# When approximate design for fast homomorphic computation provides differential privacy guarantees

arXiv: https://arxiv.org/abs/2304.02959 · HTML: https://mlsanity.com/paper/2304.02959/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 6 Apr 2023.

## Builds on (most cited first, 13 of 13)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Semi-supervised Knowledge Transfer for Deep Learning from Private Training Data](https://mlsanity.com/paper/1610.05755/) (2016)
- [Scalable Private Learning with PATE](https://mlsanity.com/paper/1802.08908/) (2018)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [cpSGD: Communication-efficient and differentially-private distributed SGD](https://mlsanity.com/paper/1805.10559/) (2018)
- [Distributed Differential Privacy via Shuffling](https://mlsanity.com/paper/1808.01394/) (2018)
- [Privacy-Preserving Machine Learning with Fully Homomorphic Encryption for Deep Neural Network](https://mlsanity.com/paper/2106.07229/) (2021)
- [Prochlo: Strong Privacy for Analytics in the Crowd](https://mlsanity.com/paper/1710.00901/) (2017)
- [Federated Heavy Hitters Discovery with Differential Privacy](https://mlsanity.com/paper/1902.08534/) (2019)
- [Efficient Differentially Private Secure Aggregation for Federated Learning via Hardness of Learning with Errors](https://mlsanity.com/paper/2112.06872/) (2021)
- [Tight Lower Bounds for Locally Differentially Private Selection](https://mlsanity.com/paper/1802.02638/) (2018)
- [SPEED: Secure, PrivatE, and Efficient Deep learning](https://mlsanity.com/paper/2006.09475/) (2020)
- [Shrinkwrap: Differentially-Private Query Processing in Private Data Federations](https://mlsanity.com/paper/1810.01816/) (2018)

## Abstract (arXiv)

While machine learning has become pervasive in as diversified fields as industry, healthcare, social networks, privacy concerns regarding the training data have gained a critical importance. In settings where several parties wish to collaboratively train a common model without jeopardizing their sensitive data, the need for a private training protocol is particularly stringent and implies to protect the data against both the model's end-users and the actors of the training phase. Differential privacy (DP) and cryptographic primitives are complementary popular countermeasures against privacy attacks. Among these cryptographic primitives, fully homomorphic encryption (FHE) offers ciphertext malleability at the cost of time-consuming operations in the homomorphic domain. In this paper, we design SHIELD, a probabilistic approximation algorithm for the argmax operator which is both fast when homomorphically executed and whose inaccuracy is used as a feature to ensure DP guarantees. Even if SHIELD could have other applications, we here focus on one setting and seamlessly integrate it in the SPEED collaborative training framework from "SPEED: Secure, PrivatE, and Efficient Deep learning" (Grivet S'ebert et al., 2021) to improve its computational efficiency. After thoroughly describing the FHE implementation of our algorithm and its DP analysis, we present experimental results. To the best of our knowledge, it is the first work in which relaxing the accuracy of an homomorphic calculation is constructively usable as a degree of freedom to achieve better FHE performances.