Formal Considerations and a Practical Approach to Intermediate-Level Obfuscation

The essence of obfuscation is to entangle the code and eliminate the majority of logical links in it. The offered theoretical apparatus allows describing obfuscated routines by concatenation of original and fake operational logics. This approach considers not only instructions or routines themselves, but the actions (results) they produce, what makes obfuscation a process of adding excessive functionality. The mathematical apparatus presented in the paper, discusses introductory terms, definitions, operations, and formulates a proposition about NP-completeness of a special deobfuscation problem. We formulate the problem statement and prove that the significance of operational logic in the obfuscated routine is an NP-complete problem. We point out the applicability limits of this proposition, and offer a practical approach that can noticeably reduce the probability of having a deobfuscator running in polynomial time. This paper also offers recommendations for constructing obfuscating transformations and points out a practical approach to creation of intermediatelevel obfuscating algorithm. Key-Words: Obfuscation, operational logic, global context, NP-completeness, intermediate representation.