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230 CHAPTER 11. KNAPSACK CIPHERS 9. A different way to hide the super-increasing nature of the weights would be to put the “superincreasingness” inside the numbers. For example W 1 = 2900104 W 2 = 3200209 W 3 = 5500401 W 4 = 1300810 W 5 = 2401604. (The boldness only serves to show where the super-increasing is hidden.) The modulus would be correspondingly large, say P = 200785471. (a) Use e = 41233 to find the corresponding U’s. (b) Encipher huge. (c) Which of the following may be written as a sum of the W ’s a) 36902109 b) 33501123 c) 10001420 d) 9705114 (Hint: only three digits really matter. Which three. (d) Decipher 195046101, 76263779, 175978897, 160072206.
Chapter 12 RSA Take two large prime numbers, q and p. Find the product n, and the totient φ. If e and φ have GCD one and d is d’s inverse, then you’re done! For sending m raised to the e reduced mod n gives secre-c. Daniel G. Treat We have now reached our final chapter. So it is natural that we have reached the more difficult and useful cipher in the book. Fortunately, our cipher also brings us back around to the beginning of the book. We started out, in Chapter 1, with the Caesar Cipher: translate letters into numbers and add three. This was too easy to decrypt, so Chapters 3 and 4 we turned to Decimation Ciphers: translate letters into numbers and multiply by three. This also turned out to be easy to decrypt. After several other stops along the way, we now complete the triple: having used addition and multiplication how about exponentiation Example: Encipher power by raising to the 3-rd power modulo 26. plaintext p o w e r plainnumbers 16 15 23 5 18 cubed 4096 2275 12167 125 5832 ciphernumbers %26 14 13 25 21 8 ciphertext N M Y U H The ciphertext is NMYUH ⋄ 231
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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
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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
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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:
Page 179 and 180: 9.5. SUMMARY 179 9.5 Summary Polygr
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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
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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
Page 213 and 214: 10.13. EXERCISES 213 evening Adam h
Page 215 and 216: 10.13. EXERCISES 215 Several codewo
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Page 219 and 220: Chapter 11 Knapsack Ciphers Merkle
Page 221 and 222: 11.3. AN EASY KNAPSACK PROBLEM 221
Page 223 and 224: 11.4. THE KNAPSACK CIPHER SYSTEM 22
Page 225 and 226: 11.4. THE KNAPSACK CIPHER SYSTEM 22
Page 227 and 228: 11.5. PUBLIC KEY CIPHER 227 Even wi
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Page 233 and 234: 12.1. FERMAT’S THEOREM 233 Exampl
Page 235 and 236: 12.3. COMPLICATION II: A SUBSTANTIA
Page 237 and 238: 12.3. COMPLICATION II: A SUBSTANTIA
Page 239 and 240: 12.5. COMPLICATION IV: THE LAST ONE
Page 241 and 242: 12.6. PUTTING IT ALL TOGETHER 241 1
Page 243 and 244: 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
Page 249 and 250: 12.12. SUMMARY 249 cannot read the
Page 251 and 252: 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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