# Trident: Efficient 4PC Framework for Privacy Preserving Machine Learning

arXiv: https://arxiv.org/abs/1912.02631 · HTML: https://mlsanity.com/paper/1912.02631/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2019.

## Built on by (most cited first, 26 of 26)

- [CrypTen: Secure Multi-Party Computation Meets Machine Learning](https://mlsanity.com/paper/2109.00984/) (2021)
- [CryptGPU: Fast Privacy-Preserving Machine Learning on the GPU](https://mlsanity.com/paper/2104.10949/) (2021)
- [A Survey of Trustworthy Federated Learning with Perspectives on Security, Robustness, and Privacy](https://mlsanity.com/paper/2302.10637/) (2023)
- [Sisyphus: A Cautionary Tale of Using Low-Degree Polynomial Activations in Privacy-Preserving Deep Learning](https://mlsanity.com/paper/2107.12342/) (2021)
- [Privacy-Preserving Video Classification with Convolutional Neural Networks](https://mlsanity.com/paper/2102.03513/) (2021)
- [Tetrad: Actively Secure 4PC for Secure Training and Inference](https://mlsanity.com/paper/2106.02850/) (2021)
- [ScionFL: Efficient and Robust Secure Quantized Aggregation](https://mlsanity.com/paper/2210.07376/) (2022)
- [Towards Secure and Practical Machine Learning via Secret Sharing and Random Permutation](https://mlsanity.com/paper/2108.07463/) (2021)
- [SafeNet: The Unreasonable Effectiveness of Ensembles in Private Collaborative Learning](https://mlsanity.com/paper/2205.09986/) (2022)
- [Adam in Private: Secure and Fast Training of Deep Neural Networks with Adaptive Moment Estimation](https://mlsanity.com/paper/2106.02203/) (2021)
- [Comet: Accelerating Private Inference for Large Language Model by Predicting Activation Sparsity](https://mlsanity.com/paper/2505.07239/) (2025)
- [SSNet: A Lightweight Multi-Party Computation Scheme for Practical Privacy-Preserving Machine Learning Service in the Cloud](https://mlsanity.com/paper/2406.02629/) (2024)
- [CryptoTrain: Fast Secure Training on Encrypted Dataset](https://mlsanity.com/paper/2409.16675/) (2024)
- [WW-FL: Secure and Private Large-Scale Federated Learning](https://mlsanity.com/paper/2302.09904/) (2023)
- [Approximating ReLU on a Reduced Ring for Efficient MPC-based Private Inference](https://mlsanity.com/paper/2309.04875/) (2023)
- [Wildest Dreams: Reproducible Research in Privacy-preserving Neural Network Training](https://mlsanity.com/paper/2403.03592/) (2024)
- [MPClan: Protocol Suite for Privacy-Conscious Computations](https://mlsanity.com/paper/2206.12224/) (2022)
- [Private Multiparty Perception for Navigation](https://mlsanity.com/paper/2212.00912/) (2022)
- [Pencil: Private and Extensible Collaborative Learning without the Non-Colluding Assumption](https://mlsanity.com/paper/2403.11166/) (2024)
- [CrypTorch: PyTorch-based Auto-tuning Compiler for Machine Learning with Multi-party Computation](https://mlsanity.com/paper/2511.19711/) (2025)
- [ABG: A Multi-Party Mixed Protocol Framework for Privacy-Preserving Cooperative Learning](https://mlsanity.com/paper/2202.02928/) (2022)
- [Integrating Homomorphic Encryption and Trusted Execution Technology for Autonomous and Confidential Model Refining in Cloud](https://mlsanity.com/paper/2308.00963/) (2023)
- [Spin: An Efficient Secure Computation Framework with GPU Acceleration](https://mlsanity.com/paper/2402.02320/) (2024)
- [Privacy-Preserving and Trustworthy Deep Learning for Medical Imaging](https://mlsanity.com/paper/2407.00538/) (2024)
- [Protecting Confidentiality, Privacy and Integrity in Collaborative Learning](https://mlsanity.com/paper/2412.08534/) (2024)
- [EVA-S2PLoR: Decentralized Secure 2-party Logistic Regression with A Subtly Hadamard Product Protocol (Full Version)](https://mlsanity.com/paper/2501.05223/) (2025)

## Abstract (arXiv)

Machine learning has started to be deployed in fields such as healthcare and finance, which propelled the need for and growth of privacy-preserving machine learning (PPML). We propose an actively secure four-party protocol (4PC), and a framework for PPML, showcasing its applications on four of the most widely-known machine learning algorithms -- Linear Regression, Logistic Regression, Neural Networks, and Convolutional Neural Networks. Our 4PC protocol tolerating at most one malicious corruption is practically efficient as compared to the existing works. We use the protocol to build an efficient mixed-world framework (Trident) to switch between the Arithmetic, Boolean, and Garbled worlds. Our framework operates in the offline-online paradigm over rings and is instantiated in an outsourced setting for machine learning. Also, we propose conversions especially relevant to privacy-preserving machine learning. The highlights of our framework include using a minimal number of expensive circuits overall as compared to ABY3. This can be seen in our technique for truncation, which does not affect the online cost of multiplication and removes the need for any circuits in the offline phase. Our B2A conversion has an improvement of 7 × in rounds and 18 × in the communication complexity. The practicality of our framework is argued through improvements in the benchmarking of the aforementioned algorithms when compared with ABY3. All the protocols are implemented over a 64-bit ring in both LAN and WAN settings. Our improvements go up to 187 × for the training phase and 158 × for the prediction phase when observed over LAN and WAN.