Flexible Field Sizes in Secure Distributed Matrix Multiplication via Efficient Interference Cancellation
Okko Makkonen
TL;DR
The paper tackles secure distributed matrix multiplication (SDMM) under inner product partitioning, aiming to minimize the number of workers and provide straggler resilience while preserving information-theoretic security. It develops two RS-based constructions that rely on interference cancellation, requiring only a field size $q$ with $q \ge N$ and avoiding divisibility constraints or large-field algebro-geometric codes. This approach closely matches the MDS conjecture bound on minimal field size and offers a binary-field example for $X=1$, demonstrating practical feasibility. Compared to prior schemes like DFT, Secure MatDot, and HerA, the proposed method delivers greater field-size flexibility and a favorable trade-off between redundancy and recovery, with potential extensions to extended RS codes to reach the theoretical limits.
Abstract
In this paper, we propose a new secure distributed matrix multiplication (SDMM) scheme using the inner product partitioning. We construct a scheme with a minimal number of workers and no redundancy, and another scheme with redundancy against stragglers. Unlike previous constructions in the literature, we do not utilize algebraic methods such as locally repairable codes or algebraic geometry codes. Our construction, which is based on generalized Reed-Solomon codes, improves the flexibility of the field size as it does not assume any divisibility constraints among the different parameters. We achieve a minimal number of workers by efficiently canceling all interference terms with a suitable orthogonal decoding vector. Finally, we discuss how the MDS conjecture impacts the smallest achievable field size for SDMM schemes and show that our construction almost achieves the bound given by the conjecture.