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Index
Title page Copyright Contents Preface to the Second Edition Preface List of Figures List of Tables Part I Setting the Scene 1 Basic Principles
1.1 Why information security?
1.1.1 The rising profile of information security 1.1.2 Two very different office environments
An Old Office A Modern Office
1.1.3 Differing perspectives
Individual Perspective Business Perspective Government Perspective
1.1.4 The importance of security infrastructure
1.2 Security risks
1.2.1 Types of attack
Passive Attacks Active Attacks
1.2.2 Security risks for a simple scenario 1.2.3 Choosing security mechanisms
1.3 Security services
1.3.1 Basic definitions 1.3.2 Relationships between security services
Data Origin Authentication is a Stronger Notion than Data Integrity Non-Repudiation of a Source is a Stronger Notion than Data Origin Authentication Data Origin Authentication and Entity Authentication are Different Data Origin Authentication Plus a Freshness Check can Provide Entity Authentication Confidentiality Does Not Imply Data Origin Authentication
1.4 Fundamentals of cryptosystems
1.4.1 Different cryptographic concepts 1.4.2 Cryptographic primitives for security services 1.4.3 Basic model of a cryptosystem 1.4.4 Codes 1.4.5 Steganography 1.4.6 Access control 1.4.7 Two types of cryptosystem 1.4.8 Secrecy of the encryption key
1.5 Cryptosystem security assumptions
1.5.1 Standard assumptions 1.5.2 Theoretical attack models 1.5.3 Knowledge of the encryption algorithm
The Impact of Kerckhoffs’ Second Principle The Case for Publicly Known Algorithms What Happens in Practice?
1.5.4 Use of publicly known algorithms
1.6 Breaking cryptosystems
1.6.1 Some useful preliminaries
Binary Numbers XOR Exponentiation Concatenation
1.6.2 Key lengths and keyspaces 1.6.3 Breaking encryption algorithms 1.6.4 Exhaustive key searches
Conducting an Exhaustive Key Search Identifying Candidate Decryption Keys Determining the Correct Decryption Key Protecting Against Exhaustive Key Searches
1.6.5 Classes of attack 1.6.6 Academic attacks
1.7 Summary 1.8 Further reading 1.9 Activities
2 Historical Cryptosystems
2.1 Monoalphabetic ciphers
2.1.1 Caesar Cipher
Description of the Caesar Cipher Fitting the Caesar Cipher to the Basic Model Mathematical Description of the Caesar Cipher Insecurity of the Caesar Cipher
2.1.2 Simple Substitution Cipher
Permutations Description of the Simple Substitution Cipher Fitting the Simple Substitution Cipher to the Basic Model Keyspace of the Simple Substitution Cipher Insecurity of the Simple Substitution Cipher
2.1.3 Frequency analysis
The Nature of Plaintexts Letter Frequency Analysis Limitations of Letter Frequency Analysis Sufficiency of Keyspace Size
2.1.4 A study of theory versus practice
Theory: Uniqueness of the Plaintext Practice: Statistical Information The Gap Between Theory and Practice
2.2 Historical advances
2.2.1 Design improvements 2.2.2 Playfair Cipher
Preprocessing for the Playfair Cipher Encryption Using the Playfair Cipher Example of a Playfair Cipher Cryptanalysis of the Playfair Cipher Lessons from the Playfair Cipher
2.2.3 Homophonic encoding
Example of Homophonic Encoding Single Letter Frequency Analysis of Homophonic Encoding Problems with Homophonic Encoding Lesson from Homophonic Encoding
2.2.4 Vigenère Cipher
Encryption Using the Vigenère Cipher Cryptanalysis of the Vigenère Cipher Lesson from the Vigenère Cipher
2.3 Summary 2.4 Further reading 2.5 Activities
3 Theoretical versus Practical Security
3.1 Theoretical security
3.1.1 Perfect secrecy
Motivating Perfect Secrecy Defining Perfect Secrecy
3.1.2 A simple cryptosystem offering perfect secrecy
Description of the Cryptosystem The Attacker’s View Comments on the Simple Cryptosystem
3.1.3 One-time pads
Properties of a One-Time Pad One-Time Pad from the Vigenère Cipher Consequences of Key Reuse in a One-Time Pad One-Time Pad from a Latin Square Vernam Cipher
3.1.4 Theoretical security summary
3.2 Practical security
3.2.1 One-time pad in practice
Key Management Issues with a One-Time Pad One-Time Pads in Practice
3.2.2 Cover time 3.2.3 Computational complexity
Complexity of Simple Processes Polynomial and Exponential Time Computing Real Attack Times Limitations of Complexity
3.2.4 Design process of a cryptosystem
Selection or Design of a Primitive Mode of Use Implementation Key Management
3.2.5 Evaluating security
Assessing the Security of a Cryptographic Algorithm Assessing the Security of a Cryptographic Protocol Assessing the Security of a Cryptosystem
3.2.6 Adequate security 3.2.7 Towards a notion of practical security
3.3 Summary 3.4 Further reading 3.5 Activities
Part II The Cryptographic Toolkit 4 Symmetric Encryption
4.1 Classification of symmetric encryption algorithms 4.2 Stream ciphers
4.2.1 Model of a stream cipher 4.2.2 Key management of stream ciphers 4.2.3 The impact of errors 4.2.4 Properties of stream ciphers 4.2.5 Examples of stream ciphers
4.3 Block ciphers
4.3.1 Model of a block cipher 4.3.2 Properties of block ciphers 4.3.3 Block cipher algorithms
4.4 The Data Encryption Standard
4.4.1 Feistel Cipher
Encryption Using a Feistel Cipher Choosing the Round Function Decryption Using a Feistel Cipher Number of Rounds
4.4.2 Specification of DES 4.4.3 Brief history of DES
Milestones in the History of DES Early Design Criticisms DES Key Searches
4.4.4 Triple DES
3-Key Triple DES 2-Key Triple DES Triple DES in Practice
4.5 The Advanced Encryption Standard
4.5.1 Development of AES 4.5.2 Design of AES
AES Encryption AES Decryption
4.5.3 AES today
4.6 Modes of operation
4.6.1 Electronic Code Book mode
How ECB Mode Works Problems with ECB Mode
4.6.2 Cipher Block Chaining mode
Encryption Using CBC Mode Decryption Using CBC Mode Impact of Transmission Errors in CBC Mode Properties of CBC Mode
4.6.3 Cipher Feedback mode
Encryption Using CFB Mode Decryption Using CFB Mode Reduced Feedback CFB Mode Properties of CFB Mode
4.6.4 Counter mode
Encryption and Decryption Using CTR Mode Properties of CTR Mode
4.6.5 Comparing modes of operation
4.7 Use of symmetric encryption
4.7.1 Other types of symmetric encryption 4.7.2 The future for symmetric encryption
4.8 Summary 4.9 Further reading 4.10 Activities
5 Public-Key Encryption
5.1 Public-key cryptography
5.1.1 Motivation for public-key cryptography
Problems with Symmetric Cryptography History of Public-Key Cryptography
5.1.2 Properties of public-key cryptosystems
The Briefcase Protocol A Blueprint for a Public-Key Cryptosystem A Better Briefcase Analogy?
5.1.3 Some mathematical preliminaries
Primes Modular Arithmetic Some Notation
5.1.4 One-way functions for public-key cryptography
Trapdoor One-Way Functions Multiplication of Two Large Primes Modular Exponentiation with a Large Modulus Non-Modular Exponentiation
5.2 RSA
5.2.1 Setting up RSA
Generating an RSA Key Pair
5.2.2 Encryption and decryption using RSA
RSA Encryption RSA Decryption
5.2.3 Security of RSA
Decrypting a Ciphertext Without Knowledge of the Private Key Determining the Private Key Directly from the Public Key Specific Instance Attacks on RSA RSA Security Summary
5.2.4 RSA in practice
Probabilistic Encryption RSA-OAEP
5.3 ElGamal and elliptic curve variants
5.3.1 Setting up ElGamal 5.3.2 Encryption and decryption using ElGamal
Elgamal Encryption Elgamal Decryption
5.3.3 Security of ElGamal
Decrypting a Ciphertext Without Knowledge of the Private Key Determining the Private Key Directly from the Public Key Elgamal Security Summary
5.3.4 ElGamal in practice
Use of System-Wide Parameters Probabilistic Encryption Message Expansion
5.3.5 Elliptic Curve Cryptography
5.4 Comparison of RSA, ElGamal, and ECC
5.4.1 Popularity of RSA 5.4.2 Performance issues 5.4.3 Security issues
Key Lengths of Public-Key Cryptosystems Comparing Security of Public-Key Cryptosystems Exhaustive Key Searches for Private Keys Relative Key Lengths
5.5 Use of public-key encryption
5.5.1 Limiting factors 5.5.2 Hybrid encryption 5.5.3 Other types of public-key cryptosystem 5.5.4 The future for public-key cryptosystems
5.6 Summary 5.7 Further reading 5.8 Activities
6 Data Integrity
6.1 Different levels of data integrity 6.2 Hash functions
6.2.1 Properties of a hash function
Practical Property 1: Compresses Arbitrary Long Inputs into a Fixed Length Output Practical Property 2: Easy to Compute Security Property 1: Preimage Resistance Security Property 2: Second Preimage Resistance Security Property 3: Collision Resistance Relationships Between the Three Security Properties
6.2.2 Applications of hash functions
Application Requiring Preimage Resistance Application Requiring Second Preimage Resistance Application Requiring Collision Resistance
6.2.3 Attacking hash functions in theory
The Dangers of a Very Small Hash The Dangers of a Small Hash Birthday Attacks
6.2.4 Hash functions in practice
Hash Function Design A Brief History of Modern Hash Functions
6.2.5 SHA-3
SHA-3 Design SHA-3 Family Use of SHA-3
6.3 Message authentication codes
6.3.1 Does symmetric encryption provide data origin authentication? 6.3.2 MAC properties 6.3.3 CBC-MAC
Computing CBC-MAC Checking CBC-MAC Security of CBC-MAC CBC-MAC in Practice
6.3.4 HMAC 6.3.5 MACs and non-repudiation 6.3.6 Using MACs with encryption
Using Separate Primitives Authenticated-Encryption Primitives Galois Counter Mode Other Authenticated-Encryption Modes
6.4 Summary 6.5 Further reading 6.6 Activities
7 Digital Signature Schemes
7.1 Digital signatures
7.1.1 The basic idea 7.1.2 Electronic signatures 7.1.3 Digital signature scheme fundamentals
Requirements for a Digital Signature Scheme Basic Properties of a Digital Signature Scheme
7.2 Non-repudiation using symmetric techniques
7.2.1 Arbitrated digital signature schemes 7.2.2 Asymmetric trust relationships 7.2.3 Enforced trust
7.3 Digital signature schemes based on RSA
7.3.1 Complementary requirements 7.3.2 Basic model of a digital signature scheme 7.3.3 Two different approaches 7.3.4 RSA digital signature scheme with appendix
The Signing Process The Verification Process Reasons for Hashing RSA is Special
7.3.5 RSA digital signature scheme with message recovery
Advantages of Digital Signature Schemes with Message Recovery Signing and Verifying Using a Digital Signature Scheme with Message Recovery Redundancy Techniques Digital Signature Schemes with Message Recovery and Confidentiality
7.3.6 Other digital signature schemes
7.4 Digital signature schemes in practice
7.4.1 Security of digital signature schemes
Security of the Signature Key Security of the Verification Key Security of the Hash Function
7.4.2 Using digital signature schemes with encryption 7.4.3 Relationship with handwritten signatures
Environmental Differences Security Differences Practical Differences Flexibility Differences
7.4.4 Relationship with advanced electronic signatures
7.5 Summary 7.6 Further reading 7.7 Activities
8 Entity Authentication
8.1 Random number generation
8.1.1 The need for randomness 8.1.2 What is randomness? 8.1.3 Non-deterministic generators
Hardware-Based Non-Deterministic Generators Software-Based Non-Deterministic Generators Non-Deterministic Generators in Practice
8.1.4 Deterministic generators
Basic Model of a Deterministic Generator Deterministic Generators in Practice
8.2 Providing freshness
8.2.1 Clock-based mechanisms 8.2.2 Sequence numbers 8.2.3 Nonce-based mechanisms 8.2.4 Comparison of freshness mechanisms
8.3 Fundamentals of entity authentication
8.3.1 A problem with entity authentication 8.3.2 Applications of entity authentication 8.3.3 General categories of identification information
Something the Claimant Has Something the Claimant Is Something the Claimant Knows
8.4 Passwords
8.4.1 Problems with passwords 8.4.2 Cryptographic password protection
Traditional Approach to Unix Password Protection Key Stretching
8.5 Dynamic password schemes
8.5.1 Idea behind dynamic password schemes 8.5.2 Example dynamic password scheme
Dynamic Password Scheme Description Analysis of Dynamic Password Scheme Dynamic Password Schemes in Practice
8.6 Zero-knowledge mechanisms
8.6.1 Motivation for zero-knowledge 8.6.2 Zero-knowledge analogy 8.6.3 Zero-knowledge in practice
8.7 Summary 8.8 Further reading 8.9 Activities
9 Cryptographic Protocols
9.1 Protocol basics
9.1.1 Operational motivation for protocols 9.1.2 Environmental motivation for protocols 9.1.3 Components of a cryptographic protocol
9.2 From objectives to a protocol
9.2.1 Stages of protocol design 9.2.2 Challenges of the stages of protocol design
Defining the Objectives Determining the Protocol Goals Specifying the Protocol Standards for Cryptographic Protocols
9.2.3 Assumptions and actions
Assumptions Actions
9.2.4 The wider protocol design process
9.3 Analysing a simple protocol
9.3.1 A simple application
The Objectives The Protocol Goals Candidate Protocols
9.3.2 Protocol 1
Protocol Assumptions Protocol Description Protocol Analysis Remarks
9.3.3 Protocol 2
Protocol Assumptions Protocol Description Protocol Analysis Remarks
9.3.4 Protocol 3
Protocol Assumptions Protocol Description Protocol Analysis Remarks
9.3.5 Protocol 4
Protocol Assumptions Protocol Description Protocol Analysis
9.3.6 Protocol 5
Protocol Assumptions Protocol Description Protocol Analysis Remarks
9.3.7 Protocol 6
Protocol Assumptions Protocol Description Protocol Analysis Remarks
9.3.8 Protocol 7
Protocol Assumptions Protocol Description Protocol Analysis Remarks
9.3.9 Simple protocol summary
9.4 Authentication and key establishment protocols
9.4.1 Typical AKE protocol goals 9.4.2 Diffie–Hellman key agreement protocol
Idea Behind the Diffie–Hellman Protocol Instantiation of the Diffie–Hellman Protocol Analysis of the Diffie–Hellman Protocol Man-In-The-Middle Attack on the Diffie–Hellman Protocol Ake Protocols Based on Diffie–Hellman Versions of the Diffie–Hellman Protocol
9.4.3 An AKE protocol based on key distribution
Protocol Description Protocol Analysis
9.4.4 Perfect forward secrecy
9.5 Summary 9.6 Further reading 9.7 Activities
Part III Key Management 10 Key Management
10.1 Key management fundamentals
10.1.1 What is key management? 10.1.2 The key lifecycle 10.1.3 Fundamental key management requirements 10.1.4 Key management systems
10.2 Key lengths and lifetimes
10.2.1 Key lifetimes 10.2.2 Choosing a key length
10.3 Key generation
10.3.1 Direct key generation 10.3.2 Key derivation
Advantages of Key Derivation Key Derivation Functions Key Derivation From Passwords
10.3.3 Key generation from components 10.3.4 Public-key pair generation
10.4 Key establishment
10.4.1 Key hierarchies
Philosophy Behind Key Hierarchies A Simple Key Hierarchy Managing the Top-Level Keys Key Wrapping Scalable Key Hierarchies
10.4.2 Unique key per transaction schemes
Motivation for UKPT Schemes Application of UKPT Schemes Example UKPT Schemes
10.4.3 Quantum key establishment
Motivation for Quantum Key Establishment 7.1.1 The Basic Idea Quantum Key Establishment in Practice
10.5 Key storage
10.5.1 Avoiding key storage 10.5.2 Key storage in software
Storing Keys in the Clear Storing Keys Using Cryptography
10.5.3 Key storage in hardware
Hardware Security Modules Key Storage on an HSM Other Types of Hardware Communicating with Hardware Evaluating Hardware
10.5.4 Key storage risk factors 10.5.5 Key backup, archival, and recovery
Key Backup Key Archival Key Recovery
10.6 Key usage
10.6.1 Key separation
The Need for Key Separation Enforcing Key Separation Key Separation in Practice
10.6.2 Key change
The Need for Key Change Impact of Key Change Mechanisms for Changing Keys Changing Public-Key Pairs
10.6.3 Key activation 10.6.4 Key destruction
10.7 Governing key management
10.7.1 Key management policies, practices, and procedures 10.7.2 Example procedure: key generation ceremony
10.8 Summary 10.9 Further reading 10.10 Activities
11 Public-Key Management
11.1 Certification of public keys
11.1.1 Motivation for public-key certificates
A Scenario Providing Assurance of Purpose Providing a Point of Trust Using a Trusted Directory
11.1.2 Public-key certificates
Contents of a Public-Key Certificate Interpreting a Public-Key Certificate Public-Key Certificate Creators Relying on a Public-Key Certificate Digital Certificates
11.2 The certificate lifecycle
11.2.1 Differences in the certificate lifecycle 11.2.2 Certificate creation
Location of Key Pair and Certificate Creation Registration of Public Keys Proof of Possession Generating CA Public-Key Pairs
11.2.3 Key pair change
Revocation of Public-Key Certificates Revocation Techniques
11.3 Public-key management models
11.3.1 Choosing a CA 11.3.2 Public-key certificate management models
CA-Free Certification Model Reputation-Based Certification Model Closed Certification Model Connected Certification Model
11.3.3 Joining CA domains
Cross-Certification Certification Hierarchies Certificate Chains Joining CA Domains in Practice
11.4 Alternative approaches
11.4.1 Webs of trust 11.4.2 Identity-based encryption
The Idea Behind Identity-Based Encryption A Model for IBE IBE Algorithms Practical Issues with IBE More General Notions of IBE IBE in Practice
11.5 Summary 11.6 Further reading 11.7 Activities
Part IV Use of Cryptography 12 Cryptographic Applications
12.1 Cryptography for securing the Internet
12.1.1 TLS background 12.1.2 TLS security requirements 12.1.3 Cryptography used in TLS 12.1.4 TLS 1.2 and earlier versions
Handshake Protocol Description Analysis of the Handshake Protocol Handshake Protocol with Client Authentication Record Protocol
12.1.5 TLS 1.3
Motivation for TLS 1.3 What is New in TLS 1.3 TLS 1.3 Handshake Protocol Description Comments on the TLS 1.3 Handshake Protocol
12.1.6 TLS key management
Key Management System Key Generation Key Establishment Key Storage Key Usage
12.1.7 TLS security issues 12.1.8 TLS design considerations
12.2 Cryptography for wireless local area networks
12.2.1 WLAN background 12.2.2 WLAN security requirements 12.2.3 WEP
Confidentiality and Integrity Mechanisms in WEP Entity Authentication in WEP
12.2.4 Attacks on WEP
WEP Key Management Weaknesses WEP Entity Authentication Weaknesses WEP Confidentiality and Integrity Weaknesses WEP Design Flaws
12.2.5 WPA and WPA2
Mutual Entity Authentication and Key Establishment Confidentiality and Data Origin Authentication in WPA Confidentiality and Data Origin Authentication in WPA2
12.2.6 WLAN security issues 12.2.7 WLAN design considerations
12.3 Cryptography for mobile telecommunications
12.3.1 Mobile telecommunications background 12.3.2 GSM security requirements 12.3.3 Cryptography used in GSM
GSM Authentication GSM Encryption Facilitating GSM Roaming Security of GSM Algorithms
12.3.4 UMTS
UMTS Security Protocols UMTS Cryptographic Algorithms
12.3.5 LTE
LTE Key Hierarchy LTE Cryptographic Algorithms
12.3.6 GSM, UMTS, and LTE key management
Key Management System Key Generation Key Establishment Key Storage Key Usage
12.3.7 Mobile telecommunications security issues 12.3.8 Mobile telecommuncations design considerations
12.4 Cryptography for secure payment card transactions
12.4.1 Background to payment card services 12.4.2 Magnetic stripe cards
PIN Protection Card Verification Values PIN Verification Value Payment Card Authorisation
12.4.3 EMV cards
PIN Verification Offline Data Authentication Online Authentication Transaction Certificates Contactless Payments Security of Management Functions
12.4.4 Using EMV cards for internet transactions 12.4.5 Using EMV cards for authentication 12.4.6 Using EMV cards for mobile payments
Mobile Payment Schemes Tokenization Apple Pay
12.4.7 Payment card key management
Key Management System Key Generation Key Establishment Key Storage Key Usage
12.4.8 Payment card security issues 12.4.9 Payment card cryptographic design considerations
12.5 Cryptography for video broadcasting
12.5.1 Video broadcasting background 12.5.2 Video broadcasting security requirements 12.5.3 Cryptography used in video broadcasting 12.5.4 Key management for video broadcasting
Video Broadcast Key Management System Design Video Broadcast Key Establishment Video Broadcast Access Control Video Broadcast Key Storage
12.5.5 Video broadcast security issues 12.5.6 Video broadcast design considerations
12.6 Cryptography for identity cards
12.6.1 eID background 12.6.2 eID security requirements 12.6.3 Cryptography used in eID cards 12.6.4 Provision of the eID card core functions
Digital Data Presentation Digital Card Holder Authentication Digital Signature Creation
12.6.5 eID key management
eID Certificates eID Card Issuing Process eID Certificate Revocation eID Signature Validity
12.6.6 eID security issues 12.6.7 eID design considerations
12.7 Cryptography for anonymity
12.7.1 Tor background 12.7.2 Tor security requirements 12.7.3 How Tor works
Cryptography Used in Tor Onion Routing Tor Key Establishment Tor Integrity Checking Tor Communication Tor Key Management
12.7.4 Tor security issues 12.7.5 Tor design considerations
12.8 Cryptography for digital currency
12.8.1 Bitcoin background 12.8.2 Bitcoin security requirements 12.8.3 Bitcoin transactions
Bitcoin Addresses Making a Bitcoin Payment Bitcoin Key Management
12.8.4 Bitcoin blockchain
Bitcoin Blocks Lightweight Transaction Verification
12.8.5 Bitcoin mining
The Need for Bitcoin Mining The Bitcoin Mining Challenge Creation of New Bitcoin Blocks Impact of a Successful Bitcoin Mining Operation
12.8.6 Bitcoin security issues 12.8.7 Bitcoin design considerations
12.9 Summary 12.10 Further reading 12.11 Activities
13 Cryptography for Personal Devices
13.1 File protection
13.1.1 Full disk encryption
Cryptography for Full Disk Encryption XTS Mode Bitlocker Full Disk Encryption Key Management
13.1.2 Virtual disk encryption 13.1.3 Individual file encryption
In-Built File Encryption Encryption Software Application File Encryption
13.2 Email security
13.2.1 The need for email security
Email Security Requirements Issues with Email Security
13.2.2 Techniques for securing email
Email Security Standards An Identity-Based Approach Encrypting Attachments Webmail Security
13.3 Messaging security
13.3.1 WhatsApp security requirements 13.3.2 Cryptography used in WhatsApp
Cryptographic Tools Initialising a WhatsApp Session Deriving Message Keys Other Cryptographic Issues
13.4 Platform security
13.4.1 Cryptographic protection of iOS user data
Secure Enclave iOS Key Hierarchy
13.4.2 Cryptographic protection of iOS internet services
iMessage Security Facetime Security iCloud Security
13.4.3 Further iOS cryptographic support
Code Signing Secure Networking Support Other Applications
13.5 Summary 13.6 Further reading 13.7 Activities
14 Control of Cryptography
14.1 The cryptography dilemma
14.1.1 The case for controlling the use of cryptography 14.1.2 The case against controlling the use of cryptography 14.1.3 Seeking a balance 14.1.4 Strategies for controlling the use of cryptography
14.2 Backdoors in algorithms
14.2.1 Use of backdoors
Historical Use of Backdoors Modern Use of Backdoors
14.2.2 Dual_EC_DRBG
14.3 Legal mechanisms
14.3.1 Export restrictions 14.3.2 Key escrow 14.3.3 Legal requirements to access plaintext
14.4 Control of cryptography in an age of complexity
14.4.1 The Snowden revelations 14.4.2 Changes to the cryptographic environment
The World that was The World that is Consequences of the Changed Environment
14.4.3 Strategies for controlling ubiquitous cryptography
Just Looking Exploiting Vulnerabilities Targeting Flaws in Key Management Infiltrating Manufacturing Processes Advanced Data Analysis
14.5 Summary 14.6 Further reading 14.7 Activities
15 Closing Remarks Mathematics Appendix
A.1 Decimal, binary, and hex
A.1.1 Decimal
Writing a Number in Decimal Leading Zeros
A.1.2 Binary
Writing a Number in Binary Converting Binary to Decimal Converting Decimal to Binary The 3.3 Trick
A.1.3 XOR A.1.4 Hex
Writing a Number in Hex Converting Hex to Decimal Converting Between Binary and Hex
A.1.5 ASCII
A.2 Modular arithmetic
A.2.1 Motivation
Days of the Week Months of the Year
A.2.2 Modular numbers
Adding Multiples of the Modulus One Number Modulo Another Terminology and Notation Negative Modular Numbers
A.2.3 Modular arithmetic operations
Addition, Subtraction, and Multiplication Modular Reduction: Before or After?
A.3 The mathematics of RSA
A.3.1 Primes and coprimes
Primes Greatest Common Divisors Coprimes
A.3.2 Multiplicative inverses
Definition of Multiplicative Inverse Division Using Multiplicative Inverses Modular Inverses The Extended Euclidean Algorithm
A.3.3 RSA key pair setup A.3.4 Why RSA works
A.4 The mathematics of ElGamal
A.4.1 ElGamal public keys
Primitive Elements Importance of Primitive Elements to ElGamal
A.4.2 Why ElGamal works
A.5 Further reading
Bibliography Index
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