computational Problems
6.1. DEFINITIONS
6.2. STATISTICAL DISTANCE
6.3. DIFFIE-HELLMAN
6.4. RSA
6.5. LATTICE PROBLEMS
CHAPTER 7: Symmetric Cryptography
7.1. DEFINING SECURITY
7.2. CONFIDENTIALITY AND UNDERLYING PRIMITIVES
7.3. MESSAGE AUTHENTICATION CODES
7.4. CHANNELS
7.5. HASH FUNCTIONS
7.6. IDEAL MODELS
CHAPTER 8: Public Key Encryption
8.1. DEFINING SECURITY
8.2. KEY ENCAPSULATION MECHANISMS
8.3. HOMOMORPHIC ENCRYPTION
8.4. COMMITMENT SCHEMES
8.5. CRYPTOGRAPHIC VOTING
CHAPTER 9: Digital Signatures
9.1. DEFINING SECURITY
9.2. HASH AND SIGN PARADIGM
9.3. IDENTIFICATION SCHEMES
9.4. MESSAGING
CHAPTER 10: Key Exchange
10.1. KEY EXCHANGE PROTOCOLS
10.2. DEFINING SECURITY
10.3. KEY EXCHANGE FROM KEY ENCAPSULATION
10.4. SINGLE-MESSAGE KEY EXCHANGE
10.5. SINGLE-SIDED AUTHENTICATION
10.6. CONTINUOUS KEY EXCHANGE
CHAPTER 11: Arguments
11.1. ARGUMENTS
11.2. NON-INTERACTIVE ARGUMENTS
11.3. USING HVZK
11.4. FURTHER USEFUL ARGUMENTS
CHAPTER 12: Multi-party Computation
12.1. SECRET SHARING
12.2. MULTI-PARTY COMPUTATION
12.3. DISTRIBUTED DECRYPTION
CHAPTER 13: Messaging Protocols
13.1. MESSAGING PROTOCOLS
13.2. DEFINING SECURITY
13.3. INVASIVE ADVERSARIES
13.4. SOMEWHAT ANONYMOUS MESSAGING
CHAPTER 14: Cryptographic Voting
14.1. DEFINITIONS
14.2. HOW TO USE A VOTING SCHEME
14.3. CAST AS INTENDED
14.4. COERCION RESISTANCE
Index
