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 only accessible through the cloud.We state the natural efficiency and security desiderata for fast and data-oblivious delegated linear algebra. We demonstrate the existence of trapdoored matrix families based on a LPN assumption, and provide a scheme for secure delegated matrix-matrix and matrix-vectors multiplication based on the existence of trapdoored matrices. We achieve sublinear overhead for the server, dramatically reduced computation cost for the client, and various practical advantages over previous algorithms.

@article{braverman2025_2502.13060,
  title={ Practical Secure Delegated Linear Algebra with Trapdoored Matrices },
  author={ Mark Braverman and Stephen Newman },
  journal={arXiv preprint arXiv:2502.13060},
  year={ 2025 }
}