Cryptology: Classical And Modern

497 Pages·2019·9.667 MB·English

by  Richard Klima, Richard E. Klima, Neil Sigmon, Neil P. Sigmon

CRYPTOLOGY
Classical and Modern
———S E –———
ECOND DITION
Chapman & Hall/CRC Cryptography
and Network Security Series
Series Editors: Douglas R. Stinson and Jonathan Katz

Algorithmic Cryptanalysis
Antoine Joux
Cryptanalysis of RSA and Its Variants
M. Jason Hinek
Access Control, Security, and Trust: A Logical Approach
Shiu-Kai Chin and Susan Beth Older
Handbook of Financial Cryptography and Security
Burton Rosenberg
Handbook on Soft Computing for Video Surveillance
Sankar K. Pal, Alfredo Petrosino and Lucia Maddalena
Communication System Security
Lidong Chen and Guang Gong
Introduction to Modern Cryptography, Second Edition
Jonathan Katz and Yehuda Lindell
Group Theoretic Cryptography
Maria Isabel Gonzalez Vasco and Rainer Steinwandt
Guide to Pairing-Based Cryptography
Nadia El Mrabet and Marc Joye
Cryptology: Classical and Modern, Second Edition
Richard Klima and Neil Sigmon

For more information about this series, please visit:
https://www.crcpress.com/Chapman--HallCRC-Cryptography-and-
Network-Security-Series/book-series/CHCRYNETSEC
CRYPTOLOGY
Classical and Modern
———S E –———
ECOND DITION

Richard Klima
Neil Sigmon
CRC Press
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Contents
Preface xi
1 Introduction to Cryptology 1
1.1 Basic Terminology . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Cryptology in Practice . . . . . . . . . . . . . . . . . . . . . 2
1.3 Why Study Cryptology? . . . . . . . . . . . . . . . . . . . . 4
2 Substitution Ciphers 7
2.1 Keyword Substitution Ciphers. . . . . . . . . . . . . . . . . 7
2.1.1 Simple Keyword Substitution Ciphers . . . . . . . . 8
2.1.2 Keyword Columnar Substitution Ciphers . . . . . . 9
2.1.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Cryptanalysis of Substitution Ciphers . . . . . . . . . . . . 11
2.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Playfair Ciphers . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 The Navajo Code . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Transposition Ciphers 29
3.1 Columnar Transposition Ciphers . . . . . . . . . . . . . . . 29
3.1.1 Simple Columnar Transposition Ciphers . . . . . . . 30
3.1.2 Keyword Columnar Transposition Ciphers . . . . . . 32
3.1.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2 Cryptanalysis of Transposition Ciphers . . . . . . . . . . . . 36
3.2.1 Cryptanalysis of Simple Columnar Ciphers . . . . . 36
3.2.2 Cryptanalysis of KeywordColumnar Ciphers . . . . 38
3.2.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3 ADFGX and ADFGVX Ciphers. . . . . . . . . . . . . . . . 41
3.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 44
v
vi CONTENTS
4 The Enigma Machine 47
4.1 The Enigma Cipher Machine . . . . . . . . . . . . . . . . . 47
4.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 Combinatorics . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.1 The Multiplication Principle . . . . . . . . . . . . . 65
4.2.2 Permutations . . . . . . . . . . . . . . . . . . . . . . 67
4.2.3 Combinations . . . . . . . . . . . . . . . . . . . . . . 70
4.2.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 72
4.3 Security of the Enigma Machine . . . . . . . . . . . . . . . 75
4.3.1 Number of Initial Configurations . . . . . . . . . . . 75
4.3.2 Backgroundon Cryptanalysis . . . . . . . . . . . . . 78
4.3.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 81
5 The Turing Bombe 83
5.1 Cribs and Menus . . . . . . . . . . . . . . . . . . . . . . . . 83
5.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 88
5.2 Loops and Logical Inconsistencies . . . . . . . . . . . . . . . 90
5.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3 Searching for the Correct Configuration . . . . . . . . . . . 92
5.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 106
5.4 The Diagonal Board . . . . . . . . . . . . . . . . . . . . . . 114
5.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 120
5.5 The Checking Machine . . . . . . . . . . . . . . . . . . . . . 124
5.5.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 130
5.6 Turnovers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.6.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 143
5.7 Clonking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5.7.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 155
5.8 Final Observations . . . . . . . . . . . . . . . . . . . . . . . 164
5.8.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 166
6 Shift and Affine Ciphers 167
6.1 Modular Arithmetic . . . . . . . . . . . . . . . . . . . . . . 167
6.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 176
6.2 Shift Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . 178
6.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 181
6.3 Cryptanalysis of Shift Ciphers . . . . . . . . . . . . . . . . . 183
6.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 185
6.4 Affine Ciphers. . . . . . . . . . . . . . . . . . . . . . . . . . 187
6.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 189
6.5 Cryptanalysis of Affine Ciphers . . . . . . . . . . . . . . . . 190
6.5.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 192
CONTENTS
vii
7 Alberti and Vigen`ere Ciphers 195
7.1 Alberti Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . 196
7.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 199
7.2 Vigen`ere Ciphers . . . . . . . . . . . . . . . . . . . . . . . . 201
7.2.1 Vigen`ere Autokey Ciphers . . . . . . . . . . . . . . . 201
7.2.2 Vigen`ere Keyword Ciphers . . . . . . . . . . . . . . 204
7.2.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 205
7.3 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
7.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 213
7.4 The Friedman Test . . . . . . . . . . . . . . . . . . . . . . . 215
7.4.1 The Index of Coincidence . . . . . . . . . . . . . . . 216
7.4.2 Estimating the Keyword Length . . . . . . . . . . . 220
7.4.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 222
7.5 The Kasiski Test . . . . . . . . . . . . . . . . . . . . . . . . 224
7.5.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 225
7.6 Cryptanalysis of Vigen`ere Keyword Ciphers . . . . . . . . . 226
7.6.1 Finding the Keyword Length Using Signatures . . . 228
7.6.2 Finding the Keyword Letters Using Scrawls . . . . . 233
7.6.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 237
8 Hill Ciphers 249
8.1 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
8.1.1 Definition and Basic Terminology . . . . . . . . . . . 250
8.1.2 Matrix Operations . . . . . . . . . . . . . . . . . . . 251
8.1.3 Identity and Inverse Matrices . . . . . . . . . . . . . 256
8.1.4 Matrices with Modular Arithmetic . . . . . . . . . . 259
8.1.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 262
8.2 Hill Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
8.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 273
8.3 Cryptanalysis of Hill Ciphers . . . . . . . . . . . . . . . . . 275
8.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 279
9 RSA Ciphers 283
9.1 Introduction to Public-Key Ciphers . . . . . . . . . . . . . . 283
9.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 285
9.2 Introduction to RSA Ciphers . . . . . . . . . . . . . . . . . 286
9.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 289
9.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . 289
9.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 294
9.4 Modular Exponentiation . . . . . . . . . . . . . . . . . . . . 296
9.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 301
9.5 ASCII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
9.5.1 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . 302
CONTENTS
viii
9.6 RSA Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . 303
9.6.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 307
9.7 Cryptanalysis of RSA Ciphers . . . . . . . . . . . . . . . . . 309
9.7.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 312
9.8 Primality Testing . . . . . . . . . . . . . . . . . . . . . . . . 314
9.8.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 317
9.9 Integer Factorization . . . . . . . . . . . . . . . . . . . . . . 318
9.9.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 321
9.10 The RSA Factoring Challenges . . . . . . . . . . . . . . . . 321
9.10.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 322
10 ElGamal Ciphers 323
10.1 The Diffie-Hellman Key Exchange . . . . . . . . . . . . . . 324
10.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 326
10.2 Discrete Logarithms . . . . . . . . . . . . . . . . . . . . . . 328
10.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 330
10.3 ElGamal Ciphers . . . . . . . . . . . . . . . . . . . . . . . . 331
10.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 337
10.4 Cryptanalysis of ElGamal Ciphers . . . . . . . . . . . . . . 339
10.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 343
11 The Advanced Encryption Standard 345
11.1 Representations of Numbers . . . . . . . . . . . . . . . . . . 345
11.1.1 Binary . . . . . . . . . . . . . . . . . . . . . . . . . . 346
11.1.2 Hexadecimal . . . . . . . . . . . . . . . . . . . . . . 349
11.1.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 352
11.2 Stream Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . 354
11.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 358
11.3 AES Preliminaries . . . . . . . . . . . . . . . . . . . . . . . 360
11.3.1 Plaintext Format . . . . . . . . . . . . . . . . . . . . 361
11.3.2 The S-Box. . . . . . . . . . . . . . . . . . . . . . . . 362
11.3.3 Key Format and Generation. . . . . . . . . . . . . . 364
11.3.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 370
11.4 AES Encryption . . . . . . . . . . . . . . . . . . . . . . . . 371
11.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . 372
11.4.2 The Operations . . . . . . . . . . . . . . . . . . . . . 373
11.4.3 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 380
11.5 AES Decryption . . . . . . . . . . . . . . . . . . . . . . . . 383
11.5.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 393
11.6 AES Security . . . . . . . . . . . . . . . . . . . . . . . . . . 396
11.6.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 397
CONTENTS
ix
12 Message Authentication 399
12.1 RSA Signatures . . . . . . . . . . . . . . . . . . . . . . . . . 400
12.1.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 406
12.2 Hash Functions . . . . . . . . . . . . . . . . . . . . . . . . . 409
12.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 414
12.3 RSA Signatures with Hashing . . . . . . . . . . . . . . . . . 417
12.3.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 420
12.4 The Man-in-the-Middle Attack . . . . . . . . . . . . . . . . 423
12.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 425
12.5 Public-Key Infrastructures . . . . . . . . . . . . . . . . . . . 426
12.5.1 Key Formation . . . . . . . . . . . . . . . . . . . . . 427
12.5.2 Web of Trust . . . . . . . . . . . . . . . . . . . . . . 428
12.5.3 X.509 Certificates . . . . . . . . . . . . . . . . . . . 429
12.5.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 432
Bibliography 435
Hints and Answers for Selected Exercises 437
Index 469