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

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48 chapter 4 and the cipher text is E F D K L J B C A N O M H I G which is quite different from the first version. Other forms of transposition So far we have written the text in rectangles row by row but there are alternatives available and some of them would make it harder for a cryptanalyst to solve the system. In each case the text of the message is broken up into blocks of the appropriate length to fit the transposition box. Regular transposition boxes By a regular transposition box we mean a box that has columns of predictable length. The text can be written into the box in various ways but care needs to be taken, otherwise weaknesses may be introduced. Here are some examples, not all of which can be recommended. Table 4.10 A B C D E P Q R S F O X Y T G N W V U H M L K J I (i) We could use a rectangle but write the text around the rectangle in a ‘spiral’ fashion (Table 4.10). Unfortunately this is definitely not recommended. No matter what ordering of the columns is used in the transposition the pentagraph EFGHI and the trigraph STU will appear in unchanged form in the ‘cipher’. So, for example, if the message is THISXMETHODXISXNOTXSECURE and the transposition is 3-1-5-2-4 the box is as shown in Table 4.11, Table 4.11 3 1 5 2 4 T H I S X N O T X M X R E S E S U C E T I X D O H
then the cipher text is HORUX SXSEO TNXSI XMETH ITECD The pentagraph, XMETH, would soon be noticed by the cryptanalyst. The trigraph, XSE, though genuine, is not so obvious. If a rectangle with more rows than columns were used the ‘good’ polygraphs would be even more obvious. (ii) Use a ‘diamond-shaped’ box. In this box all the rows (and columns) contain an odd number of letters, starting with 1 and increasing each time by 2 up to some pre-determined number and then decreasing by 2 each time to 1. The box is obviously symmetric about the central row and column and all the columns are correctly aligned vertically (Table 4.12). Table 4.12 A B C D E F G H I J K L M N O P Q R S T U V W X Y This has the advantage that the column lengths are variable, which complicates the digraph attack. If we use the 7-digit transposition key 3-1-7- 5-2-4-6 for example (Table 4.13) Table 4.13 3 1 7 5 2 4 6 A B C D E F G H I J K L M N O P Q R S T U V W X Y the transmitted text will be EKQDH NTXJI OUACG MSWYP BFLRV Jigsaw ciphers 49 and letters which were originally adjacent will now be at distances ranging from 5 (e.g. H–I) to 21 (E–F) from each other, rather than at multiples of 5 as with a normal 5� 5 square.
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R. F. Churchhouse Codes and ciphers
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Contents Preface ix 1 Introduction
Page 9 and 10: Cryptanalysisofalinearrecurrence 10
Page 11 and 12: Preface Virtually anyone who can re
Page 13 and 14: 1 Introduction Some aspects of secu
Page 15 and 16: Not a very sophisticated method, pa
Page 17 and 18: change. As an example, anticipating
Page 19 and 20: Another form of encryption is the u
Page 21 and 22: and so is valid. On the other hand
Page 23 and 24: 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: giving B G L D I N A F K E J O C H
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 and 76: OURXSITUATI ONXISXDESPE RATEXSENDXS
Page 77 and 78: the alphabet are represented by up
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
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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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(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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