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

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6 chapter 1 Historically, two basic ideas dominated cryptography until relatively recent times and many cipher systems, including nearly all those considered in the first 11 chapters of this book were based upon one or both of them. The first idea is to shuffle the letters of the alphabet, just as one would shuffle a pack of cards, the aim being to produce what might be regarded as a random ordering, permutation, or anagram of the letters. The second idea is to convert the letters of the message into numbers, taking A�0, B�1, ..., Z�25, and then add some other numbers, which may themselves be letters converted into numbers, known as ‘the key’, to them letter by letter; if the addition produces a number greater than 25 we subtract 26 from it (this is known as (mod 26) arithmetic). The resulting numbers are then converted back into letters. If the numbers which have been added are produced by a sufficiently unpredictable process the resultant cipher message may be very difficult, or even impossible, to decrypt unless we are given the key. Interestingly, the Julius Caesar cipher, humble though it is, can be thought of as being an example of either type. In the first case our ‘shuffle’ is equivalent to simply moving the last three cards to the front of the pack so that all letters move ‘down’ three places and X, Y and Z come to the front. In the second case the key is simply the number 3 repeated indefinitely – as ‘weak’ a key as could be imagined. Translating a message into another language might be regarded as a form of encryption using a code-book (i.e. dictionary), but that would seem to be stretching the use of the word code too far. Translating into another language by looking up each word in a code-book acting as a dictionary is definitely not to be recommended, as anyone who has tried to learn another language knows.* On the other hand use of a little-known language to pass on messages of short term importance might sometimes be reasonable. It is said, for example, that in the Second World War Navajo Indian soldiers were sometimes used by the American Forces in the Pacific to pass on messages by telephone in their own language, on the reasonable assumption that even if the enemy intercepted the telephone calls they would be unlikely to have anyone available who could understand what was being said. * I recall a boy at school who wrote a French essay about a traveller in the Middle Ages arriving at an inn at night, knocking on the door and being greeted with the response ‘What Ho! Without.’ This he translated as ‘Que Ho! Sans.’ The French Master, after a moment of speechlessness, remarked that ‘You have obviously looked up the words in the sort of French dictionary they give away with bags of sugar.’
Another form of encryption is the use of some personal shorthand. Such a method has been employed since at least the Middle Ages by people, such as Samuel Pepys, who keep diaries. Given enough entries such codes are not usually difficult to solve. Regular occurrences of symbols, such as those representing the names of the days of the week, will provide good clues to certain polygraphs. A much more profound example is provided by Ventris’s decipherment of the ancient Mycenaen script known as Linear B, based upon symbols representing Greek syllables [1.4]. The availability of computers and the practicability of building complex electronic circuits on a silicon chip have transformed both cryptography and cryptanalysis. In consequence, some of the more recent cipher systems are based upon rather advanced mathematical ideas which require substantial computational or electronic facilities and so were impracticable in the pre-computer age. Some of these are described in Chapters 12 and 13. Assessing the strength of a cipher system When a new cipher system is proposed it is essential to assess its strength against all known attacks and on the assumption that the cryptanalyst knows what type of cipher system, but not all the details, is being used. The strength can be assessed for three different situations: (1) that the cryptanalyst has only cipher texts available; (2) that he has both cipher texts and their original plaintexts; (3) that he has both cipher and plain for texts which he himself has chosen. Introduction 7 The first situation is the ‘normal’ one; a cipher system that can be solved in a reasonable time in this case should not be used. The second situation can arise, for example, if identical messages are sent both using the new cipher and using an ‘old’ cipher which the cryptanalyst can read. Such situations, which constitute a serious breach of security, not infrequently occur. The third situation mainly arises when the cryptographer, wishing to assess the strength of his proposed system, challenges colleagues, acting as the enemy, to solve his cipher and allows them to dictate what texts he should encipher. This is a standard procedure in testing new systems. A very interesting problem for the cryptanalyst is how to construct texts which when enciphered will provide him with the maximum information on the details of the system. The format of these
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Page 5 and 6: R. F. Churchhouse Codes and ciphers
Page 7 and 8: 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: change. As an example, anticipating
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 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
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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
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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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