An In-Place Simplification on Mixed Boolean-Arithmetic Expressions

Abstract

Mixed Boolean-arithmetic (MBA) expression, which involves both bitwise operations (e.g., NOT, AND, and OR) and arithmetic operations (e.g., + , − , and ∗ ), is a software obfuscation scheme. On the other side, multiple methods have been proposed to simplify MBA expressions. Among them, table-based solutions are the most powerful simplification research. However, a fundamental limitation of the table-based solutions is that the space complexity of the transformation table drastically explodes with the number of variables in the MBA expression. In this study, we propose a novel method to simplify MBA expressions without any precomputed requirements. First, a bitwise expression can be transformed into a unified form, and we provide a mathematical proof to guarantee the correctness of this transformation. Then, the arithmetic reduction is smoothly performed to further simplify the expression and produce a concise result. We implement the proposed scheme as an open-source tool, named MBA-Flatten, and evaluate it on two comprehensive benchmarks. The evaluation results show that MBA-Flatten is a general and effective MBA simplification method. Furthermore, MBA-Flatten can assist malware analysis and boost SMT solvers’ performance on solving MBA equations.