Code and ciphers: Julius Caesar, the Enigma and the internet

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236 name index Piper, F. 233 Poe, E. A. ix Pomerance, C. 234 Press, W. H. 232 Price, W. L. 233, 234 Pujol, J. see garbo Rabin, M. O. 212, 234 Rivest, R. L. 171, 234 Rota, G.-C. 233 Scherbius, A. 111 Shamir, A. 171, 234 Singh, S. 234 Solovay, R. 212, 234 Strassen, V. 212, 234 Stripp, A. 231 and passim Teukolsky, S. A. 232 Tuchman, B. 231 Turing, A. M. 161 Vajda, S. 231 Vallée-Poussin, C. de la 233 Ventris, M. 7, 230 Vetterling, W. T. 232 Welsh, D. 230 Wiles, A. 234 Wittgenstein, L. 23, 230 Wright, E. M. 232, 233 Wright, E. V. 230 Zimmermann, A. 65, 231 Zimmermann, P. 187
Subject index Abwehr Enigma 124, 132 active pins 136 algorithm 5 amplifier noise 97–8 anagram ix, 40 arithmetic, modular 10, 68, 209 authentication 165, 188–9 avalanche test (DES) 184 Beale cipher 230 binary key stream 100–3 improving security 104–6 binary linear recurrence 198–202 birthdays paradox 191–2 Bletchley ix, 131, Plate 11. 1 book cipher 36, 75–87 decipher table 78 disastrous error in using 86 encipher table 77 letter frequencies in 79, 194–5 solving 79–85 breaking ciphers 4 Brown corpus 23, 42 bruteforceattack 27, 44, 142, 158, 187, 215 C36 cipher machine 133 C38 cipher machine 133 C41 cipher machine 133 Caesar’s cipher Chapter 2 and passim cage ‘good’ 141 number of 141, 206–7 cathode ray tube storage 161 cipher 1918 German Army 57 Beale 230 block 183 book see book cipher Caesar’s see Caesar’s cipher digraph-to-digraph 58 garbo’s see garbo German double Playfair 61–2 Japanese naval 58 Jefferson’s cylinder 37–9 jigsaw see jigsaw cipher MDTM 56 monograph-to-digraph 54 Playfair 59–60 simple substitution Chapter 2 and passim stencil 73–4 transposition Chapter 4 two-letter Chapter 5 unbreakable 36, 74 Vigenère Chapter 3 cipher system 3 strength of 7 classical sieve formula 190 Clipper 187 code 5, Chapter 6 error-detecting 8, 164 Hamming 8 ISBN 8 Italian naval 67 Japanese naval 67 Mengarini 67 Morse 65 one-part 65–6 two-part 66–7 U-boat 67 code-book 4 codebreaker 4 codebreaking ix, 4 code group 5, 38, 65 coin spinning 95–6 Colossus 159 combinations 207 combinatorics 206 [237]
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R. F. Churchhouse Codes and ciphers
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Contents Preface ix 1 Introduction
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Cryptanalysisofalinearrecurrence 10
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Preface Virtually anyone who can re
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1 Introduction Some aspects of secu
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Not a very sophisticated method, pa
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change. As an example, anticipating
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Another form of encryption is the u
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and so is valid. On the other hand
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When the modulus is 10 only the num
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2 From Julius Caesar to simple subs
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Table 2.3 Shift Message 12 OUI 12 Y
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worry about but, on the other hand,
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then it is probably THE and the unk
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From Julius Caesar to simple substi
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Table 2.6 From Julius Caesar to sim
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and the key which provides the enci
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Further examination reveals that th
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ALTHOUGH I AM AN OLD MAN NIGHT IS G
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Polyalphabetic systems 35 messages
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Before leaving Vigenère try the fo
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Polyalphabetic systems 39 blocks of
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eginning at the top, but it is then
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first row above, for example, we fi
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Table 4.4 Key 3 1 5 2 4 1 2 3 4 5 6
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giving B G L D I N A F K E J O C H
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then the cipher text is HORUX SXSEO
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The plaintext digraphs are now sepa
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ox increases. By enumerating the po
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Example 5.1 HAPPY BIRTHDAY encipher
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Encryption The ‘plaintext’ is A
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plaintext digraphs according to som
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Cryptanalytic aspects of Playfair P
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OURXSITUATI ONXISXDESPE RATEXSENDXS
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the alphabet are represented by up
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From a cryptographic point of view
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3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0
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If we generate the same sequence (m
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Stencil ciphers The example above i
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Book ciphers A spy must avoid arous
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Table 7.2 Encipher table for a book
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Letter frequencies in book ciphers
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If then we try subtracting THE from
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where row F (the row of the cipher
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Ciphers for spies 85 that were nece
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mistake can occur if the sender lea
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inks and ciphers were provided by h
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Example 7.6 Encipher the message AG
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Ciphers for spies 93 simply a ‘ra
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going into the mathematical criteri
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numbers, 0 to 31 inclusive, into bi
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Linear recurrences The sequences lo
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Having converted the characters of
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What about sequences of higher orde
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combining the keys of two or more l
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Example 8.3 (1) Use the mid-square
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Problem 8.3 Starting with U 0 �1
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The Enigma cipher machine 111 syste
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The Enigma cipher machine 113 Plate
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The Enigma cipher machine 115 Plate
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Figure 9.2. wheel. For example, if
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wheel and then through the three wh
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first day of usage and so the asses
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The Enigma cipher machine 123 The m
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show how, in a typical encipherment
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interested reader can find it in [9
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great deal of data and many pages o
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It should be realised, of course, t
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10 The Hagelin cipher machine Histo
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ut there was no cryptographic advan
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of each cipher period, to which sid
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value can be expected to occur two
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Since some cages are obviously very
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2, there are 26! possible simple su
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The Hagelin cipher machine 145 Exam
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values are repeating at the appropr
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Overlapping will obviously affect t
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Table 10.6 The Hagelin cipher machi
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11 Beyond the Enigma The SZ42: a pr
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Description of the SZ42 machine The
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P1 41 43 Z1 (4) the five bits from
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which is approximately 1.6�10 19
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12 Public key cryptography Historic
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part of the story of what has been
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Public key cryptography 165 graphic
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(4) Now (k x ) y �(k y ) x �m x
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Public key cryptography 169 Despite
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If the cryptographer were prepared
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number of tests increased by a fact
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In this case the remainder is 4, no
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key, d, we use the Euclidean Algori
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the decipher key, d, is used instea
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and and, since Table 13.1 n N�2 n
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The Data Encryption Standard (DES)
Page 197 and 198: the message were known to relate to
Page 199 and 200: whereas in block cipher systems, su
Page 201 and 202: (1) X precedes M with information w
Page 203 and 204: ways, since choosing to pair, say,
Page 205 and 206: For example; if someone claims that
Page 207 and 208: depth, mentioned in Chapter 3. If w
Page 209 and 210: M9 Combining two biased streams of
Page 211 and 212: and so 2�4�6�12 �(4095)�4
Page 213 and 214: Verification Let the recurrence be
Page 215 and 216: the lettersatsetting2ofthewheel,and
Page 217 and 218: M16 Probability of a ‘depth’ in
Page 219 and 220: (2) In how many ways can N be repre
Page 221 and 222: Chapter 13 M21 (Rate of increase of
Page 223 and 224: Multiply each of these by M: M, 2M,
Page 225 and 226: If x 3 �0 divide x 2 by x 3 to gi
Page 227 and 228: then k�[ log 2 n], where [z] deno
Page 229 and 230: Mathematical aspects 217 problem un
Page 231 and 232: RHAPSODY and SYMPHONY agree in posi
Page 233 and 234: 4.2 (Number of possible transpositi
Page 235 and 236: Table S.5 R H A P S O D Y B C E F G
Page 237 and 238: Chapter 8 8.1 (Recurrences of order
Page 239 and 240: columns in each case, are full of c
Page 241 and 242: Chapter 11 11.1 (Pin-setting errors
Page 243 and 244: [2.4] Moroney, M.J.: Facts from Fig
Page 245 and 246: [10.3] Almost any elementary book o
Page 247: Name index Adelman, L. 171, 234 And
Page 251 and 252: active pin 136 cage:‘good’ 141;
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Code and ciphers: Julius Caesar, the Enigma and the internet

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