Codes and Ciphers: Julius Caesar, the Enigma, and the Internet

✍ Scribed by Churchhouse, Robert

• Publisher: Cambridge University Press
• Year: 2005
• Tongue: English
• Leaves: 252
• Category: Library

✦ Synopsis

The design of code and cipher systems has undergone major changes in modern times. Powerful personal computers have resulted in an explosion of e-banking, e-commerce and e-mail, and as a consequence the encryption of communications to ensure security has become a matter of public interest and importance. This book describes and analyzes many cipher systems ranging from the earliest and elementary to the most recent and sophisticated, such as RSA and DES, as well as wartime machines such as the ENIGMA and Hagelin, and ciphers used by spies. Security issues and possible methods of attack are discussed and illustrated by examples. The design of many systems involves advanced mathematical concepts and this is explained in detail in a major appendix. This book will appeal to anyone interested in codes and ciphers as used by private individuals, spies, governments and industry throughout history and right up to the present day.

✦ Table of Contents

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 11
Some aspects of secure communication......Page 13
Julius Caesar’s cipher......Page 14
Some basic definitions......Page 15
Three stages to decryption: identification, breaking and setting......Page 16
Codes and ciphers......Page 17
Assessing the strength of a cipher system......Page 19
Error detecting and correcting codes......Page 20
Other methods of concealing messages......Page 21
Modular arithmetic......Page 22
Gender......Page 23
End matter......Page 24
Julius Caesar ciphers and their solution......Page 25
Simple substitution ciphers......Page 27
How to solve a simple substitution cipher......Page 29
Letter frequencies in languages other than English......Page 36
How many letters are needed to solve a simple substitution cipher?......Page 38
Strengthening Julius Caesar: Vigenère ciphers......Page 40
How to solve a Vigenère cipher......Page 42
Indicators......Page 45
Recognising ‘depths’......Page 46
Jefferson’s cylinder......Page 49
Simple transposition......Page 52
Double transposition......Page 56
Regular transposition boxes......Page 60
Irregular transposition boxes......Page 62
Assessment of the security of transposition ciphers......Page 63
Double encipherment in general......Page 64
Monograph to digraph......Page 66
MDTM ciphers......Page 68
Digraph to digraph......Page 70
Playfair encipherment......Page 71
Playfair decipherment......Page 72
Double Playfair......Page 73
Characteristics of codes......Page 76
One-part and two-part codes......Page 77
Code plus additive......Page 79
7 Ciphers for spies......Page 84
Stencil ciphers......Page 85
Using a book cipher......Page 87
Solving a book cipher......Page 91
Disastrous errors in using a book cipher......Page 98
‘GARBO’’S ciphers......Page 100
GARBO’S second cipher......Page 101
One-time pad......Page 104
Random sequences......Page 106
Coin spinning......Page 107
Throwing dice......Page 108
Amplifier noise......Page 109
Pseudo-random sequences......Page 110
Linear recurrences......Page 111
Using a binary stream of key for encipherment......Page 112
Binary linear sequences as key generators......Page 113
Improving the security of binary keys......Page 116
The mid-square method......Page 118
Linear congruential generators......Page 119
Historical background......Page 122
The original Enigma......Page 124
Encipherment using wired wheels......Page 128
Encipherment by the Enigma......Page 130
The Achilles heel of the Enigma......Page 133
The indicator ‘chains’ in the Enigma......Page 137
Identifying R1 and its setting......Page 140
The Abwehr Enigma......Page 144
Historical background......Page 145
Structure of the Hagelin machine......Page 146
Encipherment on the Hagelin......Page 147
Choosing the cage for the Hagelin......Page 150
The theoretical ‘work factor’ for the Hagelin......Page 154
Solving the Hagelin from a stretch of key......Page 155
The slide......Page 159
Overlapping......Page 160
Solving the Hagelin from cipher texts only......Page 162
The SZ42: a pre-electronic machine......Page 165
Encipherment on the SZ42......Page 167
Breaking and setting the SZ42......Page 170
Modifications to the SZ42......Page 171
Historical background......Page 173
Protection of programs and data......Page 175
Encipherment of programs, data and messages......Page 176
The Diffie–Hellman key exchange system......Page 178
Strength of the Diffie–Hellman system......Page 180
Generalisation of simple substitution......Page 182
Factorisation of large integers......Page 183
The standard method of factorisation......Page 184
Fermat’s ‘Little Theorem’......Page 186
Encipherment and decipherment keys in the RSA system......Page 187
The encipherment and decipherment processes in the RSA system......Page 190
How does the key-owner reply to correspondents?......Page 194
The encipherment procedure......Page 195
Security of the DES......Page 196
Using both RSA and DES......Page 198
Beyond the DES......Page 199
Authentication and signature verification......Page 200
Elliptic curve cryptography......Page 201
M2 Reciprocal alphabets weaken security......Page 202
M3 The birthdays paradox......Page 203
M4 Euclid’s proof that there are an infinite number of primes......Page 204
M5 The Fibonacci sequence......Page 205
M6 Letter frequencies in a book cipher......Page 206
M7 One-time pad cipher cannot be solved......Page 207
M8 Frequency of occurrence in a page of random numbers......Page 208
M10 Fibonacci type sequence......Page 209
M11 Binary linear recurrences......Page 210
M12 Recovery of a binary linear recurrence from a stretch of key......Page 211
M14 Wheel wirings in the Enigma......Page 214
M15 Number of possible Enigma reflectors......Page 216
M17 Expected number of indicators needed to obtain full chains......Page 217
M18 Number of possible Hagelin cages......Page 218
M19 Maximum multiple of the kick which can occur when differencing Hagelin key......Page 219
M20 Determination of Hagelin slide by correlation coefficient......Page 220
M22 Calculating remainder using modular arithmetic......Page 221
M23 Proof of the Fermat–Euler Theorem......Page 222
M25 The Euclidean Algorithm......Page 224
M26 Efficiency of finding powers by repeated squaring......Page 226
M28 Elliptic Curve Cryptography......Page 227
3.1 (Three Vigenère messages)......Page 230
4.1 (Simple transposition)......Page 232
5.1 (MDTM)......Page 233
6.1 (Fibonacci key)......Page 235
7.3 (Continuation of example solution)......Page 236
8.3 (Cycle lengths in linear congruences)......Page 237
9.1 (Mini-Enigma)......Page 238
10.1 (Hagelin message)......Page 239
13.1 (Self-encipherment in the RSA system)......Page 241
Chapter 2......Page 242
Chapter 6......Page 243
Chapter 10......Page 244
Chapter 12......Page 245
Chapter 13......Page 246
Name index......Page 247
Subject index......Page 249

✦ Subjects

Nonfiction;Science;Mathematics;History