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4 CONTENTS 5 Monoalphabetic Ciphers 71 5.1 Keyword Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.2 Keyword Mixed Ciphers . . . . . . . . . . . . . . . . . . . . . . . 73 5.3 Keyword Transposed Ciphers . . . . . . . . . . . . . . . . . . . . 74 5.4 Interrupted Keyword Ciphers . . . . . . . . . . . . . . . . . . . . 75 5.5 Frequency Counts and Exhaustion . . . . . . . . . . . . . . . . . 76 5.6 Basic Letter Characteristics . . . . . . . . . . . . . . . . . . . . . 77 5.7 Aristocrats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.9 Topics and Techniques . . . . . . . . . . . . . . . . . . . . . . . . 81 5.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6 Decrypting Monoalphabetic Ciphers 89 6.1 Letter Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . 90 6.2 Decrypting Monoalphabetic Ciphers . . . . . . . . . . . . . . . . 91 6.3 Sukhotin’s Method for Finding Vowels . . . . . . . . . . . . . . . 97 6.4 Final Monoalphabetic Tricks . . . . . . . . . . . . . . . . . . . . 99 6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.6 Topics and Techniques . . . . . . . . . . . . . . . . . . . . . . . . 102 6.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 7 Vigenère Ciphers 109 7.1 Alberti, the Father of Western Cryptology . . . . . . . . . . . . . 110 7.2 Trithemius, the Father of Bibliography . . . . . . . . . . . . . . . 111 7.3 Belaso, the Unknown and Porta, the Great . . . . . . . . . . . . 113 7.4 Vigenère Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 7.5 Variants and Beaufort . . . . . . . . . . . . . . . . . . . . . . . . 116 7.6 How to Break Vigenère Ciphers . . . . . . . . . . . . . . . . . . . 117 7.7 The Kasiski Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 7.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7.9 Topics and Techniques . . . . . . . . . . . . . . . . . . . . . . . . 124 7.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 8 Polyalphabetic Ciphers 135 8.1 Coincidences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 8.2 The Measure of Roughness . . . . . . . . . . . . . . . . . . . . . 138 8.3 The Friedman Test . . . . . . . . . . . . . . . . . . . . . . . . . . 142 8.4 Multiple Encipherings . . . . . . . . . . . . . . . . . . . . . . . . 145 8.5 Vigenère’s Auto Key Cipher . . . . . . . . . . . . . . . . . . . . . 149 8.6 Perfect Secrecy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 8.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 8.8 Terms and Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 8.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
CONTENTS 5 9 Digraphic Ciphers 167 9.1 Polygraphic Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . 167 9.2 Hill Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 9.3 Recognizing and Breaking Polygraphic Ciphers . . . . . . . . . . 174 9.4 Playfair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 9.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 9.6 Topics and Techniques . . . . . . . . . . . . . . . . . . . . . . . . 179 9.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 10 Transposition Ciphers 189 10.1 Route Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 10.2 Geometrical Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . 190 10.3 Turning Grilles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 10.4 Columnar Transposition . . . . . . . . . . . . . . . . . . . . . . . 192 10.5 Transposition vs. Substitution . . . . . . . . . . . . . . . . . . . 195 10.6 Letter Connections . . . . . . . . . . . . . . . . . . . . . . . . . 196 10.7 Breaking the Columnar Transposition Cipher . . . . . . . . . . . 198 10.8 Double Transposition . . . . . . . . . . . . . . . . . . . . . . . . 201 10.9 Transposition during the Civil War . . . . . . . . . . . . . . . . 202 10.10 The Battle of the Civil War Ciphers . . . . . . . . . . . . . . . . 207 10.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 10.12 Topics and Techniques . . . . . . . . . . . . . . . . . . . . . . . 208 10.13 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 11 Knapsack Ciphers 219 11.1 The Knapsack Problem . . . . . . . . . . . . . . . . . . . . . . . 219 11.2 A Related Knapsack Problem . . . . . . . . . . . . . . . . . . . . 220 11.3 An Easy Knapsack Problem . . . . . . . . . . . . . . . . . . . . . 221 11.4 The Knapsack Cipher System . . . . . . . . . . . . . . . . . . . . 223 11.5 Public Key Cipher . . . . . . . . . . . . . . . . . . . . . . . . . . 227 11.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 11.7 Topics and Techniques . . . . . . . . . . . . . . . . . . . . . . . . 228 11.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 12 RSA 231 12.1 Fermat’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 232 12.2 Complication I: a small one . . . . . . . . . . . . . . . . . . . . . 234 12.3 Complication II: a substantial one . . . . . . . . . . . . . . . . . 235 12.4 Complication III: a mini one . . . . . . . . . . . . . . . . . . . . 238 12.5 Complication IV: the last one . . . . . . . . . . . . . . . . . . . 239 12.6 Putting It All Together . . . . . . . . . . . . . . . . . . . . . . . 241 12.7 Exponential Problems (and answers) . . . . . . . . . . . . . . . 241 12.8 RSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 12.9 RSA and Public Keys . . . . . . . . . . . . . . . . . . . . . . . . 245 12.10 How to break RSA . . . . . . . . . . . . . . . . . . . . . . . . . . 245 12.11 Authenticity – Proof of Authorship . . . . . . . . . . . . . . . . 248
Page 1 and 2: Cryptology: An Historical Introduct
Page 3: Contents List of Figures 8 1 Caesar
Page 7 and 8: List of Figures 1.1 Saint Cyr Slide
Page 9 and 10: Chapter 1 Caesar Ciphers There are
Page 11 and 12: 11 Examples: Encipher or decipher t
Page 13 and 14: 1.1. SAINT CYR SLIDE 13 paper turne
Page 15 and 16: 1.3. FREQUENCY ANALYSIS 15 PX PBEE
Page 17 and 18: 1.3. FREQUENCY ANALYSIS 17 A bit mo
Page 19 and 20: 1.3. FREQUENCY ANALYSIS 19 Examples
Page 21 and 22: 1.4. LINQUIST’S METHOD 21 the cip
Page 23 and 24: 1.7. EXERCISES 23 12. What is the m
Page 25 and 26: 1.7. EXERCISES 25 (d) VTXLTKBTG LXV
Page 27 and 28: 1.7. EXERCISES 27 (d) IKSUT JKIOT K
Page 29 and 30: Chapter 2 Cryptologic Terms Cryptog
Page 31 and 32: Chapter 3 The Introduction of Numbe
Page 33 and 34: 3.1. THE REMAINDER OPERATOR 33 Exam
Page 35 and 36: 3.1. THE REMAINDER OPERATOR 35 Perf
Page 37 and 38: 3.1. THE REMAINDER OPERATOR 37 As a
Page 39 and 40: 3.2. MODULAR ARITHMETIC 39 While %
Page 41 and 42: 3.3. DECIMATION CIPHERS 41 previous
Page 43 and 44: 3.4. DECIPHERING DECIMATION CIPHERS
Page 45 and 46: 3.6. KOBLITZ’S KID-RSA AND PUBLIC
Page 47 and 48: 3.6. KOBLITZ’S KID-RSA AND PUBLIC
Page 49 and 50: 3.9. EXERCISES 49 8. How do we enci
Page 51 and 52: 3.9. EXERCISES 51 (c) Encipher 54 4
Page 53 and 54: 3.9. EXERCISES 53 (b) Encipher secr
Page 55 and 56:
Chapter 4 The Euclidean Algorithm I
Page 57 and 58:
4.2. GCD’S AND THE EUCLIDEAN ALGO
Page 59 and 60:
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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Page 95 and 96:
Page 97 and 98:
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
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7.2. TRITHEMIUS, THE FATHER OF BIBL
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7.3. BELASO, THE UNKNOWN AND PORTA,
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7.4. VIGENÈRE CIPHERS 115 to encip
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7.6. HOW TO BREAK VIGENÈRE CIPHERS
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7.6. HOW TO BREAK VIGENÈRE CIPHERS
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7.7. THE KASISKI TEST 121 Kasiski
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7.8. SUMMARY 123 Repetition Start P
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7.10. EXERCISES 125 2. Little Miss
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7.10. EXERCISES 127 to Gen. E. K. S
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7.10. EXERCISES 129 MEJMY JKXCD LCN
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7.10. EXERCISES 131 22. (a) Use Kas
Page 133 and 134:
7.10. EXERCISES 133 (a) Construct a
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Chapter 8 Polyalphabetic Ciphers Th
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8.1. COINCIDENCES 137 (being born o
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8.2. THE MEASURE OF ROUGHNESS 139 I
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8.2. THE MEASURE OF ROUGHNESS 141 P
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8.3. THE FRIEDMAN TEST 143 The Frie
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8.4. MULTIPLE ENCIPHERINGS 145 Bein
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8.4. MULTIPLE ENCIPHERINGS 147 Just
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8.5. VIGENÈRE’S AUTO KEY CIPHER
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8.5. VIGENÈRE’S AUTO KEY CIPHER
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8.6. PERFECT SECRECY 153 invent now
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8.8. TERMS AND TOPICS 155 multiple
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8.9. EXERCISES 157 6. As is this on
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8.9. EXERCISES 159 13. It has been
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8.9. EXERCISES 161 This is Equation
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8.9. EXERCISES 163 A: AB CDE FGH I
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8.9. EXERCISES 165 26. Decipher SVQ
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Chapter 9 Digraphic Ciphers Althoug
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9.1. POLYGRAPHIC CIPHERS 169 f a g
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9.2. HILL CIPHERS 171 th 2.96 es 1.
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9.2. HILL CIPHERS 173 We will be us
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9.3. RECOGNIZING AND BREAKING POLYG
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9.4. PLAYFAIR 177 Playfair Ciphers:
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9.5. SUMMARY 179 9.5 Summary Polygr
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9.7. EXERCISES 181 (b) The use of
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9.7. EXERCISES 183 10. Just as we c
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9.7. EXERCISES 185 (d) (For those(
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9.7. EXERCISES 187 The rules that W
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Chapter 10 Transposition Ciphers In
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10.3. TURNING GRILLES 191 1 2 3 7 4
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10.4. COLUMNAR TRANSPOSITION 193 co
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10.5. TRANSPOSITION VS. SUBSTITUTIO
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10.6. LETTER CONNECTIONS 197 F 2 G
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10.7. BREAKING THE COLUMNAR TRANSPO
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10.8. DOUBLE TRANSPOSITION 201 Sinc
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10.9. TRANSPOSITION DURING THE CIVI
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10.9. TRANSPOSITION DURING THE CIVI
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10.10. THE BATTLE OF THE CIVIL WAR
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10.13. EXERCISES 209 14. What is a
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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
Page 223 and 224:
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
Page 231 and 232:
Chapter 12 RSA Take two large prime
Page 233 and 234:
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
Page 245 and 246:
12.9. RSA AND PUBLIC KEYS 245 There
Page 247 and 248:
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
Page 253 and 254:
12.14. EXERCISES 253 Bob is going t
Page 255 and 256:
Bibliography [Antonucci] Michael An
Page 257:
BIBLIOGRAPHY 257 [Shamir] [SRA] A.
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