Cryptology - Unofficial St. Mary's College of California Web Site

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2 Copyright 2013 All rights reserved Jim Sauerberg Saint Mary’s College
Contents List of Figures 8 1 Caesar Ciphers 9 1.1 Saint Cyr Slide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2 Running Down the Alphabet . . . . . . . . . . . . . . . . . . . . 14 1.3 Frequency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Linquist’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.6 Topics and Techniques . . . . . . . . . . . . . . . . . . . . . . . . 22 1.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2 Cryptologic Terms 29 3 The Introduction of Numbers 31 3.1 The Remainder Operator . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Modular Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.3 Decimation Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.4 Deciphering Decimation Ciphers . . . . . . . . . . . . . . . . . . 42 3.5 Multiplication vs. Addition . . . . . . . . . . . . . . . . . . . . . 44 3.6 Koblitz’s Kid-RSA and Public Key Codes . . . . . . . . . . . . . 44 3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.8 Topics and Techniques . . . . . . . . . . . . . . . . . . . . . . . . 48 3.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4 The Euclidean Algorithm 55 4.1 Linear Ciphers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.2 GCD’s and the Euclidean Algorithm . . . . . . . . . . . . . . . . 56 4.3 Multiplicative Inverses . . . . . . . . . . . . . . . . . . . . . . . . 59 4.4 Deciphering Decimation and Linear Ciphers . . . . . . . . . . . . 63 4.5 Breaking Decimation and Linear Ciphers . . . . . . . . . . . . . . 65 4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.7 Topics and Techniques . . . . . . . . . . . . . . . . . . . . . . . . 67 4.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3
Page 1: Cryptology: An Historical Introduct
Page 5 and 6: CONTENTS 5 9 Digraphic Ciphers 167
Page 7 and 8: List of Figures 1.1 Saint Cyr Slide
Page 9 and 10: Chapter 1 Caesar Ciphers There are
Page 11 and 12: 11 Examples: Encipher or decipher t
Page 13 and 14: 1.1. SAINT CYR SLIDE 13 paper turne
Page 15 and 16: 1.3. FREQUENCY ANALYSIS 15 PX PBEE
Page 17 and 18: 1.3. FREQUENCY ANALYSIS 17 A bit mo
Page 19 and 20: 1.3. FREQUENCY ANALYSIS 19 Examples
Page 21 and 22: 1.4. LINQUIST’S METHOD 21 the cip
Page 23 and 24: 1.7. EXERCISES 23 12. What is the m
Page 25 and 26: 1.7. EXERCISES 25 (d) VTXLTKBTG LXV
Page 27 and 28: 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
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4.6. SUMMARY 67 To put it more blun
Page 69 and 70:
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
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 93 and 94:
Page 95 and 96:
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
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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
Page 111 and 112:
7.2. TRITHEMIUS, THE FATHER OF BIBL
Page 113 and 114:
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
Page 127 and 128:
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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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
Page 219 and 220:
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
Page 231 and 232:
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
Page 245 and 246:
12.9. RSA AND PUBLIC KEYS 245 There
Page 247 and 248:
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
Page 253 and 254:
12.14. EXERCISES 253 Bob is going t
Page 255 and 256:
Bibliography [Antonucci] Michael An
Page 257:
BIBLIOGRAPHY 257 [Shamir] [SRA] A.
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