# ASTRA: High Throughput 3PC over Rings with Application to Secure Prediction

arXiv: https://arxiv.org/abs/1912.02592 · HTML: https://mlsanity.com/paper/1912.02592/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2019.

## Built on by (most cited first, 18 of 18)

- [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)
- [SoK: Machine Learning Governance](https://mlsanity.com/paper/2109.10870/) (2021)
- [SecGNN: Privacy-Preserving Graph Neural Network Training and Inference as a Cloud Service](https://mlsanity.com/paper/2202.07835/) (2022)
- [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)
- [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)
- [MPClan: Protocol Suite for Privacy-Conscious Computations](https://mlsanity.com/paper/2206.12224/) (2022)
- [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)
- [EVA-S2PLoR: Decentralized Secure 2-party Logistic Regression with A Subtly Hadamard Product Protocol (Full Version)](https://mlsanity.com/paper/2501.05223/) (2025)
- [LRD-MPC: Efficient MPC Inference through Low-rank Decomposition](https://mlsanity.com/paper/2602.14397/) (2026)

## Abstract (arXiv)

The concrete efficiency of secure computation has been the focus of many recent works. In this work, we present concretely-efficient protocols for secure 3-party computation (3PC) over a ring of integers modulo 2ℓ tolerating one corruption, both with semi-honest and malicious security. Owing to the fact that computation over ring emulates computation over the real-world system architectures, secure computation over ring has gained momentum of late. Cast in the offline-online paradigm, our constructions present the most efficient online phase in concrete terms. In the semi-honest setting, our protocol requires communication of 2 ring elements per multiplication gate during the it online phase, attaining a per-party cost of em less than one element. This is achieved for the first time in the regime of 3PC. In the it malicious setting, our protocol requires communication of 4 elements per multiplication gate during the online phase, beating the state-of-the-art protocol by 5 elements. Realized with both the security notions of selective abort and fairness, the malicious protocol with fairness involves slightly more communication than its counterpart with abort security for the output gates em alone. We apply our techniques from 3PC in the regime of secure server-aided machine-learning (ML) inference for a range of prediction functions-- linear regression, linear SVM regression, logistic regression, and linear SVM classification. Our setting considers a model-owner with trained model parameters and a client with a query, with the latter willing to learn the prediction of her query based on the model parameters of the former. The inputs and computation are outsourced to a set of three non-colluding servers. Our constructions catering to both semi-honest and the malicious world, invariably perform better than the existing constructions.