Sublinear-Overhead Secure Linear Algebra on a Dishonest Server

2025-02-18

AI Summary

To address efficiency and security challenges in privacy-preserving linear algebra computation over untrusted cloud servers, this paper proposes the first data-independent secure delegation framework based on the Learning Parity with Noise (LPN) assumption. Our approach leverages lightweight homomorphic encoding and optimized protocol design to achieve sublinear (o(n)) server-side computation and only O(√n) client-side local computation—breaking the performance bottleneck of traditional homomorphic encryption. The framework supports core operations including large-scale dense and sparse matrix multiplication, while providing strong security guarantees under the LPN assumption. It significantly reduces both communication and computational overhead compared to prior art. Experimental evaluation demonstrates end-to-end speedups of 10–100× over the state-of-the-art, achieving a rare balance between practical efficiency and theoretical rigor.

Technology Category

• Machine Learning: Privacy
• Natural Language Processing: Safety and Robustness
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Data and user privacy-enhancing technologies for the Web

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 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. Keywords: Data Privacy, Data-Oblivious Computation, Delegation, Homomorphic Encryption, Cloud Computing, Algorithm Efficiency, Sublinear Overhead, LPN, Matrix Multiplication.

Problem

• Secure remote linear algebra
• Data privacy in cloud computing
• Efficient data-oblivious computation

Innovation

• Sublinear overhead server computation
• Secure data-oblivious linear algebra
• Efficient client-side cryptographic assumptions