# Single-Server Private Linear Transformation: The Joint Privacy Case

arXiv: https://arxiv.org/abs/2106.05220 · HTML: https://mlsanity.com/paper/2106.05220/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 14 of 14)

- [Lagrange Coded Computing: Optimal Design for Resiliency, Security and Privacy](https://mlsanity.com/paper/1806.00939/) (2018)
- [The Capacity of Private Information Retrieval](https://mlsanity.com/paper/1602.09134/) (2016)
- [The Capacity of Robust Private Information Retrieval with Colluding Databases](https://mlsanity.com/paper/1605.00635/) (2016)
- [The Capacity of Private Information Retrieval from Coded Databases](https://mlsanity.com/paper/1609.08138/) (2016)
- [Multi-Message Private Information Retrieval: Capacity Results and Near-Optimal Schemes](https://mlsanity.com/paper/1702.01739/) (2017)
- [Private Function Retrieval](https://mlsanity.com/paper/1711.04677/) (2017)
- [Capacity-Achieving Private Information Retrieval Codes with Optimal Message Size and Upload Cost](https://mlsanity.com/paper/1808.07536/) (2018)
- [Private Information Retrieval with Side Information](https://mlsanity.com/paper/1709.00112/) (2017)
- [Fundamental Limits of Cache-Aided Private Information Retrieval with Unknown and Uncoded Prefetching](https://mlsanity.com/paper/1709.01056/) (2017)
- [The Capacity of Cache Aided Private Information Retrieval](https://mlsanity.com/paper/1706.07035/) (2017)
- [The Capacity of T-Private Information Retrieval with Private Side Information](https://mlsanity.com/paper/1709.03022/) (2017)
- [Cache-Aided Private Information Retrieval with Partially Known Uncoded Prefetching: Fundamental Limits](https://mlsanity.com/paper/1712.07021/) (2017)
- [The Asymptotic Capacity of Private Search](https://mlsanity.com/paper/1801.05768/) (2018)
- [The Role of Coded Side Information in Single-Server Private Information Retrieval](https://mlsanity.com/paper/1910.07612/) (2019)

## Built on by (most cited first, 1 of 1)

- [Federated One-Shot Learning with Data Privacy and Objective-Hiding](https://mlsanity.com/paper/2504.21182/) (2025)

## Abstract (arXiv)

This paper introduces the problem of Private Linear Transformation (PLT) which generalizes the problems of private information retrieval and private linear computation. The PLT problem includes one or more remote server(s) storing (identical copies of) K messages and a user who wants to compute L independent linear combinations of a D-subset of messages. The objective of the user is to perform the computation by downloading minimum possible amount of information from the server(s), while protecting the identities of the D messages required for the computation. In this work, we focus on the single-server setting of the PLT problem when the identities of the D messages required for the computation must be protected jointly. We consider two different models, depending on whether the coefficient matrix of the required L linear combinations generates a Maximum Distance Separable (MDS) code. We prove that the capacity for both models is given by L/(K-D+L), where the capacity is defined as the supremum of all achievable download rates. Our converse proofs are based on linear-algebraic and information-theoretic arguments that establish connections between PLT schemes and linear codes. We also present an achievability scheme for each of the models being considered.