REMaQE: Reverse Engineering Math Equations from Executables

Cybersecurity attacks on embedded devices for industrial control systems and cyber-physical systems may cause catastrophic physical damage as well as economic loss. This could be achieved by infecting device binaries with malware that modifies the physical characteristics of the system operation. Mitigating such attacks benefits from reverse engineering tools that recover sufficient semantic knowledge in terms of mathematical equations of the implemented algorithm. Conventional reverse engineering tools can decompile binaries to low-level code, but offer little semantic insight. This article proposes the REMaQE automated framework for reverse engineering of math equations from binary executables. Improving over state-of-the-art, REMaQE handles equation parameters accessed via registers, the stack, global memory, or pointers, and can reverse engineer equations from object-oriented implementations such as C++ classes. Using REMaQE, we discovered a bug in the Linux kernel thermal monitoring tool “tmon.” To evaluate REMaQE, we generate a dataset of 25,096 binaries with math equations implemented in C and Simulink. REMaQE successfully recovers a semantically matching equation for all 25,096 binaries. REMaQE executes in 0.48 seconds on average and in up to 2 seconds for complex equations. Real-time execution enables integration in an interactive math-oriented reverse engineering workflow.