RSA and Public-Key Cryptography

by R.A. Mollin

TABLE OF CONTENTS:

Chapter 1: History and Basic Cryptographic Concepts....1

1.1 Terminology................ 1

1.2 Classical Ciphers.................... 13

1.3 Classification of Attacks.................... 25

Chapter 2: Protocols, Discrete Log, and Diffie-Hellman....33

2.1 Cryptographic Protocols...............33

2.2 The Discrete Log Problem.....................39

2.3 Exponentiation Ciphers and Diffie-Hellman.........47

Chapter 3: Public-Key Cryptography....53

3.1 One-Way Functions...............53

3.2 Public-Key Cryptosystems and RSA.....................60

3.3 ElGamal Cryptosystems.........67

3.4 Symmetric vs. Asymmetric Cryptosystems........73

3.5 Secret History of Public-Key Cryptography..............77

Chapter 4: Probabilistic Primality Tests.................79

4.1 Introduction....................79

4.2 Pseudoprimes and Carmichael Numbers................81

4.3 Solovay-Strassen Test...............87

Chapter 5: Factoring................93

5.1 Universal Exponent Method............93

5.2 Pollard's p-1 Method.............96

5.3 Lenstra's Elliptic Curve Method (optional).............99

5.4 Multipolynomial Quadratic Sieve...................104

5.5 The Number Field Sieve (optional)..................108

Chapter 6: Security of RSA.........................111

6.1 Implementation Attacks.....................111

6.2 Exponent Attacks............115

6.3 Strong Moduli..............120

6.4 Generation of Random Primes.................124

Chapter 7: Authentication......................127

7.1 Identification, Impersonation, and Signatures........127

7.2 Digital Signature Schemes..................135

7.3 Digital Cash and Electronic Commerce...........143

Chapter 8: Key Management.............153

8.1 Secret Sharing..................153

8.2 Key Establishment.....................160

8.3 Public-Key Infrastructure (PKI)............713

Chapter 9: Applications and the Future.................179

9.1 Secrecy and Authentication...........179

9.2 Other Threats to System Security.................185

9.3 Wireless Security.......................190

9.4 Smart Cards and Biometrics...............198

Appendix A: Letter Frequency Analysis......................203

Appendix B: Elementary Complexity Theory....................205

Appendix C: Fundamental Facts.......................212

Solutions to Odd-Numbered Exercises..........224

Bibliography.............249

List of Symbols.................267

Index.....................268

 Last updated: September 2, 2002

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