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184 CHAPTER 9. DIGRAPHIC CIPHERS pairs of letters by e modulo N, and decipher by multiplying by d. (The resulting ciphertexts will be numbers, rather than letters.) (a) If the modulus N is chosen to be 2999, show that e = 100 is a proper enciphering key. Find the corresponding deciphering key d. (b) Use e = 100 and N = 2999 to encipher blocks. (c) Use the deciphering key found in part (a) to decipher 2543-1513- 1460. (d) If N = 3001 and e = 29, find d. (e) Use e = 29 and N = 3001 to encipher number. (f) Use the deciphering key found in part (d) to decipher 218-2644-17- 2037. 13. (Continuing the ideas of Exercise 12.) A problem with the cipher from Exercise 12 is that the ciphertext is numbers not letters. If we want a bigram-decimation cipher, perhaps we should use 676 = 26 2 as the modulus, rather than 26. Here is one way to try to do this: Choose a key k with 1 ≤ k < 676, relatively prime to 26. For each pair of plaintext letters p 1 p 2 , first convert the letters into their numerical equivalent, then compute the cipher-number c = ( k ∗ (p 1 ∗ 26 + p 2 ) ) %676. The ciphertext is then C 1 C 2 , where C 1 and C 2 are the quotient and remainder when c is divided by 26. For example, let k = 19. Then to = 20 15 has ciphernumber c = ( 19 ∗ (20 ∗ 26 + 15) ) %676 = (19 ∗ 535)%676 = 25. Since 25 ÷ 26 = 0 = Z and 25%26 = 25 = Y, to is enciphered to ZY. To decipher, first find the inverse of 19 modulo 676, which is 427. Then multiply ZY = 25 = 00225 by 427%676 to receive 535. Finally 535 ÷ 26 = 20 = t and 535%26 = 15 = o. (a) Use k = 101 to encipher stat. (b) Use k = 219 to encipher data. (c) Find the inverse of k = 87 modulo 676, and use it to decipher BONO. (d) Carefully examine the ciphertexts from this Exercise. What appears to be happening What does this say about the value of this cipher In particular, how “digraphic” is this digraphic ciphers 14. It was hinted in the text that Hill Ciphers are simply a fancy Decimation Cipher. In this Exercise we see why this is so. (a) Find the form the enciphering matrix takes if we choose a = 0. (b) Encipher the “message” p 1 p 2 p 3 p 4 p 5 p 6 using the matrix you found in part (a). (c) Is the cipher performed in part (b) a Decimation Cipher If not, how close is it
9.7. EXERCISES 185 (d) (For those( who have ) done Exercise 11.) The general Hill matrix has a b the form . What choices do we need to make for a, b, c and c d d so that performing Hill encipherment with this matrix is the same as a Decimation Cipher with key k 15. You’ve somehow capture a ciphertext sent via Hill Cipher. The signature is CVVOFY and you’ve reason to think that this is Lester. Use this information to compute the matrix used. 16. Encipher or decipher the following texts using a Playfair cipher based on the normal ordering of the alphabet. Add an x if double letters need to be divided. (a) Blue Balloons (b) Pat the Bunny (c) IMYNC OKHIS NPYNSC. (d) CBSMV DTBYC CLDA. 17. Encipher or decipher the following texts using a Playfair cipher based on the given keyword. (a) Keyword Northeast. Message Nine battalions will attack from the north at noon. (b) Keyword South. Message Enemy unit crossing river. (c) Keyword Western. Message ATCWS WEDDF TWSRW SCEFC HV. (d) Keyword Eastmarch. Message CPULD OHVFR QEQPH PSKPO. 18. One Army Signal School used as an example of Playfair the following message enciphered with the keyword CLIQUE [SSA1]. CP LE AH RZ PF IG TP NZ GA FG DG ZM PS PN TE CA MT PH CG DA FG OB OA IW CA BY What was the message 19. Use a Playfair cipher with keyword Poems to decipher the following three phrases: (a) QKMSE WPQ. (b) OZCEMRHSXP. (c) XHRPGVAMEMUTZY. 20. [Kahn, pg 198] The first known demonstration of the Playfair Cipher was at a dinner party in January 1854 when Baron Playfair explained “Wheatstone’s newly-discovered symmetrical cipher” to Prince Albert, Queen Victoria’s husband, and Lord Palmerston, Home Secretary and future Prime Minister, among others. The earliest remaining written description appears on page 199 of Kahn, and is transcribed as follows.
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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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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
Page 181 and 182: 9.7. EXERCISES 181 (b) The use of
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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
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Page 197 and 198: 10.6. LETTER CONNECTIONS 197 F 2 G
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Page 211 and 212: 10.13. EXERCISES 211 and the second
Page 213 and 214: 10.13. EXERCISES 213 evening Adam h
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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
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Page 227 and 228: 11.5. PUBLIC KEY CIPHER 227 Even wi
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Page 231 and 232: Chapter 12 RSA Take two large prime
Page 233 and 234: 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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