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

2026-01-19

AI Summary

This study investigates whether the public topology of gate-hiding garbled circuits alone is sufficient to recover the hidden functionality, thereby exposing a practical threat to functional privacy through topological leakage. To this end, the authors propose a SAT-based function recovery attack that integrates compositional, topology-preserving formal simplification theorems with an incremental solving strategy, substantially reducing the search space. Experimental evaluations on ISCAS benchmarks, secure computation circuits, and fault-tolerant sensor fusion architectures demonstrate that the method efficiently reconstructs complex circuit functionalities within practical timeframes, achieving up to a 159× speedup over baseline approaches. This work provides the first evidence that topological information alone can effectively enable reverse engineering of concealed logic.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Probabilistic Circuits and Graphical Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

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.

Problem

• Function Recovery
• Gate-Hiding Garbled Circuits
• Topology Leakage
• Semi-Private Function Evaluation
• Function Privacy

Innovation

• SAT solving
• function recovery
• gate-hiding garbled circuits
• topology leakage
• incremental SAT framework