Striking a balance between protecting data privacy and enabling collaborative computation is a critical challenge for distributed machine learning. While privacy-preserving techniques for federated learning have been extensively developed, methods for scenarios involving bitwise operations, such as tree-based vertical federated learning (VFL), are still underexplored. Traditional mechanisms, including Shamir's secret sharing and multi-party computation (MPC), are not optimized for bitwise operations over binary data, particularly in settings where each participant holds a different part of the binary vector. This paper addresses the limitations of existing methods by proposing a novel binary multi-party computation (BiMPC) framework. The BiMPC mechanism facilitates privacy-preserving bitwise operations, with a particular focus on dot product computations of binary vectors, ensuring the privacy of each individual bit. The core of BiMPC is a novel approach called Dot Product via Modular Addition (DoMA), which uses regular and modular additions for efficient binary dot product calculation. To ensure privacy, BiMPC uses random masking in a higher field for linear computations and a three-party oblivious transfer (triot) protocol for non-linear binary operations. The privacy guarantees of the BiMPC framework are rigorously analyzed, demonstrating its efficiency and scalability in distributed settings.

翻译：在保护数据隐私与实现协同计算之间取得平衡，是分布式机器学习面临的关键挑战。尽管面向联邦学习的隐私保护技术已得到广泛发展，但涉及位运算场景（例如基于树的纵向联邦学习）的方法仍待深入探索。传统机制（包括Shamir秘密共享和多方计算）并未针对二进制数据的位运算进行优化，特别是在每个参与者持有二进制向量不同部分的场景中。本文通过提出一种新型二进制多方计算框架，解决了现有方法的局限性。该机制支持保护隐私的位运算，尤其聚焦于二进制向量的点积计算，确保每个独立比特的隐私性。其核心是一种称为“基于模加的点积”的创新方法，该方法利用常规加法与模加法实现高效的二进制点积计算。为保障隐私性，该框架在更高数域中使用随机掩码处理线性计算，并采用三方不经意传输协议处理非线性二进制运算。本文对该框架的隐私保障机制进行了严格的理论分析，证明了其在分布式环境中的高效性与可扩展性。