Practical Secure Delegated Linear Algebra with Trapdoored Matrices
Mark Braverman, Stephen Newman
TL;DR
The paper addresses secure delegated linear algebra in cloud contexts where a client offloads computations such as $AB$ or $Mv$ to a server without revealing the operands. It introduces Trapdoored-Matrix and Targeted-Trapdoored-Matrix constructions based on the $LPN$ problem to enable additively masked computations that can be quickly unraveled via trapdoors. Two-phase protocols (initialization and online) achieve sublinear server overhead and substantially reduced client computation, with detailed cost analyses and security proofs, plus an implementation and benchmarks demonstrating practical viability. By offering a scalable alternative to fully homomorphic encryption or general secure multiparty computation for large-scale linear algebra, the work opens pathways for efficient cloud-based linear algebra with strong privacy guarantees and suggests directions for broader applicability and refinement.
Abstract
Most heavy computation occurs on servers owned by a second party. This reduces data privacy, resulting in interest in data-oblivious computation, which typically severely degrades performance. Secure and fast delegated computation is particularly important for linear algebra, which comprises a large fraction of total computation and is best run on highly specialized hardware often accessible only through the cloud. We state the natural efficiency and security desiderata for fast and data-oblivious delegated linear algebra. We demonstrate the existence of \textit{Trapdoored-Matrix} families based on an LPN assumption, and provide a scheme for secure delegated matrix-matrix and matrix-vector multiplication based on the existence of trapdoored matrices. We achieve sublinear overhead for the server, dramatically reduced computation for the client, and various practical advantages over previous protocols.