PolySys: an Algebraic Leakage Attack Engine

In this work, we propose a novel framework called PolySys for modeling and designing leakage attacks as constraint-solving algorithms over polynomial systems. PolySys formalizes the design of attacks using invertible encodings, structural and leakage equations, and efficient constraint-solving algorithms including SAT and constraint solvers. It is capable of modeling resolution, known-data, and inference attacks for common leakage patterns. To demonstrate the practicality of our framework, we implement a PolySys attack engine in Python and apply it to state-of-the-art query recovery, data resolution, and query inference attacks on point and range multi-maps. Our results show that PolySys outperforms all existing attacks under identical assumptions, achieving up to 60× higher recovery rates in some scenarios. While scalability remains a challenge for larger datasets, PolySys represents a promising step toward a general-purpose framework for designing leakage attacks. We believe future work can further enhance its efficiency to scale to larger and more complex workloads.