Efficient and High-Accuracy Secure Two-Party Protocols for a Class of Functions with Real-number Inputs

In two-party secret sharing scheme, values are typically encoded as unsigned integers $\mathsf{uint}(x)$, whereas real-world applications often require computations on signed real numbers $\mathsf{Real}(x)$. To enable secure evaluation of practical functions, it is essential to computing $\mathsf{Real}(x)$ from shared inputs, as protocols take shares as input. At USENIX'25, Guo et al. proposed an efficient method for computing signed integer values $\mathsf{int}(x)$ from shares, which can be extended to compute $\mathsf{Real}(x)$. However, their approach imposes a restrictive input constraint $|x| < \frac{L}{3}$ for $x \in \mathbb{Z}_L$, limiting its applicability in real-world scenarios. In this work, we significantly relax this constraint to $|x| < B$ for any $B \leq \frac{L}{2}$, where $B = \frac{L}{2}$ corresponding to the natural representable range in $x \in \mathbb{Z}_L$. This relaxes the restrictions and enables the computation of $\mathsf{Real}(x)$ with loose or no input constraints. Building upon this foundation, we present a generalized framework for designing secure protocols for a broad class of functions, including integer division ($\lfloor \frac{x}{d} \rfloor$), trigonometric ($\sin(x)$) and exponential ($e^{-x}$) functions. Our experimental evaluation demonstrates that the proposed protocols achieve both high efficiency and high accuracy. Notably, our protocol for evaluating $e^{-x}$ reduces communication costs to approximately 31% of those in SirNN (S&P 21) and Bolt (S&P 24), with runtime speedups of up to $5.53 \times$ and $3.09 \times$, respectively. In terms of accuracy, our protocol achieves a maximum ULP error of $1.435$, compared to $2.64$ for SirNN and $8.681$ for Bolt.