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80 CHAPTER 5. MONOALPHABETIC CIPHERS Turning to the frequency count 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 0 5 2 8 3 7 6 5 0 5 5 3 4 0 0 3 6 0 1 1 1 0 3 1 1 2 the most common letters are BDFGHJKQ. Of these, F, J and Q each occur three times as final letters. Let’s guess that one of these is e. It cannot be F, a consonant, nor Q, as then the word TDQJ would end in an e-vowel combination. So e must be J. Next, BQJ=BQe, so Q must be a consonant, and from LBQ, B is probably a vowel, hence a or o. Trying B=o doesn’t work. But when we try B=a, we quickly see Q=r, making YDQ = YDr = Yor = for, as o is the only vowel then left. At this point the cipher looks like *oli*i*s is *ore *an*ero*s **an *ar, for in *ar *o* are onl* *ille* on*e. *in*on ***r**ill. From here the quotation should be pretty easy to complete. 5 ⋄ Clearly this example worked out a little too nicely, in part because we hid some false starts and in part because time spent thinking and scratching one’s head is hard to indicate in text. But it should still give an idea of how Aristocrats are attacked. 5.8 Summary A monoalphabetic cipher is one in which the each plaintext letter is replaced by the same ciphertext letter throughout the entire message. The Caesar or Shift Ciphers, Decimation Ciphers and Linear Ciphers are all monoalphabetic, as are the various types of Keyword Ciphers introduced in this chapter. The Keyword Ciphers all use a keyword to develop an ordering of the ciphertext alphabet. The more important ones are the Keyword Mixed and Keyword Transposed Ciphers. Select a keyword and drop any repeated letters in it. Then write the remainder of the alphabet underneath in as many columns as remain in the keyword. For a Mixed Cipher the ciphertext alphabet is then the columns pulled off in order, left-to-right, while for a Transposed Cipher the alphabet is pulled off in alphabetical order of the top row. A popular type of decryption puzzle is an Aristocrat, which is generally a short quote enciphered with a monoalphabetic cipher. Word divisions and punctuation are generally kept, and a hint is often given. The keys to decrypting these ciphers include the usual frequency count, some knowledge of initial and final letters of words, and very often the use of common short words. 5 Politics is more dangerous than war, for in war you are only killed once. Winston Churchill.
5.9. TOPICS AND TECHNIQUES 81 5.9 Topics and Techniques 1. What is the chief characteristic of a Monoalphabetic Cipher 2. What is a Keyword Cipher How do we encipher and decipher with it 3. What is a Keyword Mixed Cipher How do we encipher and decipher with it 4. Keyword Ciphers and Keyword Mixed Ciphers use their keyword differently. Explain the difference. 5. What is a Keyword Transposed Cipher How do we encipher and decipher with it 6. How do Keyword Mixed Ciphers and Keyword Transposed Ciphers differ 7. What letters most commonly begin words in English 8. What letters most commonly end words in English 9. What are the most common one-letter words in English Two-letter words Three-letter words 10. What are the most common words in English 11. What is an Aristocrat 12. What steps help decrypt an Aristocrat 5.10 Exercises 1. Encipher or decipher the following words using a Keyword Cipher with the given keyword. (a) democrat with REPUBLICAN. (b) chocolate with HOT. (c) JUIES OP with LETTERS. (d) DSTLQ with TAILS. (e) SQGSI LT with BASEBALL. 2. Encipher or decipher the following words using a Keyword Mixed Cipher with keyword COLORS. (a) canary. (b) eggplant. (c) fuchsia.
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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
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)
Page 61 and 62: 4.3. MULTIPLICATIVE INVERSES 61 (2)
Page 63 and 64: 4.4. DECIPHERING DECIMATION AND LIN
Page 65 and 66: 4.5. BREAKING DECIMATION AND LINEAR
Page 67 and 68: 4.6. SUMMARY 67 To put it more blun
Page 69 and 70: 4.8. EXERCISES 69 5. Here we work w
Page 71 and 72: Chapter 5 Monoalphabetic Ciphers He
Page 73 and 74: 5.2. KEYWORD MIXED CIPHERS 73 Examp
Page 75 and 76: 5.4. INTERRUPTED KEYWORD CIPHERS 75
Page 77 and 78: 5.6. BASIC LETTER CHARACTERISTICS 7
Page 79: 5.7. ARISTOCRATS 79 the 69971 or 42
Page 83 and 84: 5.10. EXERCISES 83 (h) DYVTP KKIQ.
Page 85 and 86: 5.10. EXERCISES 85 13. Ciphers in w
Page 87 and 88: 5.10. EXERCISES 87 17. General Pier
Page 89 and 90: Chapter 6 Decrypting Monoalphabetic
Page 91 and 92: 6.2. DECRYPTING MONOALPHABETIC CIPH
Page 97 and 98: 6.3. SUKHOTIN’S METHOD FOR FINDIN
Page 99 and 100: 6.4. FINAL MONOALPHABETIC TRICKS 99
Page 101 and 102: 6.5. SUMMARY 101 our ciphertext muc
Page 103 and 104: 6.7. EXERCISES 103 Frequency count:
Page 105 and 106: 6.7. EXERCISES 105 53++!305))6*;482
Page 107 and 108: 6.7. EXERCISES 107 93 93 82 48 39 6
Page 109 and 110: 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
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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:
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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
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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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