EVFLR: Efficient Vertical Federated Logistic Regression Based on Batch Operations

Vertical federated learning (VFL), where multiple participants with non-overlapping features for the same set of instances jointly train models, plays an increasingly important role in federated learning. This paper discusses vertical federated logistic regression (VFLR), one of the most popular VFL models. In existing VFLR solutions, homomorphic encryption (HE) is widely used to guarantee privacy. However, HE also entails huge communication and computation burdens. To solve this problem, we propose a method of packaging data by applying the Chinese remainder representation (CRR) to encode multiple smaller numbers into a single larger number through modulo operations. The classical Chinese Remainder Theorem shows that this process of packaging is a one-toone correspondence in a certain range and preserves algebraic operations like addition and multiplication. Hence, it fits well with VFLR involving matrix multiplication. As far as we know, this is the first batch operation method that supports multiplication in federated learning. Additionally, the dACIQ clipping technique and the multiplicative symmetric quantization method are adopted to eliminate the obstacles in CRR application. The effectiveness of our method has also been confirmed through extensive experiments, showing a reduction in traffic between participants of 32-54 times while achieving a training speedup of 3.6-14.6 times.