Obfuscation of Abstract Data-Types - Rowan

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CHAPTER 2. OBFUSCATIONS FOR INTERMEDIATE LANGUAGE 39 irred jump(replace vertex(Jump,Branch) : nil):− exists ({ }; { }∗ ) (entry,Header), exists ({ }; { }∗ ) (Header,Header), exists ({ }; { }∗ ) (entry,Before), exists ({ } ) (Before,Header), not (exists ({ }; { }∗ ) (Header,Before)), exists ({ }; { }∗ ) (Header,InLoop), exists ({ }∗; {not ( ′ is node (Header)) } ) (InLoop,InLoop), all ({ }∗; { ′ def (X), X = expr type(localvar( ),int(true,b32))}; { } ) (entry,Jump), not (exists ({ }; { }∗ ) (Header,Jump)), jump cond(X,C), @vlabel(Jump,instr label(Label,Inst)), outedges(Jump,Edges), @fresh label(NewLabel), @new vertex(instr label(NewLabel : nil,Inst), Edges,Then), new edge(Then,ThenEdge), new edge(InLoop,InLoopEdge), @new vertex(instr label(Label,branch(cond(C),NewLabel)), ThenEdge : InLoopEdge : nil,Branch). Figure 2.10: Code for the irred jump method
CHAPTER 2. OBFUSCATIONS FOR INTERMEDIATE LANGUAGE 40 Finally, we need to find the declaration of a local variable (in our case, we look for an integer variable) that occurs before the loop. We bind the node Jump to the node after the declaration. all ({ }∗; { ′ def (X), X = expr type(localvar( ),int(true,b32))}; { } ) (entry,Jump), not (exists ({ }; { }∗ ) (Header,Jump)) Now that we have found a loop and a suitable variable, we are ready to create the jump. We aim to replace the node Jump with a node Branch which is a conditional expression. If the test of the conditional is True then we perform the instructions that were at Jump but if the test is False then we jump to InLoop. We create an expression for the test using the predicate jump cond — so jump cond(X,C) uses the variable X to bind C to a representation of the condition. For example, here is a predicate that creates X × X ≥ 0: jump cond(X, expr type(applyatom( compare(geq(true)), expr type(applyatom(mul(false,true),X,X), int(true,b32)), expr type(applyatom(ldc(int(true,b32), 0)), int(true,b32))), bool)). We must ensure that the predicate that we build evaluates to True. Since we are replacing the node Jump, we need to know what label Label, instruction Inst and outgoing edges Edges are at Jump. We then create a new node Then (for when the condition is True) which has the label NewLabel and contains the instruction Inst and has outgoing edges Edges. Next we create two new incoming edges: ThenEdge and InLoopEdge. Finally, we can build the node Branch. This node has the same label as Jump and contains a conditional jump — if True we go to the node Then and if False we go to InLoop. If we had nested loops then this specification would be able to produce only a jump from outside the outermost loop. We have to write many conditions just to find a loop — it would be convenient to use a language that includes loops. 2.4 Related Work We briefly summarise some work related to the specifications of IL transformations. 2.4.1 Forms of IL In Section 2.3.2 we outlined a form of IL that replaced stack expressions with assignments which we called EIL. As we discussed in Section 2.3.8, it would
Page 1 and 2: Obfuscation of Abstract Data-Types
Page 3 and 4: Contents I The Current View of Obfu
Page 5 and 6: 5.4.3 Third Definition . . . . . .
Page 7 and 8: List of Figures 1 An example of obf
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
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CHAPTER 4. SPLITTING HEADACHES 90 T
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Chapter 5 Sets and the Splitting Bu
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CHAPTER 5. SETS AND THE SPLITTING 9
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CHAPTER 6. THE MATRIX OBFUSCATED 10
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CHAPTER 7. CULTIVATING TREE OBFUSCA
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Chapter 8 Conclusions and Further W
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CHAPTER 8. CONCLUSIONS AND FURTHER
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CHAPTER 8. CONCLUSIONS AND FURTHER
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BIBLIOGRAPHY 140 [13] Thomas H. Cor
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BIBLIOGRAPHY 142 [43] Simon Peyton
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Appendix A List assertion We want t
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APPENDIX A. LIST ASSERTION 146 Case
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APPENDIX A. LIST ASSERTION 148 For
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APPENDIX A. LIST ASSERTION 150 Case
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APPENDIX A. LIST ASSERTION 152 1 +
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APPENDIX A. LIST ASSERTION 154 0 +
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APPENDIX A. LIST ASSERTION 156 The
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APPENDIX A. LIST ASSERTION 158 The
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APPENDIX B. SET OPERATIONS 160 Now
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APPENDIX B. SET OPERATIONS 162 Proo
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APPENDIX B. SET OPERATIONS 164 B.2
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Appendix C Matrices We prove the as
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APPENDIX C. MATRICES 168 Base Case
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APPENDIX D. PROVING A TREE ASSERTIO
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APPENDIX E. OBFUSCATION EXAMPLE 186
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