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130 CHAPTER 7. VIGENÈRE CIPHERS 20. A common reinvention of the Vigenère Cipher reduces it to a progressive key cipher. From [Pall] we have “The Pass-Word Cipher.” To use it, select a keyword, say PRUDENTIA, and then encipher using the table produced, using a new line for each new word. 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 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 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 r 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 u 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 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 d e 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 n 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 t 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 i 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 a The example given is JXU KGDVAWJK HPODIT JSV BFSY CT PCWNOUFMA BDYYUH VT EH LZWQ RDGG VIZSPX YT HVS YHYGS. Decipher it. 21. Graf Gronsfeld suggested that the Vigenère keyword be replaced by a short series of numbers. For example, come here enciphered with keynumber 1403 is DSMH IIRH. Now known as the Gronsfeld Cipher, in effect it is a Vigenère Cipher as a composite of Shift Ciphers, rather than the usual composite of Caesar Ciphers. (a) Encipher Gronsfeld with keynumber 296. (b) Decipher JVIMZ HTXLL LR. The keynumber was 34870. (c) Decipher EMSLH MCOF. The keynumber was 2625. (d) Considering the example given in the question, what makes this a good cipher (e) For a sizable ciphertext, we can use the techniques for decrypting a Vigenère Cipher to decrypt a Gronsfeld Cipher. But because of the restricted choice of keys (really, only words made up from the first ten letters of the alphabet), the Gronsfeld is considerably less secure than the Vigenère. The following ciphertext has been enciphered using a Gronsfeld Cipher in which the keynumber uses only (some of) 0’s, 1’s, 2’s and 3’s. By trial-and-error, can you decrypt the message (Hint: each ciphertext letter could come from at most four plaintext letters: D from a, b, c, or d. Neatly list them, and see if you cannot build a message.) LHEBE SQGLL OUSWB KRZBA TRIGA YFP.
7.10. EXERCISES 131 22. (a) Use Kasiski’s method to decrypt the message: CT OSB UHGI TP IPEWF H CEWIL NSTTLE FJNVX XTYLS FWKKHI BJLSI SQ VOI BKSM XMKUL SK NVPONPN GSW OL IEAG NPSI HYJISFZ CYY NPUXQG TPRJA VXMSI AP EHVPPR TH WPPNEL UVZUA MMYVSF KNTS ZSZ UAJPQ DLMMJXL JR RA PORTELOGJ CSULTWNI XMKUHW XGLN ELCPOWY OL ULJTL BVJ TLBWTPZ XLD K ZISZNK OSY DL RYJUAJSJF ZIEQN ASC YQ LNFFTR CIKQYF XMG TBWY KU TSRG VVXBCYE FTWUE Z JUZFP HTLXW BKSM RTV IF WHTBUMSKGFH XQ ZIEWRSZ EX RHTWJPNFVX VOFVJ CYF XMQZF AMQ DJPQ NLU CTW ROSB OF NSAGTFRYU MPV YJL QSQKJF QFA ABQUGY XM YJ FPYW EVSVJUWPRIGUDI GWA MEYGY PR BJLO LZG HOH HTF IEAG KJII FVXR BKSM PJV FPY PPVX EQN (b) This message appears in Parker Hitt’s book [Hitt, page 59]. He claims it appeared in the “personals” column of a London newspaper, and after breaking hit he looked back at the column from the day before and found the message “M.B. Will deposit £27 14s 5d tomorrow.” How are the messages related 23. Trithemius’ tabula recta is used in three different ways to produce the Vigenère Cipher, Beaufort Cipher and their Variant Cipher. In the chart below we encipher money with SEND using a Vigenère cipher as usual. Next to it, the letters are converted to their equivalent numbers. plaintext m o n e y plain numbers 13 15 14 5 25 key S E N D S key numbers 18 4 13 3 18 ciphertext E S A H Q cipher numbers 31≡5 19 27≡1 8 43≡17 (a) Using P , C and K to represent the plaintext, ciphertext and key, respectively, how, mathematically, do P and K determine C That is, give an equation C =, where is some combination of P and K. This gives a mathematical formulation of enciphering with Vigenère. (b) Find the similar formula for deciphering a Vigenère cipher. (c) Create similar charts, using the same plaintext and key, but this time using a Beaufort Cipher. Use your charts to find the mathematical formulation of enciphering with the Beaufort. (d) Find the similar formula for deciphering a Beaufort cipher. (e) Repeat parts (c) and (d) but this time using a Variant Cipher. (f) What does this problem tell us about the possibility for other polyalphabetic ciphers
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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
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 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: 7.10. EXERCISES 129 MEJMY JKXCD LCN
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
Page 167 and 168: Chapter 9 Digraphic Ciphers Althoug
Page 169 and 170: 9.1. POLYGRAPHIC CIPHERS 169 f a g
Page 171 and 172: 9.2. HILL CIPHERS 171 th 2.96 es 1.
Page 173 and 174: 9.2. HILL CIPHERS 173 We will be us
Page 175 and 176: 9.3. RECOGNIZING AND BREAKING POLYG
Page 177 and 178: 9.4. PLAYFAIR 177 Playfair Ciphers:
Page 179 and 180: 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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