Obfuscation of Abstract Data-Types - Rowan

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Obfuscation of Abstract Data Types Stephen Drape St John’s College University of Oxford Thesis submitted for the degree of Doctor of Philosophy Trinity Term 2004 Abstract An obfuscation is a behaviour-preserving program transformation whose aim is to make a program “harder to understand”. Obfuscations are applied to make reverse engineering of a program more difficult. Two concerns about an obfuscation are whether it preserves behaviour (i.e. it is correct) and the degree to which it maintains efficiency. Obfuscations are applied mainly to objectoriented programs but constructing proofs of correctness for such obfuscations is a challenging task. It is desirable to have a workable definition of obfuscation which is more rigorous than the metric-based definition of Collberg et al. and overcomes the impossibility result of Barak et al. for their strong cryptographic definition. We present a fresh approach to obfuscation by obfuscating abstract datatypes allowing us to develop structure-dependent obfuscations that would otherwise (traditionally) not be available. We regard obfuscation as data refinement enabling us to produce equations for proving correctness and we model the datatype operations as functional programs making our proofs easy to construct. For case studies, we examine different data-types exploring different areas of computer science. We consider lists letting us to capture array-based obfuscations, sets reflecting specification based software engineering, trees demonstrating standard programming techniques and as an example of numerical methods we consider matrices. Our approach has the following benefits: obfuscations can be proved correct; obfuscations for some operations can be derived and random obfuscations can be produced (so that different program executions give rise to different obfuscations). Accompanying the approach is a new definition of obfuscation based on measuring the effectiveness of an obfuscation. Furthermore in our case studies the computational complexity of each obfuscated operations is comparable with the complexity of the unobfuscated version. Also, we give an example of how our approach can be applied to implement imperative obfuscations. 1
Contents I The Current View of Obfuscation 11 1 Obfuscation 12 1.1 Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2 Obfuscation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Examples of obfuscations . . . . . . . . . . . . . . . . . . . . . . 14 1.3.1 Commercial Obfuscators . . . . . . . . . . . . . . . . . . . 15 1.3.2 Opaque predicates . . . . . . . . . . . . . . . . . . . . . . 16 1.3.3 Variable transformations . . . . . . . . . . . . . . . . . . . 16 1.3.4 Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.3.5 Array transformations . . . . . . . . . . . . . . . . . . . . 18 1.3.6 Array Splitting . . . . . . . . . . . . . . . . . . . . . . . . 18 1.3.7 Program transformation . . . . . . . . . . . . . . . . . . . 19 1.3.8 Array Merging . . . . . . . . . . . . . . . . . . . . . . . . 20 1.3.9 Other obfuscations . . . . . . . . . . . . . . . . . . . . . . 20 1.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2 Obfuscations for Intermediate Language 22 2.1 .NET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.1.1 IL Instructions . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2 IL obfuscations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2.1 Variable Transformation . . . . . . . . . . . . . . . . . . . 25 2.2.2 Jumping into while loops . . . . . . . . . . . . . . . . . . 26 2.3 Transformation Toolkit . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.1 Path Logic Programming . . . . . . . . . . . . . . . . . . 28 2.3.2 Expression IL . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.3 Predicates for EIL . . . . . . . . . . . . . . . . . . . . . . 31 2.3.4 Modifying the graph . . . . . . . . . . . . . . . . . . . . . 32 2.3.5 Applying transformations . . . . . . . . . . . . . . . . . . 33 2.3.6 Variable Transformation . . . . . . . . . . . . . . . . . . . 33 2.3.7 Array Splitting . . . . . . . . . . . . . . . . . . . . . . . . 34 2.3.8 Creating an irreducible flow graph . . . . . . . . . . . . . 37 2.4 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.4.1 Forms of IL . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.4.2 Transformation Systems . . . . . . . . . . . . . . . . . . . 41 2.4.3 Correctness . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2
Page 1: Obfuscation of Abstract Data-Types
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Page 7 and 8: List of Figures 1 An example of obf
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CHAPTER 3. TECHNIQUES FOR OBFUSCATI
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Part III Data-Type Case Studies 62
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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 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 156 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 C Matrices We prove the as
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APPENDIX C. MATRICES 168 Base Case
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APPENDIX E. OBFUSCATION EXAMPLE 186
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