Introduction to Cryptography with Coding

For advanced undergraduate courses in cryptography and network security in departments of math and computer science. Assumes a minimal background in programming and a level of math sophistication equivalent to a course in linear algebra.

Preface

xi

Overview

1

(11)

Secure Communications

2

(7)

Cryptographic Applications

9

(3)

Classical Cryptosystems

12

(47)

Shift Ciphers

13

(1)

Affine Ciphers

14

(2)

The Vigenere Cipher

16

(7)

Substitution Ciphers

23

(3)

Sherlock Holmes

26

(3)

The Playfair and ADFGX Ciphers

29

(4)

Block Ciphers

33

(4)

Binary Numbers and ASCII

37

(1)

One-Time Pads

38

(2)

Pseudo-random Bit Generation

40

(2)

Linear Feedback Shift Register Sequences

42

(7)

Enigma

49

(5)

Exercises

54

(2)

Computer Problems

56

(3)

Basic Number Theory

59

(38)

Basic Notions

59

(6)

Solving ax + by = d

65

(1)

Congruences

66

(6)

The Chinese Remainder Theorem

72

(2)

Modular Exponentiation

74

(1)

Fermat and Euler

75

(4)

Primitive Roots

79

(1)

Inverting Matrices Mod n

80

(1)

Square Roots Mod n

81

(2)

Finite Fields

83

(8)

Exercises

91

(4)

Computer Problems

95

(2)

The Data Encryption Standard

97

(30)

Introduction

97

(1)

A Simplified DES-Type Algorithm

98

(4)

Differential Cryptanalysis

102

(5)

DES

107

(8)

Models of Operation

115

(3)

Breaking DES

118

(5)

Password Security

123

(2)

Exercises

125

(2)

AES: Rijndael

127

(10)

The Basic Algorithm

128

(1)

The Layers

129

(4)

Decryption

133

(3)

Design Considerations

136

(1)

The RSA Algorithm

137

(28)

The RSA Algorithm

137

(5)

Attacks on RSA

142

(3)

Primality Testing

145

(4)

Factoring

149

(5)

The RSA Challenge

154

(2)

An Application to Treaty Verification

156

(1)

The Public Key Concept

156

(3)

Exercises

159

(3)

Computer Problems

162

(3)

Discrete Logarithms

165

(12)

Discrete Logarithms

165

(1)

Computing Discrete Logs

166

(7)

Bit Commitment

173

(1)

The ElGamal Public Key Cryptosystem

173

(2)

Exercises

175

(1)

Computer Problems

176

(1)

Digital Signatures

177

(19)

RSA Signatures

178

(1)

The EIGamal Signature Scheme

179

(3)

Hash Functions

182

(4)

Birthday Attacks

186

(4)

The Digital Signature Algorithm

190

(1)

Exercises

191

(3)

Computer Problems

194

(2)

E-Commerce and Digital Cash

196

(12)

Secure Electronic Transaction

197

(2)

Digital Cash

199

(7)

Exercises

206

(2)

Secret Sharing Schemes

208

(11)

Secret Splitting

208

(1)

Threshold Schemes

209

(6)

Exercises

215

(2)

Computer Problems

217

(2)

Games

219

(9)

Flipping Coins over the Telephone

219

(2)

Poker over the Telephone

221

(5)

Exercises

226

(2)

Zero-Knowledge Techniques

228

(8)

The Basic Setup

228

(3)

Feige-Fiat-Shamir Identification Scheme

231

(2)

Exercises

233

(3)

Key Establishment Protocols

236

(14)

Key Agreement Protocols

237

(2)

Key Pre-distribution

239

(2)

Key Distribution

241

(5)

Public Key Infrastructures (PKI)

246

(2)

Exercises

248

(2)

Information Theory

250

(22)

Probability Review

251

(2)

Entropy

253

(5)

Huffman Codes

258

(2)

Perfect Secrecy

260

(3)

The Entropy of English

263

(5)

Exercises

268

(4)

Elliptic Curves

272

(23)

The Addition Law

272

(4)

Elliptic Curves Mod n

276

(4)

Factoring with Elliptic Curves

280

(4)

Elliptic Curves in Characteristic 2

284

(3)

Elliptic Curve Cryptosystems

287

(3)

Exercises

290

(3)

Computer Problems

293

(2)

Error Correcting Codes

295

(58)

Introduction

295

(6)

Error Correcting Codes

301

(4)

Bounds on General Codes

305

(6)

Linear Codes

311

(8)

Hamming Codes

319

(1)

Golay Codes

320

(9)

Cyclic Codes

329

(6)

BCH Codes

335

(8)

Reed-Solomon Codes

343

(2)

The McEliece Cryptosystem

345

(3)

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Introduction to Cryptography with Coding Theory

Summary

Table of Contents

Supplemental Materials