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Introduction to Security Reduction 2018 ed. [Hardback]

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  • Formāts: Hardback, 253 pages, height x width: 235x155 mm, weight: 4063 g, XV, 253 p., 1 Hardback
  • Izdošanas datums: 09-Jul-2018
  • Izdevniecība: Springer International Publishing AG
  • ISBN-10: 3319930486
  • ISBN-13: 9783319930480
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Introduction to Security Reduction 2018 ed.Palielināt
  • Formāts: Hardback, 253 pages, height x width: 235x155 mm, weight: 4063 g, XV, 253 p., 1 Hardback
  • Izdošanas datums: 09-Jul-2018
  • Izdevniecība: Springer International Publishing AG
  • ISBN-10: 3319930486
  • ISBN-13: 9783319930480
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783319930480.html

This monograph illustrates important notions in security reductions and essential techniques in security reductions for group-based cryptosystems. Using digital signatures and encryption as examples, the authors explain how to program correct security reductions for those cryptographic primitives. Various schemes are selected and re-proven in this book to demonstrate and exemplify correct security reductions.

This book is suitable for researchers and graduate students engaged with public-key cryptography.


1 Guide to This Book
1(4)
2 Notions, Definitions, and Models
5(8)
2.1 Digital Signatures
5(2)
2.2 Public-Key Encryption
7(2)
2.3 Identity-Based Encryption
9(2)
2.4 Further Reading
11(2)
3 Foundations of Group-Based Cryptography
13(16)
3.1 Finite Fields
13(3)
3.1.1 Definition
13(1)
3.1.2 Field Operations
14(1)
3.1.3 Field Choices
14(1)
3.1.4 Computations over a Prime Field
15(1)
3.2 Cyclic Groups
16(6)
3.2.1 Definitions
16(1)
3.2.2 Cyclic Groups of Prime Order
17(1)
3.2.3 Group Exponentiations
17(1)
3.2.4 Discrete Logarithms
18(1)
3.2.5 Cyclic Groups from Finite Fields
19(1)
3.2.6 Group Choice 1: Multiplicative Groups
19(1)
3.2.7 Group Choice 2: Elliptic Curve Groups
20(2)
3.2.8 Computations over a Group
22(1)
3.3 Bilinear Pairings
22(3)
3.3.1 Symmetric Pairing
23(1)
3.3.2 Asymmetric Pairing
24(1)
3.3.3 Computations over a Pairing Group
25(1)
3.4 Hash Functions
25(1)
3.5 Further Reading
26(3)
4 Foundations of Security Reduction
29(118)
4.1 Introduction to Basic Concepts
29(8)
4.1.1 Mathematical Primitives and Superstructures
29(1)
4.1.2 Mathematical Problems and Problem Instances
30(1)
4.1.3 Cryptography, Cryptosystems, and Schemes
31(1)
4.1.4 Algorithm Classification 1
31(1)
4.1.5 Polynomial Time and Exponential Time
32(1)
4.1.6 Negligible and Non-negligible
32(1)
4.1.7 Insecure and Secure
33(1)
4.1.8 Easy and Hard
33(1)
4.1.9 Algorithm Classification 2
34(1)
4.1.10 Algorithms in Cryptography
34(1)
4.1.11 Hard Problems in Cryptography
35(1)
4.1.12 Security Levels
35(1)
4.1.13 Hard Problems and Hardness Assumptions
36(1)
4.1.14 Security Reductions and Security Proofs
36(1)
4.2 An Overview of Easy/Hard Problems
37(10)
4.2.1 Computational Easy Problems
37(5)
4.2.2 Computational Hard Problems
42(1)
4.2.3 Decisional Easy Problems
43(1)
4.2.4 Decisional Hard Problems
44(1)
4.2.5 How to Prove New Hard Problems
45(2)
4.2.6 Weak Assumptions and Strong Assumptions
47(1)
4.3 An Overview of Security Reduction
47(9)
4.3.1 Security Models
47(2)
4.3.2 Weak Security Models and Strong Security Models
49(1)
4.3.3 Proof by Testing
49(1)
4.3.4 Proof by Contradiction
50(1)
4.3.5 What Is Security Reduction?
50(1)
4.3.6 Real Scheme and Simulated Scheme
51(1)
4.3.7 Challenger and Simulator
51(1)
4.3.8 Real Attack and Simulation
52(1)
4.3.9 Attacks and Hard Problems
52(1)
4.3.10 Reduction Cost and Reduction Loss
53(1)
4.3.11 Loose Reduction and Tight Reduction
53(1)
4.3.12 Security Level Revisited
54(1)
4.3.13 Ideal Security Reduction
55(1)
4.4 An Overview of Correct Security Reduction
56(5)
4.4.1 What Should Bob Do?
56(1)
4.4.2 Understanding Security Reduction
57(1)
4.4.3 Successful Simulation and Indistinguishable Simulation
57(1)
4.4.4 Failed Attack and Successful Attack
58(1)
4.4.5 Useless Attack and Useful Attack
59(1)
4.4.6 Attack in Simulation
59(1)
4.4.7 Successful/Correct Security Reduction
60(1)
4.4.8 Components of a Security Proof
60(1)
4.5 An Overview of the Adversary
61(8)
4.5.1 Black-Box Adversary
61(1)
4.5.2 What Is an Adaptive Attack?
61(1)
4.5.3 Malicious Adversary
62(1)
4.5.4 The Adversary in a Toy Game
63(1)
4.5.5 Adversary's Successful Attack and Its Probability
63(1)
4.5.6 Adversary's Computational Ability
64(1)
4.5.7 The Adversary's Computational Ability in a Reduction
64(2)
4.5.8 The Adversary in a Reduction
66(1)
4.5.9 What the Adversary Knows
66(1)
4.5.10 What the Adversary Never Knows
67(1)
4.5.11 How to Distinguish the Given Scheme
67(1)
4.5.12 How to Generate a Useless Attack
68(1)
4.5.13 Summary of Adversary
69(1)
4.6 An Overview of Probability and Advantage
69(6)
4.6.1 Definitions of Probability
69(2)
4.6.2 Definitions of Advantage
71(2)
4.6.3 Malicious Adversary Revisited
73(1)
4.6.4 Adaptive Choice Revisited
73(1)
4.6.5 Useless, Useful, Loose, and Tight Revisited
74(1)
4.6.6 Important Probability Formulas
74(1)
4.7 An Overview of Random and Independent
75(8)
4.7.1 What Are Random and Independent?
76(1)
4.7.2 Randomness Simulation with a General Function
76(3)
4.7.3 Randomness Simulation with a Linear System
79(2)
4.7.4 Randomness Simulation with a Polynomial
81(1)
4.7.5 Indistinguishable Simulation and Useful Attack Together
82(1)
4.7.6 Advantage and Probability in Absolutely Hard Problems
83(1)
4.8 An Overview of Random Oracles
83(6)
4.8.1 Security Proof with Random Oracles
84(1)
4.8.2 Hash Functions vs Random Oracles
84(1)
4.8.3 Hash List
85(1)
4.8.4 How to Program Security Reductions with Random Oracles
86(1)
4.8.5 Oracle Response and Its Probability Analysis
86(2)
4.8.6 Summary of Using Random Oracles
88(1)
4.9 Security Proofs for Digital Signatures
89(5)
4.9.1 Proof Structure
89(1)
4.9.2 Advantage Calculation
90(1)
4.9.3 Simulatable and Reducible
91(1)
4.9.4 Simulation of Secret Key
91(1)
4.9.5 Partition
92(1)
4.9.6 Tight Reduction and Loose Reduction Revisited
92(1)
4.9.7 Summary of Correct Security Reduction
93(1)
4.10 Security Proofs for Encryption Under Decisional Assumptions
94(15)
4.10.1 Proof Structure
94(1)
4.10.2 Classification of Ciphertexts
95(1)
4.10.3 Classification of the Challenge Ciphertext
96(1)
4.10.4 Simulation of the Challenge Ciphertext
96(1)
4.10.5 Advantage Calculation 1
97(1)
4.10.6 Probability PT of Breaking the True Challenge Ciphertext
98(1)
4.10.7 Probability PF of Breaking the False Challenge Ciphertext
98(1)
4.10.8 Advantage Calculation 2
99(1)
4.10.9 Definition of One-Time Pad
100(1)
4.10.10 Examples of One-Time Pad
101(2)
4.10.11 Analysis of One-Time Pad
103(1)
4.10.12 Simulation of Decryption
103(1)
4.10.13 Simulation of Challenge Decryption Key
104(1)
4.10.14 Probability Analysis for PF
105(1)
4.10.15 Examples of Advantage Results for AK/F and AI/F
106(2)
4.10.16 Advantage Calculation 3
108(1)
4.10.17 Summary of Correct Security Reduction
109(1)
4.11 Security Proofs for Encryption Under Computational Assumptions
109(10)
4.11.1 Random and Independent Revisited
109(1)
4.11.2 One-Time Pad Revisited
110(1)
4.11.3 Solution to Hard Problem Revisited
110(1)
4.11.4 Simulation of Challenge Ciphertext
111(1)
4.11.5 Proof Structure
112(1)
4.11.6 Challenge Ciphertext and Challenge Hash Query
113(1)
4.11.7 Advantage Calculation
114(1)
4.11.8 Analysis of No Advantage
115(1)
4.11.9 Requirements of Decryption Simulation
116(1)
4.11.10 An Example of Decryption Simulation
116(2)
4.11.11 Summary of Correct Security Reduction
118(1)
4.12 Simulatable and Reducible with Random Oracles
119(4)
4.12.1 H-Type: Hashing to Group
119(2)
4.12.2 C-Type: Commutative
121(1)
4.12.3 I-Type: Inverse of Group Exponent
122(1)
4.13 Examples of Incorrect Security Reductions
123(7)
4.13.1 Example 1: Distinguishable
124(2)
4.13.2 Example 2: Useless Attack by Public Key
126(2)
4.13.3 Example 3: Useless Attack by Signature
128(2)
4.14 Examples of Correct Security Reductions
130(9)
4.14.1 One-Time Signature with Random Oracles
130(3)
4.14.2 One-Time Signature Without Random Oracles
133(3)
4.14.3 One-Time Signature with Indistinguishable Partition
136(3)
4.15 Summary of Concepts
139(8)
4.15.1 Concepts Related to Proof
139(1)
4.15.2 Preliminaries and Proof by Contradiction
140(1)
4.15.3 Security Reduction and Its Difficulty
141(1)
4.15.4 Simulation and Its Requirements
142(2)
4.15.5 Towards a Correct Security Reduction
144(2)
4.15.6 Other Confusing Concepts
146(1)
5 Digital Signatures with Random Oracles
147(26)
5.1 BLS Scheme
147(2)
5.2 BLS+ Scheme
149(3)
5.3 BLS# Scheme
152(3)
5.4 BBRO Scheme
155(2)
5.5 ZSS Scheme
157(3)
5.6 ZSS+ Scheme
160(2)
5.7 ZSS# Scheme
162(3)
5.8 BLSG Scheme
165(8)
6 Digital Signatures Without Random Oracles
173(20)
6.1 Boneh-Boyen Scheme
173(4)
6.2 Gentry Scheme
177(3)
6.3 GMS Scheme
180(5)
6.4 Waters Scheme
185(4)
6.5 Hohenberger-Waters Scheme
189(4)
7 Public-Key Encryption with Random Oracles
193(16)
7.1 Hashed ElGamal Scheme
193(2)
7.2 Twin Hashed ElGamal Scheme
195(3)
7.3 Iterated Hashed ElGamal Scheme
198(4)
7.4 Fujisaki-Okamoto Hashed ElGamal Scheme
202(7)
8 Public-Key Encryption Without Random Oracles
209(6)
8.1 ElGamal Scheme
209(2)
8.2 Cramer-Shoup Scheme
211(4)
9 Identity-Based Encryption with Random Oracles
215(14)
9.1 Boneh-Franklin Scheme
215(3)
9.2 Boneh-BoyenRO Scheme
218(3)
9.3 Park-Lee Scheme
221(3)
9.4 Sakai-Kasahara Scheme
224(5)
10 Identity-Based Encryption Without Random Oracles
229(20)
10.1 Boneh-Boyen Scheme
229(4)
10.2 Boneh-Boyen+ Scheme
233(4)
10.3 Waters Scheme
237(5)
10.4 Gentry Scheme
242(7)
References 249