Practical Secure Delegated Linear Algebra with Trapdoored Matrices

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 textitTrapdoored-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.