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

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2 chapter 1 buy or sell a large number of shares at once or, in war, an order by an army commander to attack in a certain direction at dawn next day. On other occasions the information may have long term value and must be kept secret for as long as possible, such as a message which relates to the planning of a large scale military operation. The effort required by a rival, opponent or enemy to read the message is therefore relevant. If, using the best known techniques and the fastest computers available, the message can’t be read by an unauthorised recipient in less time than that for which secrecy or confidentiality is essential then the sender can be reasonably happy. He cannot ever be entirely happy since success in reading some earlier messages may enable the opponent to speed up the process of solution of subsequent messages. It is also possible that a technique has been discovered of which he is unaware and consequently his opponent is able to read the message in a much shorter time than he believed possible. Such was the case with the German Enigma machine in the 1939–45 war, as we shall see in Chapter 9. Julius Caesar’s cipher The problem of ensuring the security of messages was considered by the ancient Greeks and by Julius Caesar among others. The Greeks thought of a bizarre solution: they took a slave and shaved his head and scratched the message on it. When his hair had grown they sent him off to deliver the message. The recipient shaved the slave’s head and read the message. This is clearly both a very insecure and an inefficient method. Anyone knowing of this practice who intercepted the slave could also shave his head and read the message. Furthermore it would take weeks to send a message and get a reply by this means. Julius Caesar had a better idea. He wrote down the message and moved every letter three places forward in the alphabet, so that, in the English alphabet, A would be replaced by D, B by E and so on up to W which would be replaced by Z and then X by A, Y by B and finally Z by C. If he had done this with his famous message VENI. VIDI. VICI. (I came. I saw. I conquered.) and used the 26-letter alphabet used in English-speaking countries (which, of course, he would not) it would have been sent as YHQL. YLGL. YLFL.
Not a very sophisticated method, particularly since it reveals that the message consists of three words each of four letters, with several letters repeated. It is difficult to overcome such weaknesses in a naïve system like this although extending the alphabet from 26 letters to 29 or more in order to accommodate punctuation symbols and spaces would make the word lengths slightly less obvious. Caesar nevertheless earned a place in the history of cryptography, for the ‘Julius Caesar’ cipher, as it is still called, is an early example of an encryption system and is a special case of a simple substitution cipher as we shall see in Chapter 2. Some basic definitions Introduction 3 Since we shall be repeatedly using words such as digraph, cryptography and encryption we define them now. A monograph is a single letter of whatever alphabet we are using. A digraph is any pair of adjacent letters, thus AT is a digraph. A trigraph consists of three adjacent letters, so THE is a trigraph, and so on. A polygraph consists of an unspecified number of adjacent letters. A polygraph need not be recognisable as a word in a language but if we are attempting to decipher a message which is expected to be in English and we find the heptagraph MEETING it is much more promising than if we find a heptagraph such as DKRPIGX. A symbol is any character, including letters, digits, and punctuation, whilst a string is any adjacent collection of symbols. The length of the string is the number of characters that it contains. Thus A3£%$ is a string of length 5. A cipher system, or cryptographic system, is any system which can be used to change the text of a message with the aim of making it unintelligible to anyone other than intended recipients. The process of applying a cipher system to a message is called encipherment or encryption. The original text of a message, before it has been enciphered, is referred to as the plaintext; after it has been enciphered it is referred to as the cipher text. The reverse process to encipherment, recovering the original text of a message from its enciphered version, is called decipherment or decryption. These two words are not, perhaps, entirely synonymous. The intended recipient of a message would think of himself as deciphering it whereas an unintended recipient who is trying to make sense of it would think of himself as decrypting it.
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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: 1 Introduction Some aspects of secu
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 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
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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
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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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