Making the Best Switch: Encoding Strategy Management for Efficient TFHE Circuit Evaluation

This work addresses the synthesis of efficient torus fully homomorphic encryption (TFHE) circuits for private Boolean function evaluation through encoding strategy management. Modern TFHE implementations support multiple plaintext encoding spaces, each offering distinct trade-offs between computational cost and the expressiveness enabled by larger plaintext domains. Smartly switching between encoding strategies to maximize evaluation efficiency remains challenging due to the lack of algorithmic support for determining when and where such transitions should occur. To address this, we propose a synthesis framework that enables encoding-switch-aware TFHE circuit generation. Our approach leverages the structural properties of the exclusive-or sum of products (ESOP) representation to partition Boolean functions into encoding-aligned regions, enabling cost-effective evaluation while minimizing switch overhead. Experimental results demonstrate that our encoding-aware synthesis technique significantly accelerates homomorphic Boolean function evaluation – achieving up to 53.46% and 23.34% average evaluation time reduction on general-purpose Boolean benchmarks – compared to advanced synthesis baselines lacking explicit encoding-switch management. This work lays the groundwork for systematic encoding strategy management in TFHE circuits and highlights the role of logic-level design automation in advancing efficient homomorphic evaluation.