Contemporary Cryptology

, by Catalano, Dario; Cramer, Ronald; Damgard, Ivan; Crescenzo, Giovanni Di; Pointcheval, David; Takagi, Tsuyoshi

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ISBN: 9783764372941 | 376437294X
Cover: Paperback
Copyright: 9/30/2005

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The aim of this text is to treat selected topics of the subject of contemporary cryptology, structured in five quite independent but related themes: - efficient distributed computation modulo a shared secret- multiparty computation- foundations of modern cryptography- provable security for public key schemes- efficient and secure public-key cryptosystems.

Foreword

A Efficient Distributed Computation Modulo a Shared Secret

(40)

Dario Catalano

1 Introduction

(3)

1.1 Previous Work

(1)

1.2 Organization of this Lecture

(1)

2 Preliminaries

(1)

2.1 The Network Model

(1)

2.2 Definitions and Notations

(1)

3 Building Blocks

(4)

3.1 Additive Sharing over Zq

(1)

3.2 Polynomial Sharing over Zq

(1)

3.3 Additive Sharing over Z

(1)

3.4 Polynomial Sharing over Z

(1)

4 Basic Protocols

(2)

4.1 Distributed Computation Modulo q

(1)

4.2 Joint Random Sharing over Zq

(1)

4.3 Joint Random Sharing of 0 in Zq

(1)

4.4 Computing Shares of the Inverse of a Shared Secret

(1)

4.5 Joint Random Invertible Element Sharing

(1)

5 A Different Approach

(1)

6 Converting among Different Secret Sharing Methods

(5)

6.1 Converting between Additive and Polynomial Shares

(1)

6.2 Converting between Integer Shares and Zq Shares

(3)

6.3 Computing Shares of the Binary Representation of a Secret

(1)

6.4 Approximate Truncation

(1)

7 Distributed Modular Reduction

(6)

7.1 Newton Iteration Method

(1)

7.2 First Step: Computing Shares of an Approximation of 1/ρ

(2)

7.3 Second Step: the Modular Reduction Protocol

(3)

8 Exponentiation with a Shared Exponent

(3)

8.1 Set Membership

(2)

9 Generating Shared Random Primes

(4)

9.1 The Basic Miller-Rabin Algorithm

(1)

9.2 Generation of a Shared Candidate Prime

(1)

9.3 Distributed Miller-Rabin Primality Test

(1)

9.4 Generation of Shared Random Safe Primes

(2)

10 Efficient Generation of Shared RSA Keys

(1)

11 Computing Inverses over a Shared Modulus

(6)

11.1 The Basic Idea

(1)

11.2 The Full Protocol

(3)

11.3 A Fundamental Lemma

(2)

References

(5)

B Multiparty Computation, an Introduction

Ronald Cramer and Ivan Damgård

(48)

1 Introduction

(1)

2 What is Multiparty Computation?

(8)

2.1 The MPC and VSS Problems

(1)

2.2 Adversaries and their Powers

(1)

2.3 Models of Communication

(1)

2.4 Definition of Security

(5)

3 Results on MPC

(2)

3.1 Results for Threshold Adversaries

(1)

3.2 Results for General Adversaries

(1)

4 MPC Protocols

(25)

4.1 The Passive Case

(7)

4.2 The Active Case

(5)

4.3 Realization of Fcom: Information Theoretic Scenario

(10)

4.4 Formal Proof for the Fcom: Realization

(1)

5 The Cryptographic Scenario

(2)

5.1 Using Encryption to Implement the Channels

(1)

5.2 Cryptographic Implementations of Higher-Level Functionalities

(1)

6 Protocols Secure for General Adversary Structures

(1)

A Formal Details of the General Security Model for Protocols

(7)

A.1 The Real-Life Execution

(1)

A.2 The Ideal Process

(2)

A.3 The Hybrid Models

(1)

A.4 Composing Protocols

(1)

A.5 Composing Interfaces

(1)

References

(4)

C Foundations of Modern Cryptography

Giovanni Di Crescenzo

(44)

1 Introduction

(1)

2 One-Way Functions

(9)

2.1 Definitions

(2)

2.2 Candidates from Number Theory

(2)

2.3 Weak vs. Strong One-Way Functions

(4)

3 Pseudo-Random Generators

(5)

3.1 Definitions

(1)

3.2 Constructions

100

(3)

3.3 A Cryptographic Application

103

(1)

4 Pseudo-Random Functions

103

(6)

4.1 Definitions

104

(1)

4.2 Constructions

105

(3)

4.3 Examples and Applications

108

(1)

5 Zero-Knowledge Protocols

109

(20)

5.1 Basic Definitions

110

(1)

5.2 Zero-Knowledge Proof Systems of Membership

111

(5)

5.3 Witness-Indistinguishable Proof Systems of Knowledge

116

(3)

5.4 Zero-Knowledge Proof Systems of Decision Power

119

(5)

5.5 Zero-Knowledge Transfers of Decision

124

(5)

References

129

(4)

D Provable Security for Public Key Schemes

David Pointcheval

133

(58)

1 Introduction

133

(2)

1.1 Provable Security

134

(1)

1.2 Exact Security and Practical Security

134

(1)

1.3 Outline of the Notes

135

(1)

1.4 Related Work

135

(1)

2 Security Proofs and Security Arguments

135

(3)

2.1 Computational Assumptions

135

(1)

2.2 "Reductionist" Security Proofs

136

(1)

2.3 Practical Security

136

(1)

2.4 The Random-Oracle Model

137

(1)

2.5 The General Framework

138

(1)

3 A First Formalism

138

(5)

3.1 Digital Signature Schemes

139

(1)

3.2 Public-Key Encryption

140

(3)

4 The Computational Assumptions

143

(3)

4.1 Integer Factoring and the R SA Problem

143

(2)

4.2 The Discrete Logarithm and the Diffie-Hellman Problems

145

(1)

5 Digital Signature Schemes

146

(17)

5.1 Provable Security

147

(1)

5.2 DL-Based Signatures

148

(6)

5.3 RSA-Based Signatures

154

(9)

6 Public-Key Encryption

163

(21)

6.1 History

163

(1)

6.2 A First Generic Construction

164

(3)

6.3 OAEP: the Optimal Asymmetric Encryption Padding

167

(12)

6.4 REACT: a Rapid Enhanced-security Asymmetric Cryptosystem Transform

179

(5)

7 Conclusion

184

(1)

References

185

(6)

E Efficient and Secure Public Key Cryptosystems

Tsugoshi Takagi

191

1 Efficient Integer Arithmetic

191

(5)

1.1 Modular Exponentiation

191

(1)

1.2 Window Methods

192

(2)

1.3 Montgomery Multiplication

194

(2)

2 Fast Variants of RSA Cryptosystem

196

(5)

2.1 PKCS #1 Version 2.1

196

(1)

2.2 Multi-Exponent RSA

197

(2)

2.3 Size of Secret Primes

199

(1)

2.4 Comparison

200

(1)

3 Implementation Attack on RSA-CRT

201

(3)

4 EPOC Cryptosystem

204

(10)

4.1 EPOC-2 Cryptosystem

204

(3)

4.2 Reject Timing Attack on EPOC-2

207

(5)

4.3 Relation to Other Cryptosystems

212

(1)

4.4 Other Encryption Primitives

213

(1)

5 Elliptic Curve Cryptosystem

214

(4)

5.1 Scalar Multiplication

215

(2)

5.2 Efficient Coordinate System

217

(1)

6 Side Channel Attacks on ECC

218

(2)

6.1 SPA on ECC

218

(1)

6.2 DPA and Countermeasures

219

(1)

6.3 Goubin's Power-Analysis Attack

220

(1)

7 Zero-Value Point Attack on ECC

220

(11)

7.1 Non-Zero Digit Methods

226

(1)

7.2 Montgomery Ladder Method

226

(5)

7.3 Non-Zero Window Method

231

(1)

References

231

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Contemporary Cryptology

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