book

Cryptography

Name: Cryptography
Author: Zoubir Z. Mammeri
ISBN: 9781394207480

by Zoubir Z. Mammeri

March 2024

Beginner

624 pages

29h 40m

English

Wiley

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Cover
Title Page
Copyright Page
Preface
1 Introduction to Computer Security
1.1 Introduction1.1.1 Why Do Attacks Occur?1.1.2 Are Security Attacks Avoidable?1.1.3 What Should Be Protected in Cyberspace?1.1.4 Security vs Safety1.1.5 Cybersecurity vs IT Security1.2 Security Terms and Definitions1.2.1 Assets and Attackers1.2.2 Vulnerabilities, Threats, and Risks1.3 Security Services1.3.1 Confidentiality and Privacy1.3.2 Integrity1.3.3 Availability1.3.4 Authentication and Authenticity1.3.5 Non-repudiation and Accountability1.3.6 Authorization1.4 Attacks1.4.1 Taxonomy of Attacks1.4.1.1 Attacks According to Their Origin1.4.1.2 Passive vs Active Attacks1.4.1.3 Attacks According to Their Objectives1.4.2 Taxonomy of Attackers1.4.3 Malware Taxonomy1.4.3.1 Virus1.4.3.2 Worm1.4.3.3 Trojan1.4.3.4 Ransomware1.4.3.5 Spyware and Adware1.4.3.6 Botnet1.4.3.7 Keylogger, Screen Scraper, and Web Shell1.4.3.8 Exploit, Logic Bomb, Backdoor, and Rootkit1.4.4 Daily Awareness to IT Security1.5 Countermeasures/Defenses1.5.1 Very Old Roots of Countermeasures1.5.2 Methods for Defense1.5.2.1 Prevention/Detection/Reaction Methods1.5.2.2 Level of Automation of Defense Methods1.5.2.3 Design Orientations of Defense Methods1.5.3 Overview of Security Countermeasures1.5.3.1 Organizational Measures1.5.3.2 Technical Countermeasures1.5.4 Security Penetration Testing Tools1.6 Overview of Defense Systems1.6.1 Firewalls1.6.2 Proxy Overview1.6.3 Intrusion Detection Systems1.6.4 Intrusion Protection Systems1.6.4.1 Performance Requirements Regarding IDSs and IPSs1.6.5 Honeypots1.6.6 Network Address Translation1.6.7 Virtual Private Networks1.6.8 Layered-Security Architecture1.7 Introduction to Privacy Protection1.7.1 Overview of Privacy Issues1.7.2 Introduction to the GDPR Directive1.7.2.1 Personal Data and Acts of Processing1.7.2.2 Principles of Data Protection1.8 Concluding Remarks1.9 Exercises and Solutions1.9.1 List of Exercises1.9.2 Solutions to ExercisesNotesReferences
2 Introduction to Cryptography
2.1 Definitions of Basic Terms2.1.1 Cryptography, Cryptanalysis, and Cryptology2.1.2 Brief History of Cryptography2.1.3 Basic Terms Related to Encryption Systems2.1.4 Symmetric and Asymmetric Cryptographic Systems2.1.4.1 Symmetric Cryptosystems2.1.4.2 Asymmetric Cryptosystems2.1.4.3 Symmetric vs Asymmetric Cryptosystems and Their Combination2.1.4.4 Trapdoor Functions2.2 Cryptographic Primitives2.2.1 Encryption2.2.2 Hash Functions and Data Integrity2.2.3 Message Authentication Codes2.2.4 Digital Signature2.2.5 Digital Certificates and Non-Repudiation2.2.6 Shared-Secret Generation2.2.7 Pseudorandom Number Generation2.3 Fundamental Properties of Cryptographic Algorithms2.3.1 Should Cryptographic Algorithms Be Secret or Not?2.3.2 Models of Security Proof2.3.2.1 Computational Infeasibility2.3.2.2 Provable Security2.3.3 Perfect Secrecy2.3.4 Security Strength of Cryptographic Algorithms2.4 Attacks Against Cryptographic Algorithms2.4.1 What Is Cryptanalysis?2.4.2 Categorization of Cryptanalysis Attacks2.4.2.1 First Categorization of Cryptanalysis Attacks2.4.2.2 Second Categorization of Cryptanalysis Attacks2.4.3 Attacks on Implementations of Cryptographic Algorithms2.4.3.1 Side-Channel Attacks2.4.3.2 Fault-Injection Attacks2.4.4 Practicality of Cryptanalysis Attacks2.5 Steganography2.5.1 Examples of Secret Hiding Without Using Computer2.5.2 Examples of Secret Hiding Using Computer2.6 Exercises and Problems2.6.1 List of Exercises and Problems2.6.2 Solutions to Exercises and ProblemsNotesReferences
3 Mathematical Basics and Computation Algorithms for Cryptography
3.1 Number Theory Notations, Definitions, and Theorems3.1.1 Basic Terms and Facts of Number Theory3.1.2 Sets3.1.3 Modulo Operator and Equivalence Class3.1.4 Basic Properties of Modular Arithmetic3.1.5 ℤn: Integers Modulo n3.1.6 Multiplicative Inverse3.1.7 Modular Square Roots3.1.8 List of Exercises and Problems3.2 Basic Algebraic Structures3.2.1 Groups and Rings and Their Properties3.2.2 Fields3.2.3 Extension Fields 3.2.4 Extension Fields3.2.5 List of Exercises and Problems3.3 Computation Algorithms3.3.1 Euclidean and Extended Euclidean Algorithms3.3.1.1 Euclidean Algorithm3.3.1.2 Extended Euclidean Algorithm3.3.1.3 Finding Multiplicative Inverse3.3.2 Modular Exponentiation: Square-and-Multiply3.3.3 Fast Modular Multiplication and Montgomery’s Multiplication3.3.3.1 Single-precision Montgomery Multiplication Algorithm3.3.3.2 Multi-precision Montgomery Multiplication Algorithm3.3.4 Chinese Remainder Theorem and Gauss’s Algorithm3.3.5 Finding Modular Square Roots3.3.5.1 Tonelli-Shanks Algorithm for Finding Modular Square Roots of Primes3.3.5.2 Finding Square Roots of Multiple Primes3.3.6 Test of Irreducibility3.3.6.1 Naïve Approach3.3.6.2 Efficient Approach (Rabin’s Test of Irreducibility)3.3.7 List of Exercises and Problems3.4 Birthday Paradox and Its Generalization3.5 Solutions to Exercises and ProblemsNotesReferences
4 Symmetric Ciphering: Historical Ciphers
4.1 Definitions4.2 Caesar’s Cipher4.3 Affine Ciphers4.4 Vigenere’s Cipher4.5 Enigma Machine4.5.1 Principle of Secure Communication Using Enigma4.5.2 Rotors and Reflector4.5.3 Plug Board4.5.4 Machine Setting4.5.5 Encryption and Decryption Procedures4.5.6 Enigma Decryption Correctness4.5.7 Complexity Analysis4.5.8 Breaking Enigma Code4.5.8.1 Weaknesses, Practices, and Other Features that had been Exploited4.5.8.2 Crib-based Attack4.5.8.3 Improvement of Settings Identification Process4.6 One-time Pad4.7 Exercises and Problems4.7.1 List of Exercises and Problems4.7.2 Solutions to Exercises and ProblemsNotesReferences
5 Hash Functions, Message Authentication Codes, and Digital Signature
5.1 Hash Functions5.1.1 Properties of Hash Functions5.1.2 Generic Attacks Against Hash Functions5.1.3 Overall Operation Principle of Hashing Algorithms5.1.3.1 Merkle-Damgård Construction5.1.3.2 Vulnerability to Length Extension Attack5.2 Secure Hash Algorithms (SHA)5.2.1 SHA-1 and SHA-2 Algorithms5.2.1.1 SHA-1 Algorithm5.2.1.2 SHA-256 Algorithm5.2.1.3 SHA-224 Algorithm5.2.1.4 SHA-512 Algorithm5.2.1.5 SHA-384, SHA-512/224, and SHA-512/256 Algorithms5.2.1.6 SHA-1 Security5.2.2 SHA-3 Functions5.2.2.1 Keccak-p Permutation5.2.2.2 Sponge Construction5.2.2.3 SHA-3 Functions5.3 Message Authentication Codes5.3.1 Objectives and Properties of MACs5.3.2 Hash Function-based MACs5.3.2.1 HMAC5.3.2.2 KMAC5.3.2.3 Generic Attacks Against Hash Function-based MAC Algorithms5.3.3 Block Cipher-based MACs5.4 Digital Signature5.4.1 Digital Signature in Public Key World5.4.2 Attacks Against Digital Signature Schemes5.5 Concluding Remarks5.6 Problems5.6.1 List of Problems5.6.2 Solutions to ProblemsNotesReferences
6 Stream Ciphers
6.1 Stream Ciphers6.1.1 Principles of Stream Ciphers6.1.2 Synchronous vs Self-synchronized Keystream Generators6.1.2.1 Synchronous Stream Ciphers6.1.2.2 Self-synchronized Stream Ciphers6.1.3 How to Generate Random Keystream Bits?6.1.4 Linear-Feedback Shift Registers (LFSRs)6.1.4.1 LFSR Principle and Properties6.1.4.2 Feedback Polynomial of LFSRs6.1.5 LFSRs for Building Stream Ciphers6.2 Examples of Standard Keystream Generators6.2.1 A5/1 Keystream Generator6.2.2 E0 Keystream Generator6.2.3 SNOW 3G Keystream Generator6.2.3.1 Formal Description of SNOW 3G6.2.3.2 Algorithmic Description of SNOW 3G6.2.4 ZUC Keystream Generator6.2.4.1 Principle of ZUC Keystream Generator6.2.4.2 ZUC Algorithm6.2.5 ChaCha20 Stream Cipher6.2.5.1 ChaCha20 State6.2.5.2 ChaCha20 Quarter Round6.2.5.3 ChaCha20 Keystream Block Generation6.2.5.4 Plaintext Encryption and Decryption Using ChaCha206.2.6 RC4 Stream Cipher6.2.6.1 RC4 Key-scheduling Algorithm6.2.6.2 Keystream Generation Phase6.2.7 Lightweight Cryptography Stream Ciphers6.2.7.1 Trivium Stream Cipher6.2.7.2 Enocoro Stream Cipher6.3 Exercises and Problems6.3.1 List of Exercises and Problem6.3.2 Solutions to Exercises and ProblemsNotesReferences

7 Block Ciphers: Basics, TDEA, and AES
7.1 Construction Principles for Block Cipher Design7.1.1 Confusion and Diffusion Properties7.1.1.1 Substitution Boxes7.1.1.2 Permutation7.1.1.3 Key Expansion7.1.2 Feistel Structure7.2 Triple Data Encryption Algorithm (TDEA)7.2.1 Data Encryption Algorithm (DEA)7.2.1.1 DEA Encryption and Decryption7.2.1.2 Initial Permutation and Its Inverse7.2.1.3 Function f7.2.2 TDEA Construction and Usage7.2.2.1 Bundle and DEA Keys7.2.2.2 TDEA Encryption and Decryption7.2.2.3 Key Schedule Function KS7.2.3 Security Issues7.2.3.1 Complexity of Attacks Against DES7.2.3.2 TDEA Security Limit7.2.3.3 Meet-in-the-Middle Attack Against Double DES and TDEA7.3 Advanced Encryption System (AES)7.3.1 Distinctive Features of AES7.3.2 Data Representation in AES7.3.3 Overall Structure of AES7.3.4 AES Transformation Description7.3.4.1 SubBytes and InvSubBytes Transformations7.3.4.2 ShiftRows and InvShiftRows Transformations7.3.4.3 MixColumns and InvMixColumns Transformations7.3.4.4 AddRoundKey Transformation7.3.5 Key Expansion7.3.6 Mathematical Description of AES7.3.6.1 Data Representation and Operations on Data7.3.6.2 SubBytes and InvSubBytes Transformations7.3.6.3 ShiftRows and InvShiftRows Transformations7.3.6.4 MixColumns and InvMixColumns Transformations7.3.6.5 AddRoundKey Transformation7.3.7 Security of AES7.4 Exercises and Problems7.4.1 List of Exercises and Problems7.4.2 Solutions to Exercises and ProblemsNotesReferences
8 Block Cipher Modes of Operation for Confidentiality
8.1 Introduction8.1.1 Definitions8.1.2 Overview of Standard Modes of Operation8.1.3 Notations and Common Basic Functions8.1.4 Common Aspects of Modes for Confidentiality8.1.4.1 Plaintext Length and Padding8.1.4.2 Initialization Vector8.2 ECB Mode of Operation8.3 CBC Modes of Operation8.3.1 Basic CBC Mode8.3.2 CBC Variants (CS1, CS2, CS3)8.3.2.1 CBC-CS1 Mode8.3.2.2 CBC-CS2 and CBC-CS3 Modes8.4 OFB Mode of Operation8.5 CTR Mode of Operation8.6 CFB Mode of Operation8.7 Format-Preserving Encryption Modes of Operation8.7.1 Common Aspects to FPE Modes8.7.2 Encryption and Decryption in FF1 and FF3-1 Modes8.7.3 FF1 Mode8.7.4 FF3-1 Mode8.8 XTS-AES Mode of Operation8.8.1 Overview of XTS-AES8.8.2 Encryption and Decryption Algorithms8.8.3 Some Strengths and Weaknesses of XTS-AES8.9 Comparison of Design Features of Modes for Confidentiality8.10 Security of Modes of Operation for Confidentiality8.10.1 Vulnerability to Block Repetitions and Replay8.10.2 Vulnerability to Predictable IV or Tweak8.10.3 Vulnerability to IV/Tweak that Is Not a Nonce8.10.4 Vulnerability to Birthday Attacks8.10.5 Vulnerability to Bit-Flipping Attacks8.11 Exercises and Problems8.11.1 List of Exercises and Problems8.11.2 Solutions to Exercises and ProblemsNotesReferences
9 Block Cipher Modes of Operation for Authentication and Confidentiality
9.1 Introduction9.2 Block Cipher Modes of Operation for Confidentiality and Authentication9.2.1 Authenticated Encryption and AEAD Algorithms9.2.1.1 Approaches to Data Authentication9.2.1.2 Authenticated Encryption with Associated Data Algorithms9.2.1.3 Limits of Authenticated-Decryption Modes9.2.2 CMAC Mode of Operation9.2.3 CCM Mode of Operation9.2.3.1 MAC Generation and Encryption9.2.3.2 MAC Verification and Decryption9.2.3.3 Information Formatting Function9.2.3.4 Counter Formatting Function9.2.4 GCM and GMAC Modes of Operation9.2.4.1 GCTR Encryption Mode9.2.4.2 Hash Function of GCM9.2.4.3 Authenticated Encryption with GCM9.2.4.4 Authenticated Decryption with GCM9.2.4.5 GMAC Mode9.2.4.6 Forbidden Attack Against GCM with Repeated IV9.2.5 AES-GCM-SIV Mode9.2.5.1 What Does Nonce Misuse-resistance Mean?9.2.5.2 Overview of AES-GCM-SIV Mode9.2.5.3 Key Derivation and Hash Functions9.2.5.4 Authenticated Encryption with AES-GCM-SIV9.2.5.5 Authenticated Decryption with AES-GCM-SIV9.2.6 Poly13059.2.6.1 Poly1305-AES9.2.6.2 ChaCha20-Poly1305 AEAD9.2.7 Key Wrapping Modes9.2.7.1 KW and KWP Modes of Operation9.2.7.2 TKW Mode of Operation9.2.7.3 Security of Key Wrapping Modes9.2.8 Security of Authenticated-Encryption Modes9.2.8.1 Block Repetitions and Replay9.2.8.2 Chosen-Ciphertext Attacks9.2.8.3 Birthday Attacks9.2.8.4 Bit-flipping Attacks9.2.8.5 Nonce Misuse9.3 Exercises and Problems9.3.1 List of Exercises and Problems9.3.2 Solutions to Exercises and ProblemsNotesReferences
10 Introduction to Security Analysis of Block Ciphers
10.1 Pseudorandom Functions and Permutations10.1.1 Definitions of Random and Pseudorandom Functions and Permutations10.1.2 Indistinguishability and Security of PRFs10.1.2.1 Indistinguishability and Security of PRPs10.1.2.2 PRF/PRP Switching Lemma10.2 Security of TDEA and AES10.2.1 Security Against Key Recovery Attack10.2.2 Birthday Attack Against Block Ciphers10.3 Security Analysis Modes of Operation of BC for Confidentiality10.3.1 Left-or-Right Indistinguishability10.3.2 Some Bounds of Security of Block Cipher Modes of Operation10.4 Security Analysis of Authenticity-only Schemes10.4.1 Generic Models for Security Analysis of Authenticity Schemes10.4.1.1 Game for Tag Forgery Analysis10.4.1.2 Game for MAC Indistinguishability10.4.2 Some Security Bounds for MAC Schemes10.4.2.1 Security Bounds for CMAC10.4.2.2 Security Bounds for HMAC10.5 Generic Models for Security Analysis of Authenticated-Encryption Modes10.5.1 Generic Modeling of Security of AEAD Modes10.5.2 Some Security Bounds for CCM, GCM, and AES-GCM-SIV10.5.2.1 Bounds for CCM10.5.2.2 Bounds for GCM10.5.2.3 Some Bounds for AES-GCM-SIV Security10.6 Problems and Solutions10.6.1 List of Problems10.6.2 Solutions to ProblemsNotesReferences
11 Introduction to Cryptanalysis Attacks on Symmetric Ciphers
11.1 Memory-Time Trade-off Attacks11.1.1 Hellman’s Table-based Attacks11.1.2 Offline Precomputation11.1.3 Key Search11.1.4 Rainbow Chains11.2 Linear Cryptanalysis11.2.1 Bias and Piling-up Lemma11.2.2 Constructing Linear Approximation Expressions11.2.2.1 Finding Linear Approximations Associated with an s-box11.2.2.2 Measuring Quality of Linear Approximations11.2.2.3 Finding Linear Expressions Associated with an s-box and a Key11.2.2.4 Finding Linear Expressions Associated with Two s-boxes and a Key11.2.2.5 Finding Linear Expressions Associated with a Full Cipher11.2.3 General Methodology for Performing Linear Cryptanalysis11.2.3.1 Algorithm 1: Deduction of a Bit-information about Cipher Key11.2.3.2 Algorithm 2: Recovery of the Last-round Key11.3 Differential Cryptanalysis11.3.1 Difference Distribution Table11.3.1.1 Difference Distribution Table: Construction and Properties11.3.1.2 Difference-Propagation Probability11.3.1.3 Effect of Round Key Addition11.3.2 Differential Attack Design11.3.2.1 First step: Selection of an Overall Difference-Propagation Probability11.3.2.2 Second Step: Selection of Chosen Plaintexts11.3.2.3 Third Step: Recovery of some Bits of the Last-round Key11.4 Algebraic Cryptanalysis11.5 Cube Attack11.5.1 Main Idea of Cube Attack11.5.2 Polynomial Representation11.5.3 Cube Attack Mounting11.5.3.1 Preprocessing Phase11.5.3.2 Key Recovery Phase11.6 Other Attacks Against Stream Ciphers11.6.1 Divide-and-Conquer Attack11.6.2 Correlation Attack11.7 Problems and Solutions11.7.1 List of Problems11.7.2 Solutions to ProblemsNotesReferences
12 Public-Key Cryptosystems
12.1 Introduction to Public-Key Cryptosystems12.1.1 Attacks Against Public-Key Cryptosystems12.1.1.1 Attacks Against Encryption Schemes12.1.1.2 Attacks Against Digital Signature Schemes12.2 RSA Cryptosystem12.2.1 RSA Encryption and Decryption12.2.2 Implementation Issues12.2.2.1 Fast Modular Exponentiation Methods12.2.2.2 Chinese Remainder Theorem-based RSA Decryption12.2.2.3 Why e =65537 Is Often Used in RSA Cryptosystems?12.2.3 Proof of Correctness of RSA12.2.4 RSA Security12.2.5 Optimal Asymmetric Encryption Padding (OAEP)12.2.6 RSA Signature12.2.6.1 RSA Signature Generation12.2.6.2 RSA Signature Verification12.2.6.3 Probabilistic Signature Scheme (PSS)12.3 Finite Field-based Cryptography12.3.1 Discrete Logarithm Problem12.3.1.1 What Is the Discrete Logarithm Problem?12.3.1.2 Attacks Against DLP12.3.2 Diffie-Hellman Key Exchange12.3.3 Menezes-Qu-Vanstone Key-exchange Protocol12.3.4 ElGamal Cryptosystem12.3.4.1 ElGamal Encryption12.3.4.2 ElGamal Signature12.3.4.3 ElGamal Digital Signature Security and Potential Attacks12.4 Digital Signature Algorithm (DSA)12.4.1 DSA Domain Parameters12.4.2 DSA-Keys Generation12.4.3 DSA Signature Generation12.4.4 DSA Signature Verification12.4.5 Advantages of DSA over ElGamal Signature Scheme12.5 Exercises and Problems12.5.1 List of Exercises and Problems12.5.2 Solutions to Exercises and ProblemsNotesReferences
13 Public-Key Cryptosystems: Elliptic Curve Cryptography
13.1 Introduction13.1.1 What Is Elliptic Curve Cryptography?13.1.2 What Is an Elliptic Curve?13.1.3 Order and Point Set of an Elliptic Curve13.2 Elliptic Curve Cryptography over Prime Field Fp13.2.1 Definition of Elliptic Curves over Prime Fields: E(Fp)13.2.2 Operations on Elliptic Curves13.2.3 Generator and Cofactor of EC13.2.4 Montgomery and Edwards Curves13.2.4.1 Operations on Edwards EC Points13.2.4.2 Operations on Montgomery EC Points13.3 Elliptic Curve Cryptography over Extension Fields13.3.1 Definition of EC over Extension Fields13.3.1.1 Operations on Points of Curve E F 2m 13.3.1.2 Fast Scalar Multiplication13.3.2 Set and Number of Points of an EC13.3.2.1 Finding the Set of Points on an EC13.3.2.2 Finding the Exact Number of Points on an EC13.4 Security of EC Cryptosystems13.5 Elliptic Curve-based Algorithms13.5.1 Security Strength Levels of EC Algorithms13.5.2 Domain Parameters13.5.3 EC Diffie–Hellman (ECDH) Key-Agreement Protocol13.5.3.1 Small-Subgroup Attack Against ECDH13.5.4 EC Menezes-Qu-Vanstone (ECMQV) Key-Agreement Protocol13.5.5 Elliptic-Curve Digital-Signature Algorithm (ECDSA)13.5.5.1 Setup Process13.5.5.2 ECDSA Signature Generation13.5.5.3 ECDSA Signature Verification13.5.5.4 Correctness of ECDSA Algorithm13.5.6 Edwards Curve Digital Signature Algorithm (EdDSA)13.5.6.1 EdDSA Key Pair Generation13.5.6.2 EdDSA Signature Generation13.5.6.3 EdDSA Signature Verification13.5.6.4 Comment on EdDSA Signature Verification Procedure13.5.7 Elliptic Curve Encryption Algorithms13.5.7.1 ECIES Framework13.5.7.2 ElGamal Encryption Using EC Cryptography13.6 Exercises and Problems13.6.1 List of Exercises and Problems13.6.2 Solutions to Exercises and ProblemsNotesReferences
14 Key Management
14.1 Key-Management-related Notions14.1.1 Types, Security Strengths, and Cryptoperiod of Keys14.1.1.1 Key Types14.1.1.2 Security Strengths14.1.1.3 Cryptoperiod14.1.2 Key-Management Phases and Functions14.2 Key-Generation Schemes14.2.1 Key Generation for Symmetric-Key Systems14.2.1.1 Key Generation Using DRBGs14.2.1.2 Key Derived from a Password14.2.1.3 Key-Generation by Key-Derivation Methods14.2.1.4 Key Generated by Combining Multiple Other Keys and Data14.2.1.5 Key-Derivation Functions14.2.2 Key Generation for Asymmetric-Key Cryptosystems14.2.2.1 RSA Key-Pair Generation14.2.2.2 Key-Pair Generation for DH and MQV14.2.2.3 ECC Key-Pair Generation14.3 Key-Establishment Schemes14.3.1 Overall View of Key-Establishment Schemes14.3.2 Key-Establishment Using a Key Distribution Center14.3.3 Key-Establishment Using Public-Key-based Schemes14.3.3.1 Common Mechanisms and Functions14.3.3.2 Key-Establishment Schemes Using RSA14.3.3.3 DLC-based Key-Agreement Schemes14.4.1 List of Problems14.4.2 Solutions to ProblemsNotesReferences
15 Digital Certificate, Public-Key Infrastructure, TLS, and Kerberos
15.1 Digital Certificate: Notion and X.509 Format15.1.1 Types of Digital Certificates15.1.1.1 TLS (Transport Layer Security) Certificates15.1.1.2 Code (or Software) Signing Certificates15.1.1.3 Client Certificates15.1.2 X.509 Standard Format15.2 Public-Key Infrastructure15.2.1 Components of a PKI15.2.2 Certificate Authority Hierarchy15.2.3 Registration of a Public-Key and Certificate Acquisition15.2.4 Chain of Trust and Trust Models15.2.5 Validation of Certificates and Trust Paths15.2.6 Digital-Certificate Revocation15.3 Transport Layer Security (TLS 1.3)15.3.1 TLS Certificates15.3.2 TLS 1.3 Protocols15.3.2.1 Handshake Protocol15.3.2.2 Record Protocol15.3.2.3 Alert Protocol15.4 Kerberos15.4.1 Kerberos Principles15.4.2 Message Formats and Authentication Steps of Kerberos15.4.2.1 Ticket and Authenticator Formats15.4.2.2 Protocol Actions and Message Description15.4.3 Advantages, Limits, and Security of Kerberos15.5 Exercises and Problems15.5.1 List of Exercises and Problems15.5.2 Solutions to Exercises and ProblemsNotesReferences
16 Generation of Pseudorandom and Prime Numbers for Cryptographic Applications
16.1 Introduction to Pseudorandom Number Generation16.1.1 Basic Notions and Definitions16.1.2 Entropy16.1.2.1 Source of Entropy16.1.2.2 Entropy from a Statistical Point of View16.1.3 Some Popular PRNGs (not to use in Cryptography)16.1.3.1 Middle-Square Algorithm16.1.3.2 Linear Congruential Generator16.1.3.3 Mersenne Twister PRNG16.1.4 PRNGs for Cryptography: Notions and Design Principles16.1.4.1 Properties of PRNGs for Cryptography16.1.4.2 General Guidelines for the Design of PRBGs for Cryptography16.2 Pseudorandom Bit Generators Recommended for Cryptography16.2.1 Common Mechanisms and Processes16.2.1.1 Security Strength16.2.1.2 Instantiating a DRBG16.2.1.3 Reseeding a DRBG16.2.1.4 Internal State of a DRBG16.2.1.5 Description Format of DRBG Functions16.2.2 Hash-based DRBGs16.2.3 HMAC-based DRBGs16.2.4 Block Cipher-based DRBGs16.3 Prime Number Generation16.3.1 Basics and Facts about Primes16.3.1.1 Definition of Some Prime Categories of Interest for Cryptography16.3.1.2 Distribution of Prime Numbers16.3.2 Methods for Primality Testing16.3.2.1 Deterministic Methods for Primality Testing16.3.2.2 Probabilistic Methods for Primality Testing16.3.3 Generation of Probably-Prime Pair16.3.3.1 Generation of Probably-Prime Pair for DH and MQV16.3.3.2 Generation of Probably-Prime Pair for RSA16.3.4 Generation of Provable Primes16.3.4.1 Shawe-Taylor Algorithm16.3.4.2 Generation of Provable-Prime Pair for DH and MQV16.3.4.3 Generation of Provable-Prime Pair for RSA16.4 Exercises and Problems16.4.1 List of Exercises and Problems16.4.2 Solutions to Exercises and ProblemsNotesReferences
Appendix: Multiple Choice Questions and Answers
Index
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3 Mathematical Basics and Computation Algorithms for Cryptography

Cryptography is a discipline that requires a background in mathematics. All encryption, decryption, and signature algorithms are based on notions and theorems known in number theory, modular arithmetic, and abstract algebra. Before we start the presentation and analysis of cryptographic algorithms, we need to review basics from number theory and abstract algebra. This chapter aims to review and present, with examples and exercises, the mathematical background to address cryptography algorithms. Seminal theorems are given with the names of their authors. Proofs of theorems are not included in this chapter and can be found in many books and papers on the topics [1–6].

To make attacks against cryptosystems computationally infeasible, numbers used in cryptographic algorithms are very large (in magnitude of , etc.). Therefore, optimized (in term of execution time) computation methods are needed. In addition to mathematical basics, algorithms commonly used to do fast computations in cryptographic algorithms are addressed in this chapter. Finally, the birthday paradox is presented; it is useful for the analysis of attack complexity.

According to the mathematics and computation algorithms skills of the reader, he/she may:

Skip this chapter and address directly cryptographic algorithms.
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3 Mathematical Basics and Computation Algorithms for Cryptography

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