Sublinear-Overhead Secure Linear Algebra on a Dishonest Server

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 remote 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, remote, and data-oblivious linear algebra, conjecture the existence of matrix and vector families implying satisfactory algorithms, and provide such an algorithm contingent on common cryptographic assumptions. We achieve sublinear overhead for the server, dramatically reduced computation cost for the client, and various other 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 }
}