insight - Embedded systems reverse engineering - # Reverse engineering math equations from binary executables

Core Concepts

The REMaQE framework automatically recovers mathematical equations from binary executables by leveraging symbolic execution, parameter analysis, and algebraic simplification.

Abstract

The REMaQE framework focuses on reverse engineering mathematical equations from binary executables of embedded systems. It makes the following key contributions:
Automatic parameter analysis to recognize input, output, and constant parameters in an implemented equation. This enables reverse engineering of object-oriented implementations, such as C++ classes and struct pointer based C functions.
Algebraic simplification to transform extracted symbolic expressions into easily understandable math equations. This handles much more complex expressions compared to existing approaches that use machine learning methods.
The paper demonstrates the advantages of REMaQE by uncovering a bug in the Linux kernel's thermal monitoring tool "tmon" through the recovered math equations. REMaQE is evaluated on a dataset of 25,096 compiled binary executables with 3,137 math equations implemented in C and Simulink. REMaQE successfully recovers semantically matching equations for all 25,096 binaries, executing in 0.48 seconds on average.

Stats

The Linux kernel thermal monitoring tool "tmon" uses a Proportional-Integral-Derivative (PID) controller. The recovered math equations revealed a bug in the controller's implementation, where the variables xk_1 and xk_2 were incorrectly assigned the same value, degrading the quality of the PID controller.

Quotes

"Reverse engineering the mathematical models and control algorithms implemented in the binaries can reveal the semantic knowledge necessary to understand these embedded systems."
"REMaQE employs automatic parameter analysis of functions to identify important metadata regarding the function arguments stored in register, stack, global memory, or accessed via pointer."
"Simplification of math equations in REMaQE is performed via math-aware algebraic methods. This overcomes limitations of other approaches such as machine learning methods for equation simplification and enables REMaQE to simplify complex conditional equations."

Key Insights Distilled From

by Meet Udeshi,... at **arxiv.org** 04-12-2024

Deeper Inquiries

To extend REMaQE to handle advanced mathematical operations like vector and matrix operations, several enhancements can be implemented:
Support for Vector and Matrix Data Structures: REMaQE can be modified to recognize and handle vector and matrix data structures in the binary executables. This involves identifying operations specific to vectors and matrices, such as dot products, cross products, matrix multiplications, and element-wise operations.
Symbolic Execution for Vector and Matrix Operations: The symbolic execution engine used in REMaQE can be extended to support vector and matrix operations. This includes defining the semantics of vector and matrix operations in the symbolic execution framework to accurately represent these computations during reverse engineering.
Algebraic Simplification for Vector and Matrix Equations: The algebraic simplification stage of REMaQE can be enhanced to handle complex vector and matrix equations. This involves developing algorithms to simplify expressions involving vectors and matrices, such as reducing redundant terms, combining like terms, and optimizing the representation of vector and matrix operations.
Integration with Linear Algebra Libraries: REMaQE can be integrated with linear algebra libraries or tools that provide optimized implementations of vector and matrix operations. By leveraging existing libraries, REMaQE can enhance its capabilities to reverse engineer and represent complex mathematical operations involving vectors and matrices accurately.
By incorporating these enhancements, REMaQE can effectively handle advanced mathematical operations like vector and matrix operations, providing a comprehensive solution for reverse engineering mathematical equations involving these structures.

Potential limitations of REMaQE's approach in handling obfuscated control flow or data type conversions include:
Path Explosion in Symbolic Execution: Obfuscated control flow can lead to a large number of execution paths, resulting in path explosion during symbolic execution. This can significantly increase the analysis time and complexity of reverse engineering. To address this, REMaQE can implement path pruning techniques or heuristics to reduce the number of explored paths while ensuring comprehensive coverage.
Complex Data Type Conversions: REMaQE may struggle to accurately represent complex data type conversions, especially those involving non-trivial operations or precision changes. To address this, REMaQE can incorporate a more sophisticated data type analysis module that can handle a wider range of data type conversions and precision adjustments, ensuring the accuracy of the reverse-engineered equations.
Precision Loss in Floating-Point Operations: Data type conversions and floating-point operations can introduce precision loss, leading to discrepancies between the original equations and the reverse-engineered ones. REMaQE can mitigate this limitation by implementing techniques to track and preserve precision during symbolic execution and algebraic simplification, ensuring that the recovered equations maintain the necessary precision.
Handling Non-Standard Control Flow: Obfuscated control flow techniques like anti-analysis tricks or code obfuscation can hinder the accurate representation of control flow in the reverse-engineered equations. REMaQE can address this limitation by incorporating advanced control flow analysis algorithms that can decipher and reconstruct non-standard control flow patterns, ensuring the fidelity of the recovered equations.
By addressing these limitations through advanced techniques and algorithms, REMaQE can enhance its capabilities in handling obfuscated control flow and data type conversions during reverse engineering.

Integration of the recovered math equations from REMaQE into interactive reverse engineering workflows can be achieved through the following steps:
Visualization Tools: Develop visualization tools that can display the recovered math equations alongside the decompiled code. This visual representation helps analysts understand the semantic context of the equations in relation to the code structure.
Interactive Equation Editor: Implement an interactive equation editor within the reverse engineering environment, allowing analysts to modify and annotate the recovered equations. This feature enables real-time manipulation and exploration of the mathematical relationships extracted by REMaQE.
Cross-Referencing: Enable cross-referencing between the decompiled code and the recovered equations. This functionality allows analysts to navigate between specific code segments and their corresponding mathematical representations, facilitating a deeper understanding of the system's behavior.
Integration with Debugging Tools: Integrate the recovered equations with debugging tools to correlate mathematical operations with runtime behavior. This integration provides a holistic view of the system's functionality, aiding in the identification of vulnerabilities or bugs in the implemented algorithms.
Collaborative Analysis: Facilitate collaborative analysis by enabling multiple analysts to interact with the recovered equations simultaneously. This collaborative environment promotes knowledge sharing and collective problem-solving during reverse engineering tasks.
By implementing these integration strategies, REMaQE can seamlessly incorporate the recovered math equations into interactive reverse engineering workflows, providing analysts with valuable semantic context alongside decompiled code for comprehensive analysis and understanding.

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