# Secure Sparse Matrix Multiplications and their Applications to Privacy-Preserving Machine Learning

arXiv: https://arxiv.org/abs/2510.14894 · HTML: https://mlsanity.com/paper/2510.14894/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 54 references that are in the map.
- First posted on arXiv 16 Oct 2025.

## Builds on (most cited first, 7 of 7)

- [FALCON: Honest-Majority Maliciously Secure Framework for Private Deep Learning](https://mlsanity.com/paper/2004.02229/) (2020)
- [BLAZE: Blazing Fast Privacy-Preserving Machine Learning](https://mlsanity.com/paper/2005.09042/) (2020)
- [When Homomorphic Encryption Marries Secret Sharing: Secure Large-Scale Sparse Logistic Regression and Applications in Risk Control](https://mlsanity.com/paper/2008.08753/) (2020)
- [SWIFT: Super-fast and Robust Privacy-Preserving Machine Learning](https://mlsanity.com/paper/2005.10296/) (2020)
- [Exploiting Data Sparsity in Secure Cross-Platform Social Recommendation](https://mlsanity.com/paper/2202.07253/) (2022)
- [Efficient Sparse Secure Aggregation for Federated Learning](https://mlsanity.com/paper/2007.14861/) (2020)
- [Sparse and Private Distributed Matrix Multiplication with Straggler Tolerance](https://mlsanity.com/paper/2306.15134/) (2023)

## Abstract (arXiv)

To preserve data privacy, multi-party computation (MPC) enables executing Machine Learning (ML) algorithms on private data. However, MPC frameworks do not include optimized operations on sparse data. This absence makes them unsuitable for ML applications involving sparse data; e.g., recommender systems or genomics. Even in plaintext, such applications involve high-dimensional sparse data, that cannot be processed without sparsity-related optimizations due to prohibitively large memory requirements. Since matrix multiplication is a central building block of ML algorithms, our work proposes dedicated MPC algorithms to multiply secret-shared sparse matrices. Our sparse algorithms have several advantages over secure dense matrix multiplications (i.e., the classic multiplication). On the one hand, they avoid the memory issues caused by the "dense" data representation of dense multiplications. On the other hand, our algorithms can significantly reduce communication costs (up to ×1000) for realistic problem sizes. We validate our algorithms in two machine learning applications where dense matrix multiplications are impractical. Finally, we take inspiration from real-world sparse data properties to build 3 techniques minimizing the public knowledge necessary to secure sparse algorithms.