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

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240 subject index polyalphabetic systems Chapter 3 polygraph 2 prime finding large 167 ‘probable’ 176, 212 Prime Number Theorem 209 pseudo-random number 95, 133, 202 pseudo-random number generator 106 pseudo-random sequence 95–98 public key system 171, 182 random letter 95 random number 94–5 random sequence 94 production of 95–6 reflector see Enigma repeated squaring, efficiency of 214–15 Rosetta stone 230 roulette wheel 96 RSA cipher 167–8, 175–82, 212–15 � DES 186–7 encipher/decipher key 175–6 encipher/decipher process 176 sampling with replacement 205 security 163 sequence Fibonacci 70–1, 98, 193–4, 197–8 linear 99–103 pseudo-random 95–8 random 94–5 setting, cipher machine 4 setting ring see Enigma sieve, classical formula 190 signature verification 165, 188–9 simple substitution cipher Chapter 2 and passim how to solve 17 –19 minimum length for solving 16, 26 Skipjack, encryption algorithm 187 slide see Hagelin spy Chapter 7 stencil cipher 73–4 strength of cipher system 7 string 3 length of 3 symbol 3 SZ42 cipher machine 106, Chapter 11 encipherment process 156–7 modification 159–60 wheel motion 155–6 work factor 158 transistor 162 transpositions ix, 40, 55, 74, 90 double 44–6, 89–92 irregular box 50 method of solution 42 regular box 48 security of 51 simple 40 trapdoor 143, 185 trigraph 3 Trojan horse attack 163 two-letter cipher 54 T52 cipher machine 154 U-boat code 67 Umkehrwalze see Enigma (reflector) unbreakable cipher 29, 36, 74 Vigenère cipher 28–9, 79 how to solve 29, 30 key 29 text needed 37 Virus 163 Voynich Manuscript 230 Welsh (frequencies of letters) 25 wheels see Enigma, Hagelin, SZ42 wheel wiring see Enigma wired wheel, encipherment by 116 Wittgenstein, diary of 230 World War 1 111 1918 German cipher 57, 61 World War 2 2, 6, 58, 67, 106, 133 double agent see garbo German double Playfair cipher 61–3 Italian naval cipher (Mengarini) 67 Japanese naval cipher (JN40) 58 Japanese naval code (OTSU) 67 U-boat code 67 Zimmermann telegram 65–6
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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)
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the message were known to relate to
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whereas in block cipher systems, su
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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 and 248: Name index Adelman, L. 171, 234 And
Page 249 and 250: Subject index Abwehr Enigma 124, 13
Page 251: active pin 136 cage:‘good’ 141;
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Code and ciphers: Julius Caesar, the Enigma and the internet

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