Function Recovery Attacks in Gate-Hiding Garbled Circuits using SAT Solving

Abstract: Semi-Private Function Evaluation enables joint computation while protecting both input data and function logic. A practical instantiation is gate-hiding garbled circuits, which conceal gate functionalities while revealing the circuit topology. Existing security definitions intentionally exclude leakage through circuit topology, leaving the concrete impact of such leakage on function privacy insufficiently understood. We analyze the empirical security of gate hiding under two adversarial models that capture realistic computational capabilities. We present a SAT-based function-recovery attack that reconstructs hidden gate operations from a circuit's public topology. To enable recovery on larger and more complex circuits, we develop an incremental SAT-solving framework combined with a set of composable, topology-preserving simplification theorems. These techniques jointly reduce the SAT instance size and progressively constrain the search space across repeated solving iterations. We evaluate our attack on ISCAS benchmarks, representative secure computation circuits, and fault-tolerant sensor fusion circuits under a fixed 24-hour recovery budget. Compared to baseline approaches, our optimized attack achieves up to a 159-fold speedup in recovery time without increasing the number of oracle queries. Our results demonstrate that topology leakage alone can enable effective function recovery in practice.