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

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132 chapter 9 Doubly enciphered Enigma messages The question as to whether double encipherment is worthwhile was briefly discussed in Chapter 4 where, in effect, the answer was ‘sometimes’ since it is necessary to balance the increased security (if any) against the risk that the operator will use the ciphers in the wrong order, so producing a cipher message which cannot be read by the intended recipient but which may help the cryptanalyst. The Enigma provides a nice example which illustrates both these points. During the War some particularly important Enigma messages were doubly enciphered. An officer would encipher a message using the same wheels, but a different plugboard, as the cipher clerk; the wheel settings would be chosen from a special list of 26 possibilities, denoted by the letters of the alphabet. He would then give this cipher message to the clerk preceded by the word OFFIZIER and another word beginning with the letter indicating which of the 26 settings he had used. The clerk would then encipher this message in the normal way. This undoubtedly added to the security but on at least one occasion the two encipherments were applied in the wrong order (the officer and the cipher clerk were the same person on that day). Jack Good guessed what had happened and decrypted the message nevertheless. (See [2.4], Chapter 19, 159–60.) The Abwehr Enigma The Abwehr (Secret intelligence service of the German High Command) used a modified version of the Enigma which deserves special mention. There was no plugboard, which made life easier for the cryptanalysts, but the notch rings contained 11, 17 or 19 notches instead of 1 or 2. The rotors therefore moved much more frequently than in the ‘standard’ Enigma and the reflector also moved, which made life harder. The practice of enciphering the (four-letter) indicator twice at a given ground setting was retained and so an eight-letter group preceded the cipher text. The cryptanalysts still employed the ‘chaining’ method but, in addition, were able to exploit the situation where all four rotors moved simultaneously. For more details see [9.5].
10 The Hagelin cipher machine Historical background It might be thought, quite reasonably, that any country would try to keep secret the identity of its cipher machines and this is, in general, true. If the cipher machines were designed and built in the country concerned, as was the case with the Enigma in Germany, keeping their identity and details secret would be feasible, but if a machine was purchased from elsewhere it would be almost inevitable that others would eventually know about it. Under these circumstances it may seem surprising that before and during World War II there was a cipher machine that was used by several countries on both sides, including Germany, Italy, the UK, the USA and France. This machine was made in Sweden, a neutral country, by the firm of Boris Hagelin and was sold to anyone who wanted it. It was known by a variety of names in these various countries (Hagelin, M209, C36, C38, C41,...) but, with some variation, was essentially the same machine in all cases. The basic function of the Hagelin machine was the provision of a long sequence of ‘pseudo-random’ numbers that were used as a key stream for the encipherment of plaintext by means of the equation (cipher letter)�key�(plaintext letter) (mod 26). (10.1) So, for example, if the plaintext letter was F (numerical equivalent�5) and the key was 18 the cipher letter would be N since 18�5�13 (the numerical equivalent of N). Note that equation (10.1) can be reversed, i.e. (plaintext letter)�key�(cipher letter) (mod 26), (10.2) [133]
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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
Page 93 and 94: If then we try subtracting THE from
Page 95 and 96: 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: It should be realised, of course, t
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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 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
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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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(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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