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162 CHAPTER 8. POLYALPHABETIC CIPHERS Which text is in German, and which is in French (Compute Φ of each and, remembering that monoalphabetic encipherments do not change the Φ value of the text, use part (a).) 21. Here is a variant on the auto-key method. Rather than use the message as the key, which perhaps seems rather dangerous, instead use the secret message Encipher mysterious with priming key m and use your answer to help you discuss the security of this method. 22. Joseph Willard Brown wrote “Ciphers are undiscoverable in proportion as their changes are frequent, and as the messages in each change are brief. When alphabetic ciphers are used, the aim should be never to allow any letter to appear twice alike. The number of letters under each key is to be as small as possible [Brown page 99].” Explain the meaning of this quote. 23. On March 8, 1913, the Secretary of State, William Jennings Bryan, sent the following message to all American Diplomatic and Consular Officers. “Gentleman: For the purpose of affording a means of direct secret communication between officers of the Army and Navy and the Diplomatic and Consular Service, the respective Departments are providing the necessary officers with the Larrabee Cipher Code, a copy of which is transmitted herewith. The following arrangements as to key words will be observed: (1) Key words may be arranged between officers using code either directly or through their Departments in Washington, when more direct secret communication is not possible. (2) In the absence of other agreement, the key word is to be the name of the month in which the message is sent. The Navy Department is supplying the Larrabee Cipher to the commanding officers of all ships in the service.” Enclosed with this letter was a chart, Figure 8.2, and instructions: “Write down the words, message, or cipher to be converted, and write over them, letter for letter, the key word agreed upon, repeating the key word as often as necessary. For each letter to be converted enter the table with the letter of the key word found above it, as a marginal letter. If converting message into cipher [read] in the upper line abreast the marginal letter, the letter of the message, the letter of the cipher is [then] directly below it. If converting cipher into message [read] the lower line abreast the marginal letter [, then] the letter of the cipher the letter of the message is directly above it.
8.9. EXERCISES 163 A: AB CDE FGH I J K LMNOPQRSTUVWXYZ N: ABCDEFGH I JKLMNOPQR S TUVWXY Z 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 z n o p q r s t u vw x y z a b c d e f g h i j k l m B: AB CDE FGH I J K LMNOPQRSTUVWXYZ O: ABCDEFGH I JKLMNOPQR S TUVWXY Z b c d e f g h i j k l m n o p q r s t u v w x y z a o p q r s t u vwx y z a b c d e f g h i j k l m n C: AB CDE FGH I J K LMNOPQRSTUVWXYZ P: ABCDEFGH I JKLMNOPQR S TUVWXY Z c d e f g h i j k l m n o p q r s t u vw x y z a b p q r s t u v wx y z a b c d e f g h i j k l m n o D: AB CDE FGH I J K LMNOPQRSTUVWXYZ Q: ABCDEFGH I JKLMNOPQR S TUVWXY Z d e f g h i j k l m n o p q r s t u vwx y z a b c q r s t u v w x y z a b c d e f g h i j k l m n o p E: AB CDE FGH I J K LMNOPQRSTUVWXYZ R: ABCDEFGH I JKLMNOPQR S TUVWXY Z e f g h i j k l m n o p q r s t u vwx y z a b c d r s t u vw x y z a b c d e f g h i j k l m n o p q F: AB CDE FGH I J K LMNOPQRSTUVWXYZ S: ABCDEFGH I JKLMNOPQR S TUVWXY Z f g h i j k l m n o p q r s t u v wx y z a b c d e s t u v wx y z a b c d e f g h i j k l m n o p q r G:AB CDE FGH I J K LMNOPQRSTUVWXYZ T: ABCDEFGH I JKLMNOPQR S TUVWXY Z g h i j k l m n o p q r s t u v w x y z a b c d e f t u v w x y z a b c d e f g h i j k l m n o p q r s H: AB CDE FGH I J K LMNOPQRSTUVWXYZ U: ABCDEFGH I JKLMNOPQR S TUVWXY Z h i j k l m n o p q r s t u v w x y z a b c d e f g u vw x y z a b c d e f g h i j k l m n o p q r s t I: AB CDE FGH I J K LMNOPQRSTUVWXYZ V: ABCDEFGH I JKLMNOPQR S TUVWXY Z i j k l m n o p q r s t u v w x y z a b c d e f g h vwx y z a b c d e f g h i j k l m n o p q r s t u J: AB CDE FGH I J K LMNOPQRSTUVWXYZ W:ABCDEFGH I JKLMNOPQR S TUVWXY Z j k l m n o p q r s t u v w x y z a b c d e f g h i wx y z a b c d e f g h i j k l m n o p q r s t u v K:AB CDE FGH I J K LMNOPQRSTUVWXYZ X: ABCDEFGH I JKLMNOPQR S TUVWXY Z k l m n o p q r s t u v w x y z a b c d e f g h i j x y z a b c d e f g h i j k l m n o p q r s t u v w L: AB CDE FGH I J K LMNOPQRSTUVWXYZ Y: ABCDEFGH I JKLMNOPQR S TUVWXY Z l m n o p q r s t u v w x y z a b c d e f g h i j k y z a b c d e f g h i j k l m n o p q r s t u v w x M:AB CDE FGH I J K LMNOPQRSTUVWXYZ Z: ABCDEFGH I JKLMNOPQR S TUVWXY Z m n o p q r s t u v w x y z a b c d e f g h i j k l z 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 Figure 8.2: Larrabee’s Cipher Code To apply to figures let A B C D E F G H I J represent 1 2 3 4 5 6 7 8 9 0 To indicate that figures are used, write the letter Q followed by the number of figures expressed in letters as above that follow: then for the figures write the letters, thus QEICDJF means 93406, Q indicating that figures follow, E 5 the number of figures, and ICDJF representing 03496. Example Key word Pekin Key words PEKI NPEKI NPE Message SEND QCCJJ MEN Cipher HIXL DRGTR ZTR Ordinarily however it is safer to send numbers in words, i.e. three hundred instead of 300. Before transmission the cipher is arranged in five letter groups. Thus, the above example would appear HIXLD RGTRZ TR etc. There were plans for a new codebook for the Departments of State, War and Navy, and the Larrabee Code was to be only in temporary use.
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Cryptology: An Historical Introduct
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Contents List of Figures 8 1 Caesar
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CONTENTS 5 9 Digraphic Ciphers 167
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List of Figures 1.1 Saint Cyr Slide
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Chapter 1 Caesar Ciphers There are
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11 Examples: Encipher or decipher t
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1.1. SAINT CYR SLIDE 13 paper turne
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1.3. FREQUENCY ANALYSIS 15 PX PBEE
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1.3. FREQUENCY ANALYSIS 17 A bit mo
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1.3. FREQUENCY ANALYSIS 19 Examples
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1.4. LINQUIST’S METHOD 21 the cip
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1.7. EXERCISES 23 12. What is the m
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1.7. EXERCISES 25 (d) VTXLTKBTG LXV
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1.7. EXERCISES 27 (d) IKSUT JKIOT K
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Chapter 2 Cryptologic Terms Cryptog
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Chapter 3 The Introduction of Numbe
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3.1. THE REMAINDER OPERATOR 33 Exam
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3.1. THE REMAINDER OPERATOR 35 Perf
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3.1. THE REMAINDER OPERATOR 37 As a
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3.2. MODULAR ARITHMETIC 39 While %
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3.3. DECIMATION CIPHERS 41 previous
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3.4. DECIPHERING DECIMATION CIPHERS
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3.6. KOBLITZ’S KID-RSA AND PUBLIC
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3.6. KOBLITZ’S KID-RSA AND PUBLIC
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3.9. EXERCISES 49 8. How do we enci
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3.9. EXERCISES 51 (c) Encipher 54 4
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3.9. EXERCISES 53 (b) Encipher secr
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Chapter 4 The Euclidean Algorithm I
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4.2. GCD’S AND THE EUCLIDEAN ALGO
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4.3. MULTIPLICATIVE INVERSES 59 (2)
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4.3. MULTIPLICATIVE INVERSES 61 (2)
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4.4. DECIPHERING DECIMATION AND LIN
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4.5. BREAKING DECIMATION AND LINEAR
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4.6. SUMMARY 67 To put it more blun
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4.8. EXERCISES 69 5. Here we work w
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Chapter 5 Monoalphabetic Ciphers He
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5.2. KEYWORD MIXED CIPHERS 73 Examp
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5.4. INTERRUPTED KEYWORD CIPHERS 75
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5.6. BASIC LETTER CHARACTERISTICS 7
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5.7. ARISTOCRATS 79 the 69971 or 42
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5.9. TOPICS AND TECHNIQUES 81 5.9 T
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5.10. EXERCISES 83 (h) DYVTP KKIQ.
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5.10. EXERCISES 85 13. Ciphers in w
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5.10. EXERCISES 87 17. General Pier
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Chapter 6 Decrypting Monoalphabetic
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6.2. DECRYPTING MONOALPHABETIC CIPH
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6.3. SUKHOTIN’S METHOD FOR FINDIN
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6.4. FINAL MONOALPHABETIC TRICKS 99
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6.5. SUMMARY 101 our ciphertext muc
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6.7. EXERCISES 103 Frequency count:
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6.7. EXERCISES 105 53++!305))6*;482
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6.7. EXERCISES 107 93 93 82 48 39 6
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Chapter 7 Vigenère Ciphers It was
Page 111 and 112: 7.2. TRITHEMIUS, THE FATHER OF BIBL
Page 113 and 114: 7.3. BELASO, THE UNKNOWN AND PORTA,
Page 115 and 116: 7.4. VIGENÈRE CIPHERS 115 to encip
Page 117 and 118: 7.6. HOW TO BREAK VIGENÈRE CIPHERS
Page 119 and 120: 7.6. HOW TO BREAK VIGENÈRE CIPHERS
Page 121 and 122: 7.7. THE KASISKI TEST 121 Kasiski
Page 123 and 124: 7.8. SUMMARY 123 Repetition Start P
Page 125 and 126: 7.10. EXERCISES 125 2. Little Miss
Page 127 and 128: 7.10. EXERCISES 127 to Gen. E. K. S
Page 129 and 130: 7.10. EXERCISES 129 MEJMY JKXCD LCN
Page 131 and 132: 7.10. EXERCISES 131 22. (a) Use Kas
Page 133 and 134: 7.10. EXERCISES 133 (a) Construct a
Page 135 and 136: Chapter 8 Polyalphabetic Ciphers Th
Page 137 and 138: 8.1. COINCIDENCES 137 (being born o
Page 139 and 140: 8.2. THE MEASURE OF ROUGHNESS 139 I
Page 141 and 142: 8.2. THE MEASURE OF ROUGHNESS 141 P
Page 143 and 144: 8.3. THE FRIEDMAN TEST 143 The Frie
Page 145 and 146: 8.4. MULTIPLE ENCIPHERINGS 145 Bein
Page 147 and 148: 8.4. MULTIPLE ENCIPHERINGS 147 Just
Page 149 and 150: 8.5. VIGENÈRE’S AUTO KEY CIPHER
Page 151 and 152: 8.5. VIGENÈRE’S AUTO KEY CIPHER
Page 153 and 154: 8.6. PERFECT SECRECY 153 invent now
Page 155 and 156: 8.8. TERMS AND TOPICS 155 multiple
Page 157 and 158: 8.9. EXERCISES 157 6. As is this on
Page 159 and 160: 8.9. EXERCISES 159 13. It has been
Page 161: 8.9. EXERCISES 161 This is Equation
Page 165 and 166: 8.9. EXERCISES 165 26. Decipher SVQ
Page 167 and 168: Chapter 9 Digraphic Ciphers Althoug
Page 169 and 170: 9.1. POLYGRAPHIC CIPHERS 169 f a g
Page 171 and 172: 9.2. HILL CIPHERS 171 th 2.96 es 1.
Page 173 and 174: 9.2. HILL CIPHERS 173 We will be us
Page 175 and 176: 9.3. RECOGNIZING AND BREAKING POLYG
Page 177 and 178: 9.4. PLAYFAIR 177 Playfair Ciphers:
Page 179 and 180: 9.5. SUMMARY 179 9.5 Summary Polygr
Page 181 and 182: 9.7. EXERCISES 181 (b) The use of
Page 183 and 184: 9.7. EXERCISES 183 10. Just as we c
Page 185 and 186: 9.7. EXERCISES 185 (d) (For those(
Page 187 and 188: 9.7. EXERCISES 187 The rules that W
Page 189 and 190: Chapter 10 Transposition Ciphers In
Page 191 and 192: 10.3. TURNING GRILLES 191 1 2 3 7 4
Page 193 and 194: 10.4. COLUMNAR TRANSPOSITION 193 co
Page 195 and 196: 10.5. TRANSPOSITION VS. SUBSTITUTIO
Page 197 and 198: 10.6. LETTER CONNECTIONS 197 F 2 G
Page 199 and 200: 10.7. BREAKING THE COLUMNAR TRANSPO
Page 201 and 202: 10.8. DOUBLE TRANSPOSITION 201 Sinc
Page 203 and 204: 10.9. TRANSPOSITION DURING THE CIVI
Page 205 and 206: 10.9. TRANSPOSITION DURING THE CIVI
Page 207 and 208: 10.10. THE BATTLE OF THE CIVIL WAR
Page 209 and 210: 10.13. EXERCISES 209 14. What is a
Page 211 and 212: 10.13. EXERCISES 211 and the second
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10.13. EXERCISES 213 evening Adam h
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10.13. EXERCISES 215 Several codewo
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10.13. EXERCISES 217 4. (which is t
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Chapter 11 Knapsack Ciphers Merkle
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11.3. AN EASY KNAPSACK PROBLEM 221
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11.4. THE KNAPSACK CIPHER SYSTEM 22
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11.4. THE KNAPSACK CIPHER SYSTEM 22
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11.5. PUBLIC KEY CIPHER 227 Even wi
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11.8. EXERCISES 229 2. Given the we
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Chapter 12 RSA Take two large prime
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12.1. FERMAT’S THEOREM 233 Exampl
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12.3. COMPLICATION II: A SUBSTANTIA
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12.3. COMPLICATION II: A SUBSTANTIA
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12.5. COMPLICATION IV: THE LAST ONE
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12.6. PUTTING IT ALL TOGETHER 241 1
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12.8. RSA 243 The RSA Algorithm Set
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12.9. RSA AND PUBLIC KEYS 245 There
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12.10. HOW TO BREAK RSA 247 had to
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12.12. SUMMARY 249 cannot read the
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12.14. EXERCISES 251 6. What is a
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12.14. EXERCISES 253 Bob is going t
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Bibliography [Antonucci] Michael An
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BIBLIOGRAPHY 257 [Shamir] [SRA] A.
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