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Table of Contents
Intro; Preface; Acknowledgements; Contents; Chapter 1 Guide to This Book; Chapter 2 Notions, Definitions, and Models; 2.1 Digital Signatures; 2.2 Public-Key Encryption; 2.3 Identity-Based Encryption; 2.4 Further Reading; Chapter 3 Foundations of Group-Based Cryptography; 3.1 Finite Fields; 3.1.1 Definition; 3.1.2 Field Operations; 3.1.3 Field Choices; 3.1.4 Computations over a Prime Field; 3.2 Cyclic Groups; 3.2.1 Definitions; 3.2.2 Cyclic Groups of Prime Order; 3.2.3 Group Exponentiations; 3.2.4 Discrete Logarithms; 3.2.5 Cyclic Groups from Finite Fields
3.2.6 Group Choice 1: Multiplicative Groups3.2.7 Group Choice 2: Elliptic Curve Groups; 3.2.8 Computations over a Group; 3.3 Bilinear Pairings; 3.3.1 Symmetric Pairing; 3.3.2 Asymmetric Pairing; 3.3.3 Computations over a Pairing Group; 3.4 Hash Functions; 3.5 Further Reading; Chapter 4 Foundations of Security Reduction; 4.1 Introduction to Basic Concepts; 4.1.1 Mathematical Primitives and Superstructures; 4.1.2 Mathematical Problems and Problem Instances; 4.1.3 Cryptography, Cryptosystems, and Schemes; 4.1.4 Algorithm Classification 1; 4.1.5 Polynomial Time and Exponential Time
4.1.6 Negligible and Non-negligible4.1.7 Insecure and Secure; 4.1.8 Easy and Hard; 4.1.9 Algorithm Classification 2; 4.1.10 Algorithms in Cryptography; 4.1.11 Hard Problems in Cryptography; 4.1.12 Security Levels; 4.1.13 Hard Problems and Hardness Assumptions; 4.1.14 Security Reductions and Security Proofs; 4.2 An Overview of Easy/Hard Problems; 4.2.1 Computational Easy Problems; 4.2.2 Computational Hard Problems; 4.2.3 Decisional Easy Problems; 4.2.4 Decisional Hard Problems; 4.2.5 How to Prove New Hard Problems; 4.2.6 Weak Assumptions and Strong Assumptions
4.3 An Overview of Security Reduction4.3.1 Security Models; 4.3.2 Weak Security Models and Strong Security Models; 4.3.3 Proof by Testing; 4.3.4 Proof by Contradiction; 4.3.5 What Is Security Reduction?; 4.3.6 Real Scheme and Simulated Scheme; 4.3.7 Challenger and Simulator; 4.3.8 Real Attack and Simulation; 4.3.9 Attacks and Hard Problems; 4.3.10 Reduction Cost and Reduction Loss; 4.3.11 Loose Reduction and Tight Reduction; 4.3.12 Security Level Revisited; 4.3.13 Ideal Security Reduction; 4.4 An Overview of Correct Security Reduction; 4.4.1 What Should Bob Do?
4.4.2 Understanding Security Reduction4.4.3 Successful Simulation and Indistinguishable Simulation; 4.4.4 Failed Attack and Successful Attack; 4.4.5 Useless Attack and Useful Attack; 4.4.6 Attack in Simulation; 4.4.7 Successful/Correct Security Reduction; 4.4.8 Components of a Security Proof; 4.5 An Overview of the Adversary; 4.5.1 Black-Box Adversary; 4.5.2 What Is an Adaptive Attack?; 4.5.3 Malicious Adversary; 4.5.4 The Adversary in a Toy Game; 4.5.5 Adversary's Successful Attack and Its Probability; 4.5.6 Adversary's Computational Ability
3.2.6 Group Choice 1: Multiplicative Groups3.2.7 Group Choice 2: Elliptic Curve Groups; 3.2.8 Computations over a Group; 3.3 Bilinear Pairings; 3.3.1 Symmetric Pairing; 3.3.2 Asymmetric Pairing; 3.3.3 Computations over a Pairing Group; 3.4 Hash Functions; 3.5 Further Reading; Chapter 4 Foundations of Security Reduction; 4.1 Introduction to Basic Concepts; 4.1.1 Mathematical Primitives and Superstructures; 4.1.2 Mathematical Problems and Problem Instances; 4.1.3 Cryptography, Cryptosystems, and Schemes; 4.1.4 Algorithm Classification 1; 4.1.5 Polynomial Time and Exponential Time
4.1.6 Negligible and Non-negligible4.1.7 Insecure and Secure; 4.1.8 Easy and Hard; 4.1.9 Algorithm Classification 2; 4.1.10 Algorithms in Cryptography; 4.1.11 Hard Problems in Cryptography; 4.1.12 Security Levels; 4.1.13 Hard Problems and Hardness Assumptions; 4.1.14 Security Reductions and Security Proofs; 4.2 An Overview of Easy/Hard Problems; 4.2.1 Computational Easy Problems; 4.2.2 Computational Hard Problems; 4.2.3 Decisional Easy Problems; 4.2.4 Decisional Hard Problems; 4.2.5 How to Prove New Hard Problems; 4.2.6 Weak Assumptions and Strong Assumptions
4.3 An Overview of Security Reduction4.3.1 Security Models; 4.3.2 Weak Security Models and Strong Security Models; 4.3.3 Proof by Testing; 4.3.4 Proof by Contradiction; 4.3.5 What Is Security Reduction?; 4.3.6 Real Scheme and Simulated Scheme; 4.3.7 Challenger and Simulator; 4.3.8 Real Attack and Simulation; 4.3.9 Attacks and Hard Problems; 4.3.10 Reduction Cost and Reduction Loss; 4.3.11 Loose Reduction and Tight Reduction; 4.3.12 Security Level Revisited; 4.3.13 Ideal Security Reduction; 4.4 An Overview of Correct Security Reduction; 4.4.1 What Should Bob Do?
4.4.2 Understanding Security Reduction4.4.3 Successful Simulation and Indistinguishable Simulation; 4.4.4 Failed Attack and Successful Attack; 4.4.5 Useless Attack and Useful Attack; 4.4.6 Attack in Simulation; 4.4.7 Successful/Correct Security Reduction; 4.4.8 Components of a Security Proof; 4.5 An Overview of the Adversary; 4.5.1 Black-Box Adversary; 4.5.2 What Is an Adaptive Attack?; 4.5.3 Malicious Adversary; 4.5.4 The Adversary in a Toy Game; 4.5.5 Adversary's Successful Attack and Its Probability; 4.5.6 Adversary's Computational Ability