Obfuscation of Abstract Data-Types - Rowan

More documents

Recommendations

Info

V Appendices 143 A List assertion 144 A.1 Unobfuscated version . . . . . . . . . . . . . . . . . . . . . . . . . 144 A.2 Alternating Split for Lists . . . . . . . . . . . . . . . . . . . . . . 145 A.2.1 Version 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 A.2.2 Version 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 A.3 Block Split for Lists . . . . . . . . . . . . . . . . . . . . . . . . . 149 A.4 Augmented Split . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 A.5 Augmented Block Split . . . . . . . . . . . . . . . . . . . . . . . . 154 A.6 Padded Block Split . . . . . . . . . . . . . . . . . . . . . . . . . . 156 A.7 Comparing the proofs . . . . . . . . . . . . . . . . . . . . . . . . 158 B Set operations 159 B.1 Span Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 B.2 Insertion for the alternating split . . . . . . . . . . . . . . . . . . 164 C Matrices 166 C.1 Rewriting the definition . . . . . . . . . . . . . . . . . . . . . . . 166 C.2 Using fold fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 D Proving a tree assertion 169 D.1 Producing a binary tree from a list . . . . . . . . . . . . . . . . . 169 D.1.1 Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 169 D.1.2 Proving Properties . . . . . . . . . . . . . . . . . . . . . . 170 D.1.3 Proving the assertion . . . . . . . . . . . . . . . . . . . . . 172 D.2 Producing a binary tree from a split list . . . . . . . . . . . . . . 174 D.2.1 Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 174 D.2.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 174 D.2.3 Proof of the assertion . . . . . . . . . . . . . . . . . . . . 179 D.3 Producing a ternary tree from a list . . . . . . . . . . . . . . . . 180 D.3.1 Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 180 D.3.2 Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 D.4 Producing a ternary tree from a split list . . . . . . . . . . . . . . 182 D.4.1 Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 D.5 Comparing the proofs . . . . . . . . . . . . . . . . . . . . . . . . 184 E Obfuscation Example 185 5
List of Figures 1 An example of obfuscation . . . . . . . . . . . . . . . . . . . . . . 8 1.1 Fibonacci program after an array split . . . . . . . . . . . . . . . 20 2.1 Some common IL instructions . . . . . . . . . . . . . . . . . . . . 23 2.2 IL for a GCD method . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3 Output from Salamander . . . . . . . . . . . . . . . . . . . . . . 27 2.4 Syntax for a simple subset of EIL . . . . . . . . . . . . . . . . . . 30 2.5 Some common predicates . . . . . . . . . . . . . . . . . . . . . . 32 2.6 Predicates for replacing assignments . . . . . . . . . . . . . . . . 35 2.7 Definition of replace array for assignments . . . . . . . . . . . . . 36 2.8 Flow graph to build a conditional expression . . . . . . . . . . . 37 2.9 Flow graph to create jump into a loop . . . . . . . . . . . . . . . 38 2.10 Code for the irred jump method . . . . . . . . . . . . . . . . . . 39 3.1 Data-type for Arrays . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.1 Data-type for Lists . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.2 Data-type for Split Lists . . . . . . . . . . . . . . . . . . . . . . . 72 5.1 Data-type for Sets . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.1 Data-type for Matrices . . . . . . . . . . . . . . . . . . . . . . . . 109 7.1 Data-Type for Binary Trees . . . . . . . . . . . . . . . . . . . . . 120 7.2 Data-Type for Binary Search Trees . . . . . . . . . . . . . . . . . 121 7.3 Data-Type for Ternary Trees . . . . . . . . . . . . . . . . . . . . 124 E.1 Original Program . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 6
Page 1 and 2: Obfuscation of Abstract Data-Types
Page 3 and 4: Contents I The Current View of Obfu
Page 5: 5.4.3 Third Definition . . . . . .
Page 9 and 10: 8 public class c { d t1 = new d();
Page 11 and 12: 10 • Obfuscations can be proved c
Page 13 and 14: Chapter 1 Obfuscation Scully: “No
Page 15 and 16: CHAPTER 1. OBFUSCATION 14 These thr
Page 17 and 18: CHAPTER 1. OBFUSCATION 16 by changi
Page 19 and 20: CHAPTER 1. OBFUSCATION 18 We could
Page 21 and 22: CHAPTER 1. OBFUSCATION 20 B 1 [0] =
Page 23 and 24: Chapter 2 Obfuscations for Intermed
Page 25 and 26: CHAPTER 2. OBFUSCATIONS FOR INTERME
Page 45 and 46: Chapter 3 Techniques for Obfuscatio
Page 47 and 48: CHAPTER 3. TECHNIQUES FOR OBFUSCATI
Page 57 and 58:
CHAPTER 3. TECHNIQUES FOR OBFUSCATI
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Part III Data-Type Case Studies 62
Page 65 and 66:
CHAPTER 4. SPLITTING HEADACHES 64 (
Page 67 and 68:
CHAPTER 4. SPLITTING HEADACHES 66 a
Page 69 and 70:
CHAPTER 4. SPLITTING HEADACHES 68 T
Page 71 and 72:
CHAPTER 4. SPLITTING HEADACHES 70 L
Page 73 and 74:
CHAPTER 4. SPLITTING HEADACHES 72 S
Page 75 and 76:
CHAPTER 4. SPLITTING HEADACHES 74 C
Page 77 and 78:
CHAPTER 4. SPLITTING HEADACHES 76 L
Page 79 and 80:
CHAPTER 4. SPLITTING HEADACHES 78 t
Page 81 and 82:
CHAPTER 4. SPLITTING HEADACHES 80 C
Page 83 and 84:
CHAPTER 4. SPLITTING HEADACHES 82 4
Page 85 and 86:
CHAPTER 4. SPLITTING HEADACHES 84 E
Page 87 and 88:
CHAPTER 4. SPLITTING HEADACHES 86 b
Page 89 and 90:
CHAPTER 4. SPLITTING HEADACHES 88 W
Page 91 and 92:
CHAPTER 4. SPLITTING HEADACHES 90 T
Page 93 and 94:
Chapter 5 Sets and the Splitting Bu
Page 95 and 96:
CHAPTER 5. SETS AND THE SPLITTING 9
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
CHAPTER 6. THE MATRIX OBFUSCATED 10
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
CHAPTER 7. CULTIVATING TREE OBFUSCA
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Chapter 8 Conclusions and Further W
Page 137 and 138:
CHAPTER 8. CONCLUSIONS AND FURTHER
Page 139 and 140:
CHAPTER 8. CONCLUSIONS AND FURTHER
Page 141 and 142:
BIBLIOGRAPHY 140 [13] Thomas H. Cor
Page 143 and 144:
BIBLIOGRAPHY 142 [43] Simon Peyton
Page 145 and 146:
Appendix A List assertion We want t
Page 147 and 148:
APPENDIX A. LIST ASSERTION 146 Case
Page 149 and 150:
APPENDIX A. LIST ASSERTION 148 For
Page 151 and 152:
APPENDIX A. LIST ASSERTION 150 Case
Page 153 and 154:
APPENDIX A. LIST ASSERTION 152 1 +
Page 155 and 156:
APPENDIX A. LIST ASSERTION 154 0 +
Page 157 and 158:
APPENDIX A. LIST ASSERTION 156 The
Page 159 and 160:
APPENDIX A. LIST ASSERTION 158 The
Page 161 and 162:
APPENDIX B. SET OPERATIONS 160 Now
Page 163 and 164:
APPENDIX B. SET OPERATIONS 162 Proo
Page 165 and 166:
APPENDIX B. SET OPERATIONS 164 B.2
Page 167 and 168:
Appendix C Matrices We prove the as
Page 169 and 170:
APPENDIX C. MATRICES 168 Base Case
Page 171 and 172:
APPENDIX D. PROVING A TREE ASSERTIO
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187:
APPENDIX E. OBFUSCATION EXAMPLE 186
show all

Obfuscation of Abstract Data-Types - Rowan

Create successful ePaper yourself

Delete template?

Save as template?