# Bicoptor: Two-round Secure Three-party Non-linear Computation without Preprocessing for Privacy-preserving Machine Learning

arXiv: https://arxiv.org/abs/2210.01988 · HTML: https://mlsanity.com/paper/2210.01988/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2022.

## Built on by (most cited first, 3 of 3)

- [Neural Networks with (Low-Precision) Polynomial Approximations: New Insights and Techniques for Accuracy Improvement](https://mlsanity.com/paper/2402.11224/) (2024)
- [Ents: An Efficient Three-party Training Framework for Decision Trees by Communication Optimization](https://mlsanity.com/paper/2406.07948/) (2024)
- [PrivGNN: High-Performance Secure Inference for Cryptographic Graph Neural Networks](https://mlsanity.com/paper/2511.02185/) (2025)

## Abstract (arXiv)

The overhead of non-linear functions dominates the performance of the secure multiparty computation (MPC) based privacy-preserving machine learning (PPML). This work introduces a family of novel secure three-party computation (3PC) protocols, Bicoptor, which improve the efficiency of evaluating non-linear functions. The basis of Bicoptor is a new sign determination protocol, which relies on a clever use of the truncation protocol proposed in SecureML (S&P 2017). Our 3PC sign determination protocol only requires two communication rounds, and does not involve any preprocessing. Such sign determination protocol is well-suited for computing non-linear functions in PPML, e.g. the activation function ReLU, Maxpool, and their variants. We develop suitable protocols for these non-linear functions, which form a family of GPU-friendly protocols, Bicoptor. All Bicoptor protocols only require two communication rounds without preprocessing. We evaluate Bicoptor under a 3-party LAN network over a public cloud, and achieve more than 370,000 DReLU/ReLU or 41,000 Maxpool (find the maximum value of nine inputs) operations per second. Under the same settings and environment, our ReLU protocol has a one or even two orders of magnitude improvement to the state-of-the-art works, Falcon (PETS 2021) or Edabits (CRYPTO 2020), respectively without batch processing.