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

2025-09-01

AI Summary

In secure two-party computation (2PC), existing protocols for real-valued functions impose strict input constraints (|x| < L/3), severely limiting practical applicability. This paper proposes a general framework based on signed integer secret sharing, extending the supported input range to |x| < B (where B ≤ L/2)—encompassing the natural representation interval of the integer ring modulo L. Our approach introduces efficient signed integer–real encoding/decoding, high-precision polynomial approximation, and optimized secure evaluation protocols. For the first time, it enables secure computation of nonlinear operations—including integer division, trigonometric functions, and exponentials—without any additional input constraints. Experiments demonstrate that our protocol reduces communication overhead for e⁻ˣ evaluation to 31% of SirNN and Bolt, achieves 5.53× and 3.09× higher throughput, and attains a maximum ULP error of only 1.435—significantly outperforming state-of-the-art methods in both accuracy and efficiency.

Technology Category

• Machine Learning: Hardware-aware ML
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

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 ($lfloor frac{x}{d} floor$), 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 $5.53 imes$ and $3.09 imes$, 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.

Problem

• Extending secure computation from integers to real numbers
• Relaxing input constraints for practical real-world applications
• Designing efficient protocols for functions like division and exponentials

Innovation

• Generalized framework for secure protocols with loose input constraints
• Efficient computation of real numbers from secret shared inputs
• High-accuracy evaluation of exponential trigonometric and division functions