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

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150 chapter 10 comparing the two texts. The best way for the operators to be told the kick and overlap patterns of the wheels is to provide them with a ‘map’ showing the position of the 2 lugs on each of the 27 bars of the cage. The ‘map’ could either indicate the position of every lug on every bar, which would require eight columns – six for the wheels and two for the neutral positions; or it could show only the six wheel columns and, when a bar had only 1 lug shown, leave the operator to position the other lug in one of the neutral positions. The second method is used in the following Example 10.5 The ‘good’ unoverlapped cage (9, 7, 5, 3, 2, 1) is modified to an overlapped cage (11, 9, 7, 5, 3, 1) where the first four wheels each have an overlap of 2 with the wheel to their right and the fifth wheel has an overlap of 1 with the sixth wheel. Draw up a suitable drum cage map for the cipher operators. Does the overlapped cage generate all 26 possible key values (mod 26)? Solution See Table 10.6. Examination of the set of 64 key values generated by this cage shows that 5 key values 2, 4, 13, 20 and 25 cannot occur whereas the key value 17 occurs six times. It is not therefore a particularly satisfactory cage despite posing difficulties for a cryptanalyst because of the overlapping. Problem 10.3 Find which pin combinations in the overlapped cage above produce the key value 17. Solving the Hagelin from cipher texts only Solving a Hagelin cipher message ‘from scratch’ requires a great deal of tedious work and I shall only give an indication of how the cryptanalyst would probably go about it. Detailed examples of the solution from cipher messages have been published and the interested reader should consult [10.4] or [10.5]. When Hagelin messages are first intercepted the cryptanalyst will have no knowledge of the cage or pin settings. Initially he may not even know that it is a Hagelin that is being used. If the cipher operators don’t make mistakes the cryptanalyst is in for a lot of hard work. To have any chance of success he will need
Table 10.6 The Hagelin cipher machine 151 Bar 26-Wheel 25-Wheel 23-Wheel 21-Wheel 19-Wheel 17-Wheel 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X 10 X X 11 X X 12 X 13 X 14 X 15 X 16 X 17 X X 18 X X 19 X 20 X 21 X 22 X X 23 X X 24 X 25 X X 26 X X 27 X X either one very long cipher message of several thousand letters, or several messages of even greater total length. He would then have to compute various statistics, beginning with an overall frequency count of the cipher letters, which would help to establish that a Hagelin machine was probably being used, for the nonuniform distribution of the 26 possible key values would be detectable in a sufficiently long text. If several texts had to be used it might be possible to determine their ‘slides’ relative to each other by calculating their cipher frequency correlation coefficients in pairs (if the machine was an M209, with fixed slide, this wouldn’t arise). The longest cipher text would now be written on a width of 17 columns and counts made of the cipher letters in each column. The object here is to attempt to put each column into one of two classes: those
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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
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 and 148: ut there was no cryptographic advan
Page 149 and 150: of each cipher period, to which sid
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: Overlapping will obviously affect t
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
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
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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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