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116 CHAPTER 7. VIGENÈRE CIPHERS 2. Each ambassador, messenger and spy could have their own key that could be changed easily if stolen or lost. (Generally the keywords were phrases, i.e., “God save the Queen”.) It did, however, have the reputation for being cumbersome and prone to error, which meant it was used less than one would otherwise expect. Even so, it served as a prototype for many ciphers used by professionals. 7.5 Variants and Beaufort In 1857 Admiral Sir Francis Beaufort of the Royal Navy (known for his scale of wind speed) and his brother published what they thought was a new cipher. 10 They put their Beaufort Tableaux (Figure 7.2) on 4×5-inch cards and sold these as a new way of secret writing “adapted for telegrams and postcards” (postcards having recently been invented). To use the card, they wrote Let the key for the foregoing [message] be a line of poetry or the name of some memorable person or place, which cannot easily be forgotten ... Now look in the side column for the first letter of the text (t) and run the eye across the table until it comes to the first letter of the key (v), then at the top of the column in which v stands will be found the letter c. ([Kahn], page 202.) So the plainletter t is enciphered by V to give the cipherletter C. (Actually, one can look either up or down to find the ciphertext.) Clearly this cipher method is very closely related to the Vigenère cipher. It does have one small advantage: deciphering is exactly the same process as enciphering. 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 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 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 B D E F G H I J K L M N O P Q R S T U V W X Y Z A B C E F G H I J K L M N O P Q R S T U V W X Y Z A B C D F 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 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 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 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 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 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 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 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 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 M O P Q R S T U V W X Y Z A B C D E F G H I J K L M N P 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 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 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 Q S 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 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 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 T V W X Y Z A B C D E F G H I J K L M N O P Q R S T U W 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 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 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 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 7.2: Beaufort’s Tableaux 10 It had already been studied by Giovanni Sestri in 1710.
7.6. HOW TO BREAK VIGENÈRE CIPHERS 117 The Beaufort cipher may also be performed using a Saint Cyr slide: simply replace the ciphertext slide with one on which the alphabet is reversed. Examples: (1) Encipher send supplies using keyword COMET. plaintext key ciphertext s e n d s u p p l i e s C O M E T C O M E T C O K K Z B B I Z X T L Y W The ciphertext is KKZBB IZXTL YW. (2) Encipher Admiral using the keyword NAVY. (3) Decipher GWFDY XGTPW U using keyword CASH. 11 ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ To use the Variant Beaufort (confusingly also known as the Variant Vigenère) instead of starting with the plaintext letter and moving inwards to the keyletter, we start with the keyletter and trace inwards to the plaintext letter. Examples: Using the Variant Beaufort: (1) Encipher send supplies using keyword COMET. (2) Decipher WNQ OOTA FVKD using keyword EAT. 12 ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ 7.6 How to Break Vigenère Ciphers “The method used for the preparation and reading of code messages is simple in the extreme and at the same time impossible of translation unless the key word is known.” From “A New Cipher Code” Scientific American Supplement, Jan 27, 1917, The Proceedings of the Engineer’s Club of Philadelphia. In 1550 Belaso invents the Vigenère cipher. In 1563 Porta almost figures out how to break it, but not quite. And then for the next 300 years the Vigenère is 11 (2) NXJQV AK, (3) we need money. 12 (1) QQBZZ SBDHP CE, (2) And some food.
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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
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 and 80: 5.7. ARISTOCRATS 79 the 69971 or 42
Page 81 and 82: 5.9. TOPICS AND TECHNIQUES 81 5.9 T
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: 7.4. VIGENÈRE CIPHERS 115 to encip
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 and 162: 8.9. EXERCISES 161 This is Equation
Page 163 and 164: 8.9. EXERCISES 163 A: AB CDE FGH I
Page 165 and 166: 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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