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

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136 chapter 10 Plate 10.1 A Hagelin machine with top closed, ready for use. The positions of the six wheels are visible to the operator. The ruler in front shows the machine to be only about seven inches wide. Plate 10.2 A Hagelin machine with its top open. The six wheels with some of the pins sticking out to the right and some to the left as well as some of the bars of the drum cage, with some lugs opposite wheels and some in neutral positions, can all be seen. The setting wheel and print wheel, letter counter and printer tape are also visible, on the left.
of each cipher period, to which side each pin was to be pushed. This was a tedious task since the total number of pins was 26�25�23�21�19�17�131. A pin which stuck out to the left side of a wheel would have no effect on the key and so was an inactive pin; a pin sticking out on the right side would (in an unoverlapped machine) cause the key to increase by the number of lugs opposite that wheel on the cage, i.e. by the ‘kick’ of that wheel. Such a pin was called active. Ideally, there should be approximately equal numbers of active and inactive pins on each wheel; somewhere between 40% and 60% active would be about right. At the start of each cipher period the operators would also have to move the lugs on each of the 27 bars so that the correct number were opposite each wheel, taking care that, in an unoverlapped machine, at most one lug on each bar was opposite a wheel, the other lug being left in one of the neutral positions. When the input letter had been set opposite the arrow the handle was turned and the cage rotated. Each wheel would have a pin in position opposite some lugs; if the pin was on the left side of the wheel the lugs would pass it by but if the pin was on the right side the pin would cause the lugs to move which would shift the bars on which they were placed and each such move would cause the print wheel to move one place. Thus if there were 9 lugs opposite the 26 wheel, the print wheel would be caused either to move 9 places, if the pin opposite the cage was active, or not to move at all, if the pin was inactive. When the cage had completed its rotation the wheels would all move one position and so a different set of pins would now be in positions opposite the lugs. Example 10.1 With the cage above, (4, 1, 9, 6, 5, 2), a typical keystream might be as shown in Table 10.1. Table 10.1 The Hagelin cipher machine 137 26-Wheel 14 10 14 14 0 10 0 4 10 14 10 14 14 14 0 14 0 10 10 14 25-Wheel 10 11 11 10 0 10 1 1 10 11 11 11 11 10 0 10 1 10 11 10 23-Wheel 19 19 19 10 0 19 0 0 10 19 10 19 19 10 9 19 0 10 19 19 21-Wheel 16 10 16 16 0 10 0 0 16 16 16 10 16 16 0 10 0 16 16 10 19-Wheel 10 15 15 15 0 15 0 0 15 10 15 15 10 10 0 15 0 15 10 10 17-Wheel 12 10 12 10 2 12 0 2 12 10 10 10 12 12 0 10 2 12220222 Key 21 15 27 15 2 16 1 7 13 20 12 19 22 12 9 18 3 13 16 15
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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
Page 97 and 98: Ciphers for spies 85 that were nece
Page 99 and 100: mistake can occur if the sender lea
Page 101 and 102: inks and ciphers were provided by h
Page 103 and 104: Example 7.6 Encipher the message AG
Page 105 and 106: Ciphers for spies 93 simply a ‘ra
Page 107 and 108: going into the mathematical criteri
Page 109 and 110: numbers, 0 to 31 inclusive, into bi
Page 111 and 112: Linear recurrences The sequences lo
Page 113 and 114: Having converted the characters of
Page 115 and 116: What about sequences of higher orde
Page 117 and 118: combining the keys of two or more l
Page 119 and 120: Example 8.3 (1) Use the mid-square
Page 121 and 122: Problem 8.3 Starting with U 0 �1
Page 123 and 124: The Enigma cipher machine 111 syste
Page 125 and 126: The Enigma cipher machine 113 Plate
Page 127 and 128: The Enigma cipher machine 115 Plate
Page 129 and 130: Figure 9.2. wheel. For example, if
Page 131 and 132: wheel and then through the three wh
Page 133 and 134: first day of usage and so the asses
Page 135 and 136: The Enigma cipher machine 123 The m
Page 137 and 138: show how, in a typical encipherment
Page 139 and 140: interested reader can find it in [9
Page 141 and 142: great deal of data and many pages o
Page 143 and 144: It should be realised, of course, t
Page 145 and 146: 10 The Hagelin cipher machine Histo
Page 147: ut there was no cryptographic advan
Page 151 and 152: value can be expected to occur two
Page 153 and 154: Since some cages are obviously very
Page 155 and 156: 2, there are 26! possible simple su
Page 157 and 158: The Hagelin cipher machine 145 Exam
Page 159 and 160: values are repeating at the appropr
Page 161 and 162: Overlapping will obviously affect t
Page 163 and 164: Table 10.6 The Hagelin cipher machi
Page 165 and 166: 11 Beyond the Enigma The SZ42: a pr
Page 167 and 168: Description of the SZ42 machine The
Page 169 and 170: P1 41 43 Z1 (4) the five bits from
Page 171 and 172: which is approximately 1.6�10 19
Page 173 and 174: 12 Public key cryptography Historic
Page 175 and 176: part of the story of what has been
Page 177 and 178: Public key cryptography 165 graphic
Page 179 and 180: (4) Now (k x ) y �(k y ) x �m x
Page 181 and 182: Public key cryptography 169 Despite
Page 183 and 184: If the cryptographer were prepared
Page 185 and 186: number of tests increased by a fact
Page 187 and 188: In this case the remainder is 4, no
Page 189 and 190: key, d, we use the Euclidean Algori
Page 191 and 192: the decipher key, d, is used instea
Page 193 and 194: and and, since Table 13.1 n N�2 n
Page 195 and 196: The Data Encryption Standard (DES)
Page 197 and 198: the message were known to relate to
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whereas in block cipher systems, su
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(1) X precedes M with information w
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ways, since choosing to pair, say,
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For example; if someone claims that
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depth, mentioned in Chapter 3. If w
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M9 Combining two biased streams of
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and so 2�4�6�12 �(4095)�4
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Verification Let the recurrence be
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the lettersatsetting2ofthewheel,and
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M16 Probability of a ‘depth’ in
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(2) In how many ways can N be repre
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Chapter 13 M21 (Rate of increase of
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Multiply each of these by M: M, 2M,
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If x 3 �0 divide x 2 by x 3 to gi
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then k�[ log 2 n], where [z] deno
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Mathematical aspects 217 problem un
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RHAPSODY and SYMPHONY agree in posi
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4.2 (Number of possible transpositi
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Table S.5 R H A P S O D Y B C E F G
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Chapter 8 8.1 (Recurrences of order
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columns in each case, are full of c
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Chapter 11 11.1 (Pin-setting errors
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[2.4] Moroney, M.J.: Facts from Fig
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[10.3] Almost any elementary book o
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Name index Adelman, L. 171, 234 And
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Subject index Abwehr Enigma 124, 13
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active pin 136 cage:‘good’ 141;
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Code and ciphers: Julius Caesar, the Enigma and the internet

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