On the Upload versus Download Cost for Secure and Private Matrix Multiplication
This work addresses privacy and efficiency challenges in distributed computing for applications like cloud-based data processing, though it appears incremental as it builds on prior schemes.
The paper tackles the problem of secure and private distributed matrix multiplication, where a user computes the product of a confidential matrix with a public matrix while keeping both the matrix and index private from servers, and shows an achievable tradeoff between upload and download costs with specific formulas for improvement over existing schemes.
In this paper, we study the problem of secure and private distributed matrix multiplication. Specifically, we focus on a scenario where a user wants to compute the product of a confidential matrix $A$, with a matrix $B_θ$, where $θ\in\{1,\dots,M\}$. The set of candidate matrices $\{B_1,\dots,B_M\}$ are public, and available at all the $N$ servers. The goal of the user is to distributedly compute $AB_θ$, such that $(a)$ no information is leaked about the matrix $A$ to any server; and $(b)$ the index $θ$ is kept private from each server. Our goal is to understand the fundamental tradeoff between the upload vs download cost for this problem. Our main contribution is to show that the lower convex hull of following (upload, download) pairs: $(U,D)=(N/(K-1),(K/(K-1))(1+(K/N)+\dots+(K/N)^{M-1}))$ for $K=2,\dots,N$ is achievable. The scheme improves upon state-of-the-art existing schemes for this problem, and leverages ideas from secret sharing and coded private information retrieval.