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

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186 chapter 13 Chaining Since the DES enciphers text in short blocks of only 64 bits the obvious question is: how do we encipher messages that are longer than this? The simplest way is to break the message into blocks of 8 characters (�64 bits) and encipher them sequentially using the same 64-bit key. This would mean that all the 64-bit cipher messages were ‘in depth’, but the nonlinear nature of DES encipherment makes this feature, which would be disastrous if the encipherment were linear, of little or no value to the cryptanalyst. A more secure method however is to change the key for each 8character block by making each key depend on the original key and some, or all, of the plaintext of the preceding blocks. An authorised recipient will recover the plaintext of the first block since he knows the original key; he will therefore be able to construct the key for the second block and so decipher it. He will now have the plaintext of the second block and so be able to construct the key for deciphering the third block; and so on. An unauthorised recipient who manages to break into part of the message, possibly because of some repetitive standard text, would not be able to progress further because, without knowing all of the earlier blocks of plaintext, he cannot reconstruct the other keys. Had the same key been used for each block he would have been able to decrypt the entire message. Users of encipherment systems that are based on keys applied to short blocks of text, such as the DES, are strongly recommended to use chaining. Implementation of the DES Although it is not difficult to write a program to encipher/decipher using the DES algorithm no software implementation can be approved, partly because programs can be modified. In addition, software versions would be much slower than hardware versions on specifically designed chips and, shortly after the approval of the DES, various manufacturers designed and produced devices which contained chips for carrying out the DES algorithm. These devices can encipher or decipher at rates of a hundred thousand characters and more, per second. Using both RSA and DES In public key systems, such as RSA, the encipher/decipher algorithm generally involves a great deal of computation and so may run ‘slowly’,
whereas in block cipher systems, such as DES, the encipher/decipher processes can be carried out much faster, perhaps a thousand times faster in fact. If however (1) the sender encrypts the DES key using the RSA method and sends it to the recipient, and then (2) the sender encrypts the message with the DES key, he will keep the amount of computation down considerably without reducing the security as a whole. If ‘chaining’ is being employed the RSA algorithm would only have to be used once, to encipher the initial DES key. A salutary note From a ‘brute force’ point of view simple substitution ciphers, where there are more than 10 26 possibilities to consider, should be more difficult to solve than DES encrypted messages where the number of possibilities is less than 10 17 . This once again illustrates how misleading ‘brute force’ arguments can be. Beyond the DES Encipherment and the internet 187 The original DES was given official US Government Approval for about 10 years. After that time triple DES, as described above, continued to be approved but, in addition, new encryption algorithms were sought. In 1993 an algorithm called Skipjack was authorised and implemented on a chip known as Clipper. The details of the Skipjack algorithm were initially kept secret but were declassified on June 24th 1998 [13.7]. An ‘unofficial’ encryption system (i.e. one that was developed by private individuals) that has attracted many users is PGP, which is short for ‘Pretty Good Privacy’. PGP was developed by Philip Zimmermann and is freely available to anyone who wants it. It involves the following steps: (1) a ‘random’ key is generated based upon the user’s movements of the ‘mouse’ and keystrokes; this is referred to as the session key; (2) the plaintext of the message is compressed; the extent of compression depends upon the nature and length of the text; a typical English text might be compressed by 50% without introducing ambiguities but for short texts the saving, in transmission time, may not be worthwhile; (3) the key generated in (1) is used to encipher the compressed text produced in (2) using an algorithm called IDEA (‘International Data Encryption Algorithm’) invented by Lai and Massey at ETH, Zurich [13.8];
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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
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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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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
Page 193 and 194: and and, since Table 13.1 n N�2 n
Page 195 and 196: The Data Encryption Standard (DES)
Page 197: the message were known to relate to
Page 201 and 202: (1) X precedes M with information w
Page 203 and 204: ways, since choosing to pair, say,
Page 205 and 206: For example; if someone claims that
Page 207 and 208: depth, mentioned in Chapter 3. If w
Page 209 and 210: M9 Combining two biased streams of
Page 211 and 212: and so 2�4�6�12 �(4095)�4
Page 213 and 214: Verification Let the recurrence be
Page 215 and 216: the lettersatsetting2ofthewheel,and
Page 217 and 218: M16 Probability of a ‘depth’ in
Page 219 and 220: (2) In how many ways can N be repre
Page 221 and 222: Chapter 13 M21 (Rate of increase of
Page 223 and 224: Multiply each of these by M: M, 2M,
Page 225 and 226: If x 3 �0 divide x 2 by x 3 to gi
Page 227 and 228: then k�[ log 2 n], where [z] deno
Page 229 and 230: Mathematical aspects 217 problem un
Page 231 and 232: RHAPSODY and SYMPHONY agree in posi
Page 233 and 234: 4.2 (Number of possible transpositi
Page 235 and 236: Table S.5 R H A P S O D Y B C E F G
Page 237 and 238: Chapter 8 8.1 (Recurrences of order
Page 239 and 240: columns in each case, are full of c
Page 241 and 242: Chapter 11 11.1 (Pin-setting errors
Page 243 and 244: [2.4] Moroney, M.J.: Facts from Fig
Page 245 and 246: [10.3] Almost any elementary book o
Page 247 and 248: 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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