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Codes and Ciphers : Julius Caesar, the Enigma, and the Internet - R. F. Churchhouse

Codes and Ciphers

Julius Caesar, the Enigma, and the Internet

Hardcover Published: 28th February 2007
ISBN: 9780521810548
Number Of Pages: 252

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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.

'... written in a lively and amusing style but not at the expense of mathematical rigour.' European Mathematical Society 'A fascinating account, which should appeal to a wide readership.' Mathematika '... written in a lively and amusing style ...' EMS Newsletter 'The mathematics is well within the grasp of a cultured A level mathematician and for those to whom the book is addressed, it can be recommended.' The Mathematical Gazette

Prefacep. ix
Introductionp. 1
Some aspects of secure communicationp. 1
Julius Caesar's cipherp. 2
Some basic definitionsp. 3
Three stages to decrytion: identification, breaking and settingp. 4
Codes and ciphersp. 5
Assessing the strength of a cipher systemp. 7
Error detecting and correcting codesp. 8
Other methods of concealing messagesp. 9
Modular arithmeticp. 10
Modular addition and subtraction of lettersp. 11
Genderp. 11
End matterp. 12
From Julius Caesar to simple substitutionp. 13
Julius Caesar ciphers and their solutionp. 13
Simple substitution ciphersp. 15
How to solve a simple substitution cipherp. 17
Letter frequencies in languages other than Englishp. 24
How many letters are needed to solve a simple substitution cipher?p. 26
Polyalphabetic systemsp. 28
Strengthening Julius Caesar: Vigenere ciphersp. 28
How to solve a Vigenere cipherp. 30
Indicatorsp. 33
Depthsp. 34
Recognising 'depths'p. 34
How much text do we need to solve a Vigenere cipher?p. 37
Jefferson's cylinderp. 37
Jigsaw ciphersp. 40
Transpositionsp. 40
Simple transpositionp. 40
Double transpositionp. 44
Other forms of transpositionp. 48
Assessment of the security of transposition ciphersp. 51
Double encipherment in generalp. 52
Two-letter ciphersp. 54
Monograph to digraphp. 54
MDTM ciphersp. 56
Digraph to digraphp. 58
Playfair enciphermentp. 59
Playfair deciphermentp. 60
Cryptanalytic aspects of Playfairp. 61
Double Playfairp. 61
Codesp. 64
Characteristics of codesp. 64
One-part and two-part codesp. 65
Code plus additivep. 67
Ciphers for spiesp. 72
Stencil ciphersp. 73
Book ciphersp. 75
Letter frequencies in book ciphersp. 79
Solving a book cipherp. 79
Indicatorsp. 86
Disastrous errors in using a book cipherp. 86
'Garbo"s ciphersp. 88
One-time padp. 92
Producing random numbers and lettersp. 94
Random sequencesp. 94
Producing random sequencesp. 95
Coin spinningp. 95
Throwing dicep. 96
Lottery type drawsp. 97
Cosmic raysp. 97
Amplifier noisep. 97
Pseudo-random sequencesp. 98
Linear recurrencesp. 99
Using a binary stream of key for enciphermentp. 100
Binary linear sequences as key generatorsp. 101
Cryptanalysis of a linear recurrencep. 104
Improving the security of binary keysp. 104
Pseudo-random number generatorsp. 106
The mid-square methodp. 106
Linear congruential generatorsp. 107
The Enigma cipher machinep. 110
Historical backgroundp. 110
The original Enigmap. 112
Encipherment using wired wheelsp. 116
Encipherment by the Enigmap. 118
The Enigma plugboardp. 121
The Achilles heel of the Enigmap. 121
The indicator 'chains' in the Enigmap. 125
Aligning the chainsp. 128
Identifying R1 and its settingp. 128
Doubly enciphered Enigma messagesp. 132
The Abwehr Enigmap. 132
The Hagelin cipher machinep. 133
Historical backgroundp. 133
Structure of the Hagelin machinep. 134
Encipherment on the Hagelinp. 135
Choosing the cage for the Hagelinp. 138
The theoretical 'work factor' for the Hagelinp. 142
Solving the Hagelin from a stretch of keyp. 143
Additional features of the Hagelin machinep. 147
The slidep. 147
Identifying the slide in a cipher messagep. 148
Overlappingp. 148
Solving the Hagelin from cipher texts onlyp. 150
Beyond the Enigmap. 153
The SZ42: a pre-electronic machinep. 153
Description of the SZ42 machinep. 155
Encipherment on the SZ42p. 155
Breaking and setting the SZ42p. 158
Modifications to the SZ42p. 159
Public key cryptographyp. 161
Historical backgroundp. 161
Security issuesp. 163
Protection of programs and datap. 163
Encipherment of programs, data and messagesp. 164
The key distribution problemp. 166
The Diffie-Hellman key exchange systemp. 166
Strength of the Diffie-Hellman systemp. 168
Encipherment and the internetp. 170
Generalisation of simple substitutionp. 170
Factorisation of large integersp. 171
The standard method of factorisationp. 172
Fermat's 'Little Theorem'p. 174
The Fermat-Euler Theorem (as needed in the RSA system)p. 175
Encipherment and decipherment keys in the RSA systemp. 175
The encipherment and decipherment processes in the RSA systemp. 178
How does the key-owner reply to correspondents?p. 182
The Data Encryption Standard (DES)p. 183
Security of the DESp. 184
Chainingp. 186
Implementation of the DESp. 186
Using both RSA and DESp. 186
A salutary notep. 187
Beyond the DESp. 187
Authentication and signature verificationp. 188
Elliptic curve cryptographyp. 189
Appendixp. 190
Solutions to problemsp. 218
Referencesp. 230
Name indexp. 235
Subject indexp. 237
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521810548
ISBN-10: 052181054X
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 252
Published: 28th February 2007
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.86 x 14.61  x 1.91
Weight (kg): 0.54