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114 CHAPTER 7. VIGENÈRE CIPHERS Giovanni Battista Porta (1535–1615) was probably the outstanding cryptographer of the Renaissance. In addition, he organized the first association of scientists, the “Academia Secretorum Naturae”. He was also a prolific writer: between 1586–1609 published books on human physiognomy, meteorology, the design of villas, astronomy, as well as 14 prose comedies. In 1563 8 he published De Furtivis Libetarum Notis. Its four books dealt with, respectively, ancient ciphers, modern ciphers, cryptanalysis, and linguistic peculiarities, and encompassed all the cryptologic knowledge of the time. According to Kahn, it is one of the few books of the period that is still readable. (In it it appears that Porta nearly learned out how to break the Vigenère ciphers. If he had, they probably would not have become popular, in which case this chapter wouldn’t exist. But he didn’t quite, and so here we are.) Porta’s contribution was two-fold. First, his book was very influential and made the polyalphabetic ciphers popular. Second, he combined the letter-byletter encipherments of Trithemius, the easily changed key of Belaso, and the mixed alphabet suggested by Alberti. Rather than simply using the 26 regular alphabets (from Trithemius’ table) as the ciphertext alphabets, his cipher allowed for mixed alphabets. 7.4 Vigenère Ciphers The Vigenère cipher is one of the most influential ciphers in history. It is simple to use and easy to remember, and, because it is polyalphabetic, is much more secure that the ciphers we have previously studied. Examples: (1) Encipher Meet me at the Met at the time ten twenty using the keyword CODE. plaintext key ciphertext m e e t m e a t t h e m e t a t t h e t i m e t e n t w e n t C O D E C O D E C O D E C O D E C O D E C O D E C O D E C O D O S H X O S D X V V H Q G H D X V V H X K A H X G B W A G B W Yes, this is a silly message. But notice how many times the e’s and t’s and m’s go to different letters. There are 9 e’s and 10 t’s in the plaintext, but in the ciphertext no letter appears more than 5 times. (2) As his example of Vigenére, Parker Hitt used the key GRANT to encipher All radio messages must hereafter be put in cipher. What is the ciphertext (3) Charles Dodgson (Lewis Carroll) reinvented the Vigenère cipher in 1868, calling it the Alphabet Cipher. In his diary he used the keyword VIGILANCE 8 Why did the 1500’s have this sudden explosion of interest in cryptology ”The growth of cryptology [in the west in the 1500’s] resulted directly from the flowering of modern diplomacy” [Kahn, pg 108] since permanent ambassadors needed to send home regular reports.
7.4. VIGENÈRE CIPHERS 115 to encipher Meet me on tuesday eve [Abeles, p. 326]. What did he find as the ciphertext (4) Decipher TMOQE JKCNF SJDOE ESF using the keyword HOLMES. Deciphering is set up as you probably think: ciphertext T M O Q E J K C N F S J D O E E S F H O L M E S H O L M E S H O L M E S (5) Decipher WYONT REJOL BXNUQ IZHS using the keyword AROUND. (6) During World War I the German Army used a cipher that is equivalent to a Vigenère cipher with keyword ABC. To find out in which year, decipher NJPEUGEO HOVTTFGN. (7) Joseph Willard Brown claims that IN GOD WE TRUST was used as a key to encipher the message Longstreet is marching on Fisher’s Hill [Brown]. If so, what was the ciphertext 9 ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ How does being polyalphabetic influence the frequency counts Here is an enciphered message. QNTQH PIECN SCPOE QXPZC FFILF ACNMY FRRPW XUTKK RROLV CVEQX KASFS IMGSY XYRRM POEFH MYROI OEEUO EVSET EVPIX KAEFC ZGKEQ AHTAK KXTEI EGRNA DZPKM MDCAC ZGPVT QTFHZ OXZDE RFEWX YFWVN ARIGW AANUG RNQAE FXSMT FHCZG RWTMP ZDJII YQRRN QLDCV NKTHI VTKP 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 11 0 10 5 16 12 7 6 10 1 10 3 8 9 7 10 9 14 6 11 3 8 5 9 6 8 Could this be from a monoalphabetic cipher Almost all the letters appear, and most appear between 5 and 10 times each. This frequency chart is much flatter than any we’ve see in the past. So, no, this ciphertext cannot be from a monoalphabetic cipher. Perhaps we could break this cipher by exhaustion, by trying each possible keyword Well, there are 26 one-letter keywords, 26 2 = 576 two-letter keywords, 26 3 = 17576 three-letter ones, etc.. Here I used a five-letter keyword, and there are 26 5 = 11, 881, 376 possible five-letter keywords! It takes very little imagination to realize that trying all possible keywords is impossible. The Vigenère cipher, for much of its lifetime, had two very strong advantages over the ciphers we have previously seen: 1. It was apparently unbreakable, in fact, it was basically unbroken until the 19th century. 9 (2) GCLET JZOZX YJATX YDUFM NVRRT LKEEU KGUGB TTICA KI, (3) HMKBX EBPXP MYLLY RXI, (4) my dear doctor watson, (5) what goes around comes, (6) nineteen fourteen, (7) TBTUV PVXVN ALUNX QKERZ FHXBA UKFVD MEC
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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)
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 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: 7.3. BELASO, THE UNKNOWN AND PORTA,
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 and 162: 8.9. EXERCISES 161 This is Equation
Page 163 and 164: 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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