International Association
for Cryptologic Research

Secure evaluation of non-linear functions is one of the most expensive operations in secure two-party computation, particularly for activation functions in privacy preserving machine learning (PPML). This work introduces SEAF, a novel framework for efficient Secure Evaluation on Activation Functions. SEAF is based on the linear approximation approach, but enhances it by introducing two key innovations: Trun-Eq based interval test protocols and linear approximation with dynamic precision, which have the potential for broader applicability. Furthermore, we classify common activation functions into several categories, and present specialized methods to evaluate them using our enhanced techniques. Our implementation of SEAF demonstrates $3.5 \times$ to $5.9 \times$ speedup on activation functions $\mathsf{Tanh}$ and $\mathsf{Sigmoid}$ compared to SirNN (S\&P'21). When applied on $\mathsf{GELU}$, SEAF outperforms Iron (NeurIPS'22) by more than $10 \times$ and Bolt (S\&P'24) by up to $3.4 \times$. For end-to-end secure inference on BERT, the original $\mathsf{GELU}$ accounts for $31.3 \%$ and $22.5 \%$ of the total runtime in Iron and Bolt, respectively. In contrast, our optimized $\mathsf{GELU}$ reduces these proportions to $4.3 \%$ and $9.8 \%$, eliminating $\mathsf{GELU}$ as a bottleneck in secure inference.