In this paper, we propose a novel construction for secure distributed matrix multiplication (SDMM) based on algebraic geometry (AG) codes. The proposed construction is inspired by the GASP code, where so-called gaps in a certain polynomial are utilized to achieve higher communication rates. Our construction considers the gaps in a Weierstrass semigroup of a rational place in an algebraic function field to achieve a similar increase in the rate. This construction shows that there is potential in utilizing AG codes and their subcodes in SDMM since we demonstrate a better performance compared to state-of-the-art schemes in some parameter regimes.

翻译：本文提出了一种基于代数几何码的安全分布式矩阵乘法新型构造方法。该构造受GASP码启发，通过利用特定多项式中的所谓"间隙"来实现更高的通信速率。我们考虑代数函数域中有理位Weierstrass半群中的间隙，以类似方式提升传输速率。本研究表明，在某些参数范围内，相较于现有最优方案，利用代数几何码及其子码在安全分布式矩阵乘法中具有显著性能优势，展现了该方法的潜在应用价值。