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：Translated abstract: 本文提出了一种基于代数几何(AG)码的新型安全分布式矩阵乘法(SDMM)构造。该构造灵感来自于GASP码：利用某个多项式中的所谓间隙来实现更高的通信速率。我们的构造考虑了代数函数域中有理点处的Weierstrass半群中的间隙，以实现类似的速率增加。这个构造显示出利用AG码及其子码在SDMM中存在潜力，因为我们证明在某些参数区域比现有的方案表现更好。