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

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6 Codes Characteristics of codes As was mentioned in Chapter 1, the distinction between codes and ciphers is not always clear, but one might reasonably say that whereas most codes tend to be static most ciphers are dynamic. That is to say that a letter or phrase enciphered simply by means of a code will produce the same cipher each time the code is used, whereas a letter or phrase enciphered by a cipher system will generally produce different cipher text at different times. This is because most cipher systems involve one or more parameters, such as keywords or, as we shall see later, wheel settings, which are changed at regular or irregular intervals and so cause the cipher outputs from the same plaintext to be different. The basic mechanism, or algorithm, for generating the cipher doesn’t change, but the parameters do. In general, a code has no such parameters though the entire code may itself be changed, in which case it becomes a different code. In practice this is achieved by issuing a new code-book every now and then. Using this criterion the Julius Caesar cipher would be classed as a code, because the encipherment of a fixed letter across many messages is invariably the same. We can, however, say that there is a parameter associated with Julius Caesar ciphers, namely the shift, which gives us 25 different ciphers and if the value of the shift is somehow incorporated in the message, i.e. in the indicator, the Julius Caesar system can reasonably be considered as a cipher, not as a code. Example 6.1 Although there are much earlier examples of codes the one devised by Samuel Morse (1791–1872) in 1832 for the purpose of transmitting messages by telegraphy is probably the best-known. In this code the letters of [64]
the alphabet are represented by up to four ‘dots’ and ‘dashes’, the digits 0 to 9 by five and certain punctuation symbols by six. To transmit a dot the telegraph key is depressed for about one 24th of a second; for a dash the key is depressed for about one 8th of a second; the interval between the components of a letter is the same as that for a dot and the interval between letters is equal to that for a dash. The Morse code was designed so that the most frequent letters in English had shorter transmission times than the less frequent letters. Thus E was represented by a single dot and T by a single dash whereas J required four symbols, dot dash dash dash. The reason for this was to try to minimise the time required to transmit a message. The international wireless version of the letters of the Morse code is shown in Table 6.1. Table 6.1 Morse code A ·– E · I ·· M –– Q ––·– U ··– Y –·–– B –··· F ··–· J ·––– N –· R ·–· V ···– Z ––·· C –·–· G ––· K –·– O ––– S ··· W ·–– D –·· H ···· L ·–·· P ·––· T – X –··– The Morse code was not, of course, designed to protect the secrecy of a message but merely to provide a means for transmitting it efficiently. A good wireless operator using this code would be able to transmit about 30 average words per minute. As was mentioned in Chapter 1, there are other codes which are designed to ensure the accuracy of messages or data rather than to preserve the secrecy of their contents. Among such codes are those used to transmit data from spacecraft or to store data in computer-readable form. If secrecy is not needed the details of the code will usually be available to anyone who wants them. If secrecy as well as accuracy is required the details may not be made public and some form of encryption of the data will also be applied. One-part and two-part codes Most codes involve the use of a code-book, which may contain thousands of code groups. A code used by the military would typically represent letters, numbers or phrases by code groups consisting of four or five letters or digits. It is not necessary that all the code groups contain the same number of symbols; the famous Zimmermann telegram of January 1917, which was deciphered by British cryptanalysts and which was a Codes 65
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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
Page 25 and 26: 2 From Julius Caesar to simple subs
Page 27 and 28: Table 2.3 Shift Message 12 OUI 12 Y
Page 29 and 30: worry about but, on the other hand,
Page 31 and 32: then it is probably THE and the unk
Page 33 and 34: From Julius Caesar to simple substi
Page 37 and 38: Table 2.6 From Julius Caesar to sim
Page 41 and 42: and the key which provides the enci
Page 43 and 44: Further examination reveals that th
Page 45 and 46: ALTHOUGH I AM AN OLD MAN NIGHT IS G
Page 47 and 48: Polyalphabetic systems 35 messages
Page 49 and 50: Before leaving Vigenère try the fo
Page 51 and 52: Polyalphabetic systems 39 blocks of
Page 53 and 54: eginning at the top, but it is then
Page 55 and 56: first row above, for example, we fi
Page 57 and 58: Table 4.4 Key 3 1 5 2 4 1 2 3 4 5 6
Page 59 and 60: giving B G L D I N A F K E J O C H
Page 61 and 62: then the cipher text is HORUX SXSEO
Page 63 and 64: The plaintext digraphs are now sepa
Page 65 and 66: ox increases. By enumerating the po
Page 67 and 68: Example 5.1 HAPPY BIRTHDAY encipher
Page 69 and 70: Encryption The ‘plaintext’ is A
Page 71 and 72: plaintext digraphs according to som
Page 73 and 74: Cryptanalytic aspects of Playfair P
Page 75: OURXSITUATI ONXISXDESPE RATEXSENDXS
Page 79 and 80: From a cryptographic point of view
Page 81 and 82: 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0
Page 83 and 84: If we generate the same sequence (m
Page 85 and 86: Stencil ciphers The example above i
Page 87 and 88: Book ciphers A spy must avoid arous
Page 89 and 90: Table 7.2 Encipher table for a book
Page 91 and 92: 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
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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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(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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