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92 CHAPTER 6. DECRYPTING MONOALPHABETIC CIPHERS Let us illustrate these steps with the example given earlier. We start with an example that has word breaks because these are a bit easier. To help us later lets also number the words (1)KNHHXKK (2)QS (3)PXTDQSB (4)YQFJ (5)NSISCYS (6)HQEJXUK (7)QK (8)LXTKNUXP (9)AO (10)FJXKX (11)RCNU (12)FJQSBK (13)QS (14)FJX (15)CUPXU (16)STLXP (17)EXUKXVXUTSHX (18)HTUXRND (19)LXFJCPK (20)CR (21)TSTDOKQK (22)QSFNQFQCS (23)DNHI (24)FJX (25)TAQDQFO (26)TF (27)DXTKF (28)FC (29)UXTP (30)FJX (31)DTSBNTBX (32)CR (33)FJX (34)CUQBQSTD (35)QK (36)VXUO (37)PXKQUTADX (38)ANF (39)SCF (40)XKKXSFQTD Step 1) Make a Frequency Chart: 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 4 5 10 10 2 17 0 6 2 9 17 3 0 9 4 7 18 4 16 16 12 2 0 27 2 0 Step 2) Is it a Caesar Cipher This does not look like a Caesar cipher. X is probably e, but then U is a, T is z, S is y, etc., which looks bad. Step 3) Find the common letters: The most common letters are C, D, F, J, K, Q, S, T, and X. (We usually pick the most common letters seven to ten letters.) Step 4) Make a Digraph Chart: For each letter from Step 3) we build a column that gives each appearance of that letter. Let’s work on C’s column. C’s first appearance is in word (5), where it is preceded by S and followed by Y. So we put an SY in the C column. Similarly, an RN will come from C’s next appearance, in word (11). We will use “.” to indicate a space, or no letter. So word (15) provides with a .U, in word (28) with a , we put F. Doing this for each appearance of each common letter results in Figure 6.2. Step 5) Make a Letter Behavior Table: The Digraph Table took some time, but makes it easy to build a Behavior Table. For example, there are four times .* appears in C’s column (here * just means “some letter”), so C must begin four words. Likewise one *. shows C ends one word. C D F J K Q S T X count 10 10 17 9 17 18 16 16 27 start 4 3 7 1 1 5 2 3 1 end 1 3 3 1 7 0 4 0 8 mates 9 6 9 5 10 14 10 13 15 doubles 0 0 0 0 0 2 0 0 0
6.2. DECRYPTING MONOALPHABETIC CIPHERS 93 C D F J K Q S T X SY TQ QJ F. .N .S Q. XD HK RN N. .J EX XK DS QB XK PT .U TO .J FX K. YF NI SL JU JP .N .J FQ U. HE IC US LT .R QQ XJ FX Q. .K Y. HU UP QS .X SN FC TN JS QB .S FK F. .T QQ FX XX .S Q. SD K. .R T. .J FX B. KK .T .A J. .U AX QO FX UX .S TH .F PU SF T. T. P. NF TT XK LP K. OQ FC QF XP EU .C Q. AD C. DS KV .J TF DF TB NB VU .J Q. UB QT SD H. N. XQ BS .C UA UR C. XK .K XF QD LF SQ KX KU J. FT DT UT J. B. J. VU PK D. .K KS Figure 6.2: Digraph Table Step 6) Make our first guesses: (1) X=e: it is common, ends many words, starts few words. (2) F=t: it is common, starts many words, appears a lot with the one letter J, which is probably h. (3) J also mates a lot but starts and ends few words, also like h. These three guesses I’d be pretty sure of, especially after noting the five times FJX = the appears. (4) K ends words, does not start them, appears as a double. Maybe s or r (5) S end words but does not start them. Maybe r or n (6) Q and T start words but do not end them. Maybe a or i (7) D doesn’t mate too much, but is common and both starts and ends some words. Maybe s
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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 %
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
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: 6.2. DECRYPTING MONOALPHABETIC CIPH
Page 95 and 96: 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 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
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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
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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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